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KAILASA's Nirahara Samyama
BE FOOD FREE with HDH Nithyananda Paramashivam
Nirahara Samyama means to explore and discover your body's possibilities without having any external input like food or water. Your body is the miniature of the Cosmos, with all possible intelligence in it. If a fish can swim, you can swim, if a bird can fly, you can fly. Just, you need to rediscover those possibilities from your bio-memory, reawaken those possibilities in your bio-memory.
21 Days to Change
You are about to embark on a journey of realization that the idea of living a healthy, blissful life W/O FOOD is possible. You will also meet numerous people who have reaped the rich benefits of the Bfoodfree lifestyle. These people are not monks, they are regular couples, young adults, senior citizens, middle aged people all of who have taken responsibility towards bettering their lives.
Benefits of Nirahara Samyama
Helps develop strong nervous system.
Builds glowing, shiny skin and no dehydration.
Consume energy directly from space.
Cure for Diabetes, hypertension, obesity.
Improved ability to focus & attention span.
Anti aging & disease free body as side effects.
Sign Up for Nirahara Samyama
Upcoming Nirahara Samyama Rituals and Shastra Adhyayanam
Rama Nirahara Samyama
Bhagavan Sri Rama was having forest fruits while He was meditating on Paramashiva and received the Upanishad. Having only forest fruit diet, doing sincere Shiva Puja and reading Upanishads for 21 days is RAMA NIRAHARA SAMYAMA. You develop subtle brain grooves to grasp the Upanishads, mirroring the neurons of Bhagavan Sri Rama.
You will receive:
Introduction to Upanishads (Free Ebook)
Ishavasya Upanishad (Video Series)
Kenopanishad (Video Series)
Kathopanishad (Video Series)
Krishna Nirahara Samyama
Bhagavan Sri Krishna was on a dairy diet while meditating on Paramashiva when He delivered Gita. Having only organic dairy products like milk, curd, butter, ghee and cheese, doing sincere Shiva Puja and reading Bhagavad Gita for 21 days is KRISHNA NIRAHARA SAMYAMA. You develop subtle brain grooves to grasp Bhagavad Gita, mirroring the neurons of Bhagavan Sri Krishna.
You will receive:
Bhagavad Gita Decoded (Free Ebook)
Bhagavad Gita (Video Series)
Vyasa Nirahara Samyama
Bhagavan Veda Vyasa was on a diet of basmati rice grown in Himalaya near Badrikashram, meditating on Paramashiva when He delivered Brahmasutra. Having only organic basmati rice grown in Himalayas, doing trikala sandya and agnihotram for 21 days is VYASA NIRAHARA SAMYAMA. You develop subtle brain grooves to grasp Brahmasutra, mirroring the neurons of Bhagavan Veda Vyasa.
You will receive:
Brahma Sutras (Video Series)
Sri Rama Nirahara Samyama
Purushottama Parama Pavana Bhagavan Sri Ramchandra Prabhu is the symbol of everything best in the Universe. Purushottama is a grand narrative of Hinduism. Highest powerfulness is not using your powers, even while you are attacked and waiting for the law of karma to do its job. Not at all becoming silly in the inner space. Sri RamaChandra Prabhu is the first compiler – Vyasa of Vedas. Vedas has many Vyasas, compilers. Veda Vyasa was the last one. The first compiler is Sri RamaChandra Prabhu. If you see, Rama organized and compiled all the 108 Upanishads. It is Muktika Upanishad which tells all the 108 Upanishads' names. Rama is the first compiler.
Recommended Lifestyle: Organic Fruits, Shiva Puja, Read 108 Upanishad
Srimad Valmiki Ramayana
Aranya kandam
1st Sarga
17th Sloka
पुष्पं मूलं फलं सर्वमाश्रमं च महात्मनः।
निवेदयित्वा धर्मज्ञास्ते ततः प्राञ्जलयोऽब्रुवन्।।3.1.17।।
puṣpaṃ mūlaṃ phalaṃ sarvamāśramaṃ ca mahātmanaḥ.
nivedayitvā dharmajñāste tataḥ prāñjalayo'bruvan..3.1.17..
புஷ்பம் மூலம் பலம் ஸர்வம் ஆஶ்ரமம் ச மஹாத்மன꞉.
நிவேதயித்வா தர்மஜ்ஞா: தே தத꞉ ப்ராஞ்ஜலய: அப்ருவன்..3.1.17..
The sages who were knowers of dharma saluted the noble Rama, offered fruits, roots and flowers available at the hermitage and with folded palms addressed Him
Srimad Valmiki Ramayana
Aranya kandam
1st Sarga
22nd Sloka
एवमुक्त्वा फलैर्मूलैः पुष्पैर्वन्यैश्च राघवम्।
अन्यैश्च विविधाहारैः सलक्ष्मणमपूजयन्।।3.1.22।।
evamuktvā phalairmūlaiḥ puṣpairvanyaiśca rāghavam.
anyaiśca vividhāhāraiḥ salakṣmaṇamapūjayan..3.1.22..
ஏவம் உக்த்வா பலை: மூலை꞉ புஷ்பை: வன்யை: ச ராகவம்.
அன்யை: ச விவித ஆஹாரை꞉ ஸலக்ஷ்மணம் அபூஜயன்..3.1.22..
Having said so, the sages offered with reverence – fruits, roots, flowers and other forest foods to Rama and Lakshmana.
Srimad Valmiki Ramayana
Aranya kandam
74th Sarga
17th Sloka
मया तु विविधं वन्यं सञ्चितं पुरुषर्षभ।
तवार्थे पुरुषव्याघ्र पम्पायास्तीरसम्भवम्।।3.74.17।।
mayā tu vividhaṃ vanyaṃ sañcitaṃ puruṣarṣabha.
tavārthe puruṣavyāghra pampāyāstīrasambhavam..3.74.17..
மயா து விவிதம் வன்யம் ஸஞ்சிதம் புருஷர்ஷப.
தவார்தே புருஷவ்யாக்ர பம்பாயா: தீரஸம்பவம்..3.74.17..
Sabari said-
O best among men I have collected and kept for your sake different kinds of forest food grown on the bank of Pampa.
Sri Krishna Nirahara Samyama
Beautifully Bhagavan Krishna says in Bhagavad-gita 15.15:
सर्वस्य चाहं हृदि सन्निविष्टो
मत्त: स्मृतिर्ज्ञानमपोहनं च |
वेदैश्च सर्वैरहमेव वेद्यो
वेदान्तकृद्वेदविदेव चाहम् || 15||
I am seated in everyone's heart, and from Me come remembrance, knowledge and forgetfulness. By all the Vedas, I am to be known. Indeed, I am the compiler of Vedanta, and I am the knower of the Vedas.
Bhagavan Krishna manifested as intense life. Life expressed in body as ever youthful, expressed in intellect as amazing strategist, expressed in emotion as a most beautiful pure romance, amazing artistic expression. Even when Bhagavan was teaching the greatest truths, it was done in a very poetic form. His book is called Song – Gita, because it is more poetic than anything else. Singer, dancer, musician, strategist. A beloved for everyone.
Recommended Lifestyle: 21 Days, Dairy products and Read bhagavad Gita
Ayurveda Nighantu – Bhava Prakasha
Adhikara – Dadhi varga
Sutra 6
पवित्रं दीपनं हृद्यं पुष्टिकृत्पवनापहम् |
pavitraṃ dīpanaṃ hṛdyaṃ puṣṭikṛtpavanāpaham
பவித்ரம் தீபனம் ஹ்ருத்யம் புஷ்டிக்ருத் பவனாபஹம்
Meaning – Cow's yoghurt is purifying, kindles the digestive fire, pleasant to the stomach, nourishing and removes vata dosha.
Ayurveda Nighantu – Bhava Prakasha
Purva khanda
Mishra prakarana
Adhikara– Navaneeta varga Sutra – 1
हितं वर्णबलाग्निकृत् | संग्राहि वातपित्तासृक्क्षयार्शोऽर्दितकासहृत् |
तद्धितं बालके वृद्धे विशेषादमृतं शिशोः ||१||
hitaṃ varṇabalāgnikṛt vātapittāsṛkkṣayārśo'rditakāsahṛt
taddhitaṃ bālake vṛddhe viśeṣādamṛtaṃ śiśoḥ ||1||
ஹிதம் வர்ண-பலாக்னிக்ருத் வாத-பித்தாஸ்ருக்க்ஷய- அர்ஶோ அர்தித-காஸ-ஹ்ருத்
தத் ஹிதம் பாலகே வ்ருத்தே விஶேஷாத் அம்ருதம் ஶிஶோ
Meaning – Cow's butter is beneficial to health, increases lustre, increases bodily Agni, reduces vata, pitta and blood, removes piles problems, paralysis of the muscles on one side of the face and neck. It is very much beneficial in young children and in the aged ones. It is a nectar for infants
Sri Vyasa Nirahara Samyama
Who is Bhagavan Veda Vyasa? Excerpt 16 March 2011 Nithya Satsang delivered Supreme Pontiff of Hinduism, Jagatguru Mahasannidhanam Bhagavan Nithyananda Paramashivam: "Keshava – Vishnu who came down as Vyasa –Vyasa himself came down to check Shankara's strength on this philosophy and bless Shankara. And the argument went on and on and on. How can either of them win and who can end this argument between Vyaasa and Shankara? That is when Padmapaada sings Shiva is sitting as Shankara and Vishnu as Vyasa who will win, I bow down to both of you! Then suddenly Shankara realizes it is Vishnu and Vyasa realizes it is Shiva. So they ended the argument Then both of them ended the argument and Vyaasa blesses Shankara with 16 more years of life."
Yajnavalkya smriti
Prayashchitta Adhyaya
31st sloka
कालोऽग्निः कर्म मृद् वायुर्मनो ज्ञानं तपो जलम् ।
पश्चात्तापो निराहारः सर्वेऽमी शुद्धिहेतवः ।।
kālo'gniḥ karma mṛd vāyurmano jñānaṃ tapo jalam .
paścāttāpo nirāhāraḥ sarve'mī śuddhihetavaḥ
கால: அக்னி꞉ கர்ம ம்ருத் வாயு: மனோ ஞானம் தபோ ஜலம் .
பஶ்சாத்தாப: நிராஹார꞉ ஸர்வே அமீ ஶுத்திஹேதவ꞉
Translation – Time, Fire, Action, Soil, Air, Mind, Knowledge, Penance, Water, Re-living and Nirahara – all of these are means for purification
Frequently Asked Questions
Learn How it Works!
Can I blend regular food like rice, pizza, ice cream and still consider myself a Nirahari?
No, because that is too much calorie intake and equals consuming food! Niraharis are people who break the patterns related to food, which includes the idea that body needs a certain amount of calories to survive. Niraharis only consume diluted juices, thin milk shakes with just milk and fruit. Over time, Niraharis evolve towards living on air.
I am loosing more weight than i should with Nirahara, should I stop and continue with regular food?
We would say no, don't stop if mentally becoming a Nirahari is what you want. To stop the weight loss, balance the body with drinking lots of milk with honey and religiously following up with the suggested nirahara practices. This is a tested tip, you will see the weight loss stops and you infact start building muscle without doing anything.
Can I do heavy weight lifting exercises?
Its best to wait for atleast 6 months for your body to settle with the nirahara experience before you embark on heavy aerobic exercises or pumping iron. Limit yourself to Nithyananda Yoga and light weights till then.
Can I do THE Samyama even if i did not successfully complete all 3 levels of Nirahara samyama?
No, the pre-requisite for THE Samyama mandates that you successfully complete all 21 days and 3 levels of Nirahara Samyama.
What will i do when i go to parties, social gatherings or restaurants with my loved ones?
Simple. You let them eat and you order something suitable to drink. Everyone will want to know why you are not eating. Enlighten them about your new lifestyle.
What is once in a while eating defined as?
Niraharis who want to remain niraharis can eat once in a while – like once in 4 weeks or more. This really depends on you authentically LISTENING to your body. Don't eat because some one is pressurizing you .Just make a conscious decision.
Can people with serious medical illnesses like Cancer do Nirahara programs?
The answer lies with the person's doctor and swamiji.One answer will not apply to all.
I am a Nirahari but I experience hair fall while remaining as one.
Ask yourself if you are keeping up with your practices. Niraharis will actually have great skin and hair . If you keep your tummy filled with liquids, consume neem juice and a combo of milk with honey then the temporary hear fall will stop.
Will Nirahara affect my mensturation cycle?
Well if you are facing issues in that area, nirahara will regulate your cycle and yes you can remain a nirahari even during your periods. The blood loss will not make you feel light headed , nirahara actually helps people over come anemia.
Can children do Nirahara?
Swamiji has not yet approved this. Currently the program is for 18 and plus aged people.
Can a female nirahari remain in nirahari during pregnancy?
No , she should consume solid food during the pregnancy period.
Do I need to take multivitamin supplements while being a Nirahari?
It is not needed unless your doctor has advised you to do so for some significant reason. Cosmic energy is intelligent enough to produce all the vital elements needed to keep you healthier than a for consumer. This is why Niraharis who live on just light orange juice and water will often look way more stronger than one who consumes food and supplements.
Can I repeat the Nirahara Samyama and THE Samyama?
Yes you can . Each time you do it, you will be breaking more patterns. Repetition really helps those who want to live as full time niraharis. You come to terms with doing completions with various foods and food habits.
Why am i not successful with the first level Nirahara Samyama itself?
You probably carry some strong food related patterns within you. Do the process of completion as taught by Swamiji, you will certainly see a difference.
Is "feeling connection"- being established in Mahabhava necessary for THE Samyama?
Yes, feeling connection, unclutching and ajapa jappa are the 3 pillars of Nirahara. For THE Samyama you need to authentically trust the fact based on your experience that the Master is omnipotent, omniscient and all pervading. Your feeling connection with him keeps you fed with energy.
Does Nirahara affect one's sex drive?
Nirahara is a spiritual process. Its effects in each person are unique. Most of the Nirahari couples we have talked to do not attribute lower sex drive to Nirahara.There is a greater appreciation and respect for each other's bodies. But Nirahara does help eliminate animalistic behaviors of lust, sex addictions, porn addiction, fantasy addiction etc .
Can i do nirahara samyama without a two way connection with swamiji?
NO! You have to do the program in swami's virtual presence.
Register for the upcoming 3 types of Nirahara Samyama along with rituals and Shastras
Legal Disclaimer : "These statements have not been evaluated by the U.S. Food and Drug Administration, the Food Safety and Standards Authority of India, nor any other equivalent government health agency. These statements and any related dietary or health related guidance are not intended to diagnose, treat, cure or prevent any disease. Please consult your physician before implementing any new diet, exercise and dietary supplement programs, especially if you have pre-existing medical conditions or are taking prescribed medications. These statements are for educational purposes only and are not meant to replace the advice of your physician or healthcare provider. Results are not guaranteed and individual results may vary."


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Beth Kellmurray
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I have completed my first week of work at the garden centre. 100s of petunias, pelargoniums and tomatoes have been potted up. 100 hanging baskets made. I'm working with a friendly bunch of people, the sun has been shining, the robins have been singing. A good first week. It hasn't taken my love of gardening as I've still potted up my own lupins on an evening. I have done well resisting all the plants. My only purchase this week was grass seed which would have been purchased anyway. The lawn is a mess. I'm not sure I can even refer to it as a lawn anymore. The biggest temptation at the garden centre, a 2m Acer in the reduced section, has gone so that's one less to seduce me.
This week I have been working on putting the patio back together. After a year of building work, the pots can go back on. We've had to continually shift things around. This is part of why the lawn is so bad as it had pots and garden furniture sat on it for much of last year. It's a work in progress as looking out the pots aren't quite in the right place. But, I'm happy to be able to at least make a start.
1. Shady corner
I've started the patio shift around by sorting the plants into the conditions they like. This end of the patio is shaded for more of the day. It still gets a fair amount of sun as it's south-facing but between the two walls, it has less light than the other end of the patio. The pots here contain a mixture of ferns and heucheras, grasses, hydrangeas and more. Most of the pots with irises have also got hostas in. So the irises are starting to fade now but he hostas will come out as they fade. looking at the photos I'm going to shift the pots around to try and push them up to the line of the cracked concrete floor to cover that up. I've discussed on a previous blog how I'm collecting driftwood to add a bit of edging to the pots. It gives it a bit of a feel of a path even though we don't often come out of this door. It's not obvious from the photos but the pots are raised at different heights. Some are on platforms made from tile samples on top of bricks. Others are just on bricks and some are on the ground. It still needs a bit of rearranging but I'm happy with the plants. They've largely held up well through winter and I can see signs of growth on the deciduous ones.
2. Alice's kitchen
Alice's mud kitchen I've made a feature of within the patio and the planting. She likes using it here scooping out the water onto the plants. The kokedama sat on the top seem to be happy there. The moss is gradually greening up. The pots are foxglove seedlings that I may have dumped there for now.
Then the shelves are filled with a mixture of decorative objects and things for filling, emptying and pouring. She's been quite into perfume making at the moment.
The fairy seems to have taken up residence here with the bird stake featured last week behind.
3. Display table
The table I painted a few weeks back has taken its place on the patio. These pots were Tesco specials. They have Crocus, Muscari and Tulips in. The Crocus are coming through now and then they should be followed by the Muscari, then the Tulips. Once these are done I will probably try and empty the bulbs. If I can separate them the crocus can be added to the lawn. The table and patio are filling up with charity shop finds. The urn was a 50p find. I thought the colours would complement many of the irises and fit in amongst many of the shade lovers but it has gone here for now.
Then the table is scattered with charity shop finds. Alice wanted me to have this one to go match her dragonfly lantern on her mud kitchen.
4. Plant stand and box cold frame
The plant stand has got the tins of sempervivums I featured a few weeks back. The rest is ab it of a mess. The compost is sitting here as between me, the builders and the weather the lawn is a mess. Once the weather has died down a bit and the crocus have gone over I'll spread the rest of the soil improver mixed with some grass seed on the lawn. I'd like to add some stepping stones across the back lawn and drill some drainage holes to protect in future years but I've a few other projects in mind I've already got the materials to complete.
The really useful boxes at the back are in use as cold frames. These are a cheap option that is easy to move in and out of the house if necessary. I used this method for the dahlias last year and it worked well. Currently, the most exciting thing in there is the white bleeding hearts (Lamprocapnos Spectabilis Alba) from Wilco's. These have put on good growth and should be able to go in the front garden soon.
5. Log store
The log store has been restocked last weekend. We were almost out of wood and thought we might need a bit more before it starts to warm up again. The stores also look neater oddly for being full. The pots here are largely just dumped there while I work out where they will end up. I like the Pinus mugo there but not sure about the others. The big black tub is Alice's fairy garden which is about to get an overhaul for the new season. There are agapanthus in a couple of the pots. These will hopefully return and look good in summer but not very interesting at the moment. There are two cordylines dotted around the patio. These came from my last house and have quite good stems on them. They need to go in the ground and I don't really have a space they'll suit. But, I don't have the heart to get rid of them.
I'd put up hanging brackets a few weeks back to add the solar lights. I had this lantern spare so thought that it would go nicely in the middle.
6. The backdoor
The backdoor is currently the weakest of the pot displays. The water butt proved very useful through last year and I managed much of my watering through the summer using it. The pots closest to the sliding doors have got sempervivums and agapanthus in. The barrel has a Fuschia in which hasn't really died back for winter and is already putting on new flower buds.
The pots here are more of a randomly assembled collection than the planned effect of the shaded corners. The metal tray with the conifer is Alice's dinosaur garden. The Christmas tree was bought as a cheap one for inside and hasn't found itself a proper pot yet. The tall pot with Katherin Hodgson irises is lovely but doesn't really combine with the other pots. It has a hosta in which will start rising up soon. The other metal pots have Allium karataviense in. This is a short allium with a large ivory globe. It was one of the first alliums I ever bought but currently, they just look like empty pots.
By the back door are sempervivum and sedum pots. These I like and they are in a good position for getting the sun and warmth they need. The rest of this patio area needs a bit more thought.
I've just got the one day off this week before returning to work. Then I will have Friday and Saturday off normally. I'm glad to still have one family day as it was looking like I would work each day. I'm not aiming to do many garden jobs today. I've got a few pots to tidy and some strawberry planters I want to fill with sempervivums but I'm not sure if I'll manage to get time. Enjoy your weekends.


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Want to find out what does the word cabala mean? We gathered all the possible definitions of the word cabala on our website. Our definition dictionary is updated all the time with new definitions and is ready to help you.
cabalaPart of speech: Noun
A secret science or knowledge which the Jewish rabbins alleged they possessed, and by which they professed to be able to explain all Scripture difficulties.Usage examples "cabala":
- But then, for hard words and terms, which neither he, nor you, nor I, nor anybody else could understand, he poured them out in such abundance that you'd have sworn he had been rehearsing some of the occult philosophy of Agrippa, or reading extracts from the Cabala. - "Primitive Psycho-Therapy and Quackery", Robert Means Lawrence.
- The Jewish Cabala and the Gnostics had much in common. - "The Eliminator; or, Skeleton Keys to Sacerdotal Secrets", Richard B. Westbrook.
- Is it not of the same complexion as his ungenerous reserve even in the minutest secrets of chemistry, or the numbers of his Cabala? - "Zanoni", Edward Bulwer Lytton.


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Making A Come Back... Um... Eventually
I just got all my stuff to update my site. I have over 30 comics sketched, and I'm starting to ink them into existence. In the mean time, I'm putting up daily one panelers. I got the inspiration from Saturday Morning Breakfast Cerial. Find the link in my links.-3-2-03
Déja Vu
I know I said I'd be back before, and well, TECHNICALLY I was. But this time I've decided to do it right, for the long haul. I'm currently building up my comic lineup. I've already got the first week drawn out, and I'm going to keep building until I hit one month (I've worked on the comics 2 nights so far). I'm just going to upload the lot of comics (all 30 or so) at once and let the site kind of run on it's own. I have some renovations in mind for the site too, like changing that stupid "school daze" title thing. I HATE that thing. If anybody has any good ideas for it, give me an e-mail. Oh, and I wish I could give you guys an exact time when the comics will be back up, but I'm not sure. Give it about 2 weeks from now. Ooh, I'm so excited.-1-14-03
It's Back... YA HEARD ME?!
School Daze has returned, ladies and gents. As it turns out, before I was just burnt out on comics and college searching, so I just kind of collapsed on the job. Well, now I'm back in the driver's seat and ready to kick some ass. SD is still a daily, still color, and still a sarcastic piece of trash... *sniff* God I missed it.-5-01-02
Every Time I Try To Get Out...
Well, things are FINALLY back on track here at School Daze, and I'm proud to say I'm here to stay. I've had a mentally rough week. I'm sorry to leave you all in the dark about everything for so long, but I've just been too exasperated to care lately. Here goes. My friend trouble involved me and a certain friend (obviously) getting into an argument about a certain person, who I certainly don't want to know I'm talking about him/her. I know it sounds like a line of BS, but that's all I feel comfortable revealing to the general public. The overworked part of my little vacation was having to learn about 100 bones, their parts, and other general stuff. I studied like a mad man and still only got a 65 (above the class average for the test, I might add). It gave me my first big head ache in as long as I can remember, and I just didn't feel like drawing. When I don't feel like drawing, I CAN'T. So anyway, I know it's not the grand explanation you wanted for such a long absence, and I AM truthfully sorry, but what's done is done. Now all I can do it try and be funny... god help us all.-10-15-01
- News Archives -


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Lookupuk.com - Wales Genealogy Board
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Board Name: Wales Genealogy
Janet Hamilton
Edmonton, AB Canada
Dec 13, 2001
I am searching for Thomas Owen born in Wales in 1819 and died in Illinois in 1899. He may have operated the Owen Woolen Mills or Owen Mercantile. I am trying to locate the exact place of his birth.
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Rory McGown is the founder of the award winning GYMetrix who are credited with transforming the industry's approach to kit selection and floor layout. By tracking the usage of each piece of kit, GYMetrix ensure that operators make decisions based on what members really want rather than what they assume members want. Their clients include the largest brands in the market, such as Pure Gym, The Gym Group, David Lloyd and Everyone Active, all of whom they've helped to achieve huge savings while driving up customer satisfaction and retention.
We met Rory to learn:
– Which kit is being oversupplied
– Which kit is being undersupplied
– How gyms can rearrange their kit to improve the experience for female members
– Which kit offers the best ROI


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Before getting deep dive into the question which is more dangerous and which is more efficient we let's talk about AC and DC.
What is AC Current?
The AC current changes its polarity and magnitude periodically and continuously with respect to time. The Ac current can be produced with a device named alternator that produces the alternating current.
Let's Understand the Ac current with the water analogy
Suppose a piston is inserted inside a pipe and connected with a rotating rod as in the pin pic below. Here the piston has two strokes one towards upward and the other towards backward on the upward stroke, the water moves in a clockwise direction and the backward direction the water displaces in an anticlockwise direction so in this way water direction changes its direction periodically with oscillation of the piston.
Waveforms of AC Current
Every Ac Waveforms have a divider line or called the zero voltage line that divides the waveform two halves as the Ac current changes the magnitude and direction periodically so on every one complete cycle it reaches zero volts.
AC Waveform characteristics
Time Period (T)
The total amount of time taken by a waveform to repeat itself or to repeat its one cycle is called time period. You can also say the total amount of time taken by wave form to complete its one complete cycle is called time period.
The rate at which the waveform repeats itself is called frequency or you can say the the number of times the waveform repeats in one second is called frequency.its Si unit is Hertz
Amplitude:-The magnitude of the signal is called amplitude
Types of AC Waveforms
Sine Wave
Square wave
Triangle Wave
Application of AC
- AC is used for long-distance transmission for Offices and Homes
- Energy Loss in AC is less so widely used in transmission
- The AC current can be converted into a high voltage to low voltage and low to high voltage efficiently using the transformer
- AC power is used in larger applications and appliances like Freezers, AC. Dishwashers, washing machines, Fans, Bulbs.
What is DC Current?
The DC current is a unidirectional flow of current or electric charge unlike AC it does not change the magnitude and polarity with time. The DC current has constant magnitude and direction and as the direction and magnitude not changes so the frequency of DC current is zero. The electrons in DC current flow from high electron density to low electron density.
We can get DC from Ac current using the process called rectification and the device that does this is called a rectifier.
Application of DC current
- DC current is widely used in small electronic devices and gadgets
- DC current is not good for long-distance transmission but storage of dc current is easy in form of Battery.
- DC power is used in Cell phones, laptops, radio and other electronic gadgets
- DC Current are used in flashlights
- DC current are used in EV and hybrid cars and automobile
Difference between AC and DC
- Ac current changes its direction during flow while the DC current does not changes its direction during flow and remains constant.
- The AC current has a frequency that shows how many times the direction of current flow changes during flow while the frequency of the direct current is zero as it do not change the direction of flow.
- The power factor of AC is 0 to 1 While DC is Constant Zero.
- The AC current is generated by the alternator while DC current is generated by Photovoltaic cells, generators and batteries.
- The AC load can be capacitive, inductive or resistive but the load on DC is always resistive.
- The DC current graph has a constant line showing magnitude and direction is constant while the AC current can be a sinusoidal wave, square wave or triangular wave.
- The AC converted into DC using a device named rectifier while the DC converted into AC named inverter.
- AC is widely used in industrial equipment and consumer electronics like AC, Freezer, Cooler, washing machine, lights, fans While DC is used in electronic gadgets and small devices like clocks, laptops, cell phones, Sensors.
- Ac can be transmitted over long distance with some loss while DC can be transmitted very long distance with very low loss using HVDC


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It seems Sundays are the time for me to do a bit of a deconstruction of an opinion piece from the Canberra Press Gallery. Today's subject is the well respected Michelle Grattan, who has been there for quite a long time. She seems in this piece to be pooped by the prospect of covering another election campaign that will be about very little. This is why her piece sounds more at times like an almost uncritical reporting of a product launch rather than an analysis of issues. As ever, her words in italics.
Political science: altering Abbott's polarity from negative to positive
Expect some rebranding as the Coalition campaign begins.
TONY Abbott is likely to be residing in the PM's office later this year. Even though the polls have tightened and things can change dramatically, on both sides of politics, that's the assumption.
From whom? By whom? A pretty big statement to start with – and I can only assume that it's the press gallery about which she speaks without any provided evidence to the contrary.
A second assumption is that a swag of New South Wales seats will help him get there. It's no coincidence that Abbott is starting his mini-campaign this morning with a rally (invitation only) of the Liberal faithful in western Sydney's Lidcombe. The home territory of those "Howard battlers" is fertile ground for Abbott.
It seems Michelle needs to do a bit of research before talking about areas outside Melbourne and Canberra. Lidcombe is far from being "home territory" of "Howard battlers" at all. It is in the seat of Reid, which is the home of a variety of nationalities, including many newly arrived refugees. It is also, these days, a much more marginal seat than in the Howard days, due to a number of factors. If Michelle knew Sydney well, she'd know that the "Howard Battlers" – a lazy term that fits nicely with the Liberal Party strategy documents of the Howard years – was more associated with seats like Lindsay, Greenway, Macarthur and Hughes; containing suburbs that Mark Latham called the "white flight" areas. Not Lidcombe at all. The move by Abbott to target Lidcombe as a launch site for a campaign (no, sorry, unofficial mini campaign) is more a rallying cry for a marginal seat strategy. (I am amused by the idea of the Liberal faithful setting off from their plush suburban digs and setting their GPS devices for Lidcombe.) Having seen the way members of the Canberra Press Gallery showed little understanding of the western suburbs in 2010, I'm not all that surprised that Grattan would say that Lidcombe is just a Howard battler location. It is more a location, however, where the anti-refugee policies of Abbott would have traction amongst those who live in Reid that were either refugees in another era or boat dwellers of the Anglo Celtic variety.
Labor has a total of seven seats in western Sydney and on the NSW central coast that are sitting on margins of between 0.9 per cent and 5.1 per cent. Labor was extremely lucky with some of these last time and a double miracle is unlikely, although the party will make a big effort – a government industry statement is coming, directed at manufacturing workers in such areas.
"Extremely lucky" and "miracle". Grattan appears to be positioning the Coalition as being unlucky to not win in the western suburbs seats – as if it should have been inevitable. Not a mention of the possible impact of Coalition workplace policies, which would be pretty close to the top concern of seats like Reid. Indeed, they have been quiet in the press gallery – and the Liberal Party – about IR for a while.
This week's Coalition campaigning, complete with TV advertising and a booklet detailing values, directions and those policies already in the marketplace, is all about seeking to persuade people that the Opposition Leader can be "Mr Positive". The key message is that the Coalition has a (positive) plan. It's not the first time such an attempt has been rolled out, but this time it is more extensive and serious.
The news that Grattan is discussing here is the release of an advertising campaign and summing up what the angle of that campaign is. It sounds a bit like those articles one reads in newspapers – in lifestyle sections and on page 46 of local newspapers – that just discuss new ad campaigns – that sound something like this –
"Andre Rieu has signed a contract with Chanel, where he will appear in ads where he will stand still and look wistful, with the breeze blowing through his luxuriant hair. The campaign will be seeking to say the violinist is 'Mr Soulful'. The key message is that Chanel has a (positive) plan to engage with music fans. The spend on this campaign is significant, so it looks extensive and serious".
It's a timeless meme in the media. In the 80s, it would have sounded like this –
"Warwick Capper has signed a contract with Brut, where he will appear in ads where he will stand still and look glamorous, with the breeze blowing through his luxuriant hair. The campaign will be seeking to say the Swans star is 'Mr Flamboyant'. The key message is that Brut has a (positive) plan to engage with football fans. The spend on this campaign is significant, so it looks extensive and serious".
But I digress. Onwards…
Abbott is starting the year confident but not complacent. He knows from experience how narrow the gap can be between success and failure. In 2009 he obtained the leadership by chance (Joe Hockey almost had it in the bag) and by the smallest of margins; in 2010 he failed by a whisker to get power.
More of the advertorial style, casting Abbott in a positive light. "Confident, not complacent" is a way of describing a footballer starting a season, as to not make them sound like an egotist who thinks everything is easy. Plus, "by chance" reduces the significance of the campaign by Nick Minchin, amongst others, to install Abbott as opposition leader. "By chance" is a oft repeated half truth.
No wonder he's risk averse. He won't contemplate a reshuffle – it just creates whingers. He minimises "hard" interviews. His office has made an extraordinary effort to counter Labor's claims that he is "anti-woman", with his chief of staff, Peta Credlin, willing to talk publicly about how he encouraged her to use his parliamentary fridge to store her fertility drugs.
It is here we have a list of things reported by the Press Gallery but not really examined or analysed a great deal – Grattan doesn't seem overly bothered by the idea that Abbott is being allowed to minimise those "hard" interviews, as if he has the right to avoid scrutiny.
He is obsessed with discipline, though seemingly unable to avoid periodic lapses. He knows he can be his own biggest risk. His deep personal unpopularity and his negative branding are problems to which he will apply his usual diligence. But can he change his image? And how much will it matter in the end?
"His usual diligence" is an interesting expression, as is Grattan's question as to how important his image is. Image, image, image is the focus of this article. And, as if to confirm this, Hugh Mackay is mentioned – the social researcher who is the go to person for journalists who usually write about social trends and product popularity.
Social researcher Hugh Mackay believes Abbott's brand – being negative, destructive and dismissive – has been unchanged for so long that it has become "indelible" and it's hard to see him being able to break out of it.
Abbott's Brand confirms the idea that this article is about a product. Abbott is Chanel – or possibly more accurately, Brut. What we don't see here is any exploration of why he is unpopular – that it might have something to do with more than image. Then we slip into my favourite quote in the entire article – the moment that in advertisements that are usually prefaced with the line "Don't take my word for it, let's ask one of Abbott's supporters":
But one of Abbott's senior colleagues argues: "He's strong on the tangibles. He's an alpha male. Alpha males are runners, jumpers. They build things." He believes Mr Positive will be convincing.
They build things? They are runners, jumpers? Such a blindingly simplistic view of politics just slides through unchallenged. Or maybe Grattan is just opening the door to the brain of a Modern Liberal, showing that the Liberals really are that superficial. Talking of superficial, Kevin is never far away…
If Abbott faced another Labor leader – notably Kevin Rudd – things might be different. But the chances of a change to Rudd have faded (and a switch would involve its own huge problems for Labor).
It seems Michelle has finally dropped her fantasy (a shared fantasy with the senior members of the Press Gallery, it seems) of the Rudd return. I'm surprised Malcolm didn't make an appearance.
As matters stand, Julia Gillard, while she has clawed back her ratings, is also fundamentally unpopular. Both leaders know that voters are thoroughly fed up with each of them and the hung parliament. Perhaps that's why the start of this election year has been rather slower than might have been expected. The less visible the leaders are, the happier the public. As Mackay says, this will be a contest where there is no inspirational figure.
Imagine, ratings, superficiality. It's like a Theatre of the Absurd play down there in Canberra. Guildenstern's cry – "Words, words. That's all we have to go on" from Stoppard's Rosencrantz and Guildenstern turns into "Polls, polls. That's all we have to go on". That and broad statements by "social researchers".
This week's Coalition campaign will be emphasising the team, including Julie Bishop, Warren Truss, Hockey (slimmed down with the help of surgery for the battle ahead), Andrew Robb and Malcolm Turnbull. Many promised Abbott ministers are recycled from the Howard ministry, which Abbott sells as one of his positives.
Back to explaining the ad campaign, including the helpful comment that losing weight is a good strategy for fighters. (I am personally looking forward to seeing just how Warren Truss and Andrew Robb will be "rebranded")
The Coalition speaks enthusiastically about releasing major policies. Well, soon. Those hanging out for its industrial relations policy, probably its biggest policy test, won't be getting it this week. It's hard to think Abbott won't throw out something in Thursday's National Press Club speech, but manager of opposition business Christopher Pyne said last week: "We are not planning on announcing new policy in the next week but we are planning on reminding people of what is already out there."
No policy still. I look forward to Grattan's critical reports about the non release of policy throughout the year, like we received in previous years. *crickets*
How effectively Abbott sells Mr Positive in coming months could be less important to whether he wins or loses as to the size of his majority.
A Coalition government with a modest margin and an unpopular PM would have no guarantee that fickle voters would be tolerant. Abbott almost overturned a first term Labor government in 2010. A robust buffer is needed to withstand the danger of an electorate that can quickly go sour on new rulers.
There is another reason Abbott needs to do more than just scrape in. A strong lower house vote helps the Senate vote and that could be very important for Abbott. Unless the conservatives get a right-leaning Senate, Labor and Green opposition to Abbott's promise to repeal the carbon tax might force him to meet his pledge to go to double dissolution. And that would be high risk.
This seems to be the best part of the piece, speaking of some real issues Abbott would face if indeed he has a narrow lead. It seems to be a feature of many of these articles that any decent analysis is left to the end. Pity that the rest of it sounds just like the coverage of a product launch. Or maybe that really is Grattan's whole point – that the Coalition are just about the image. I would love it if she was being that subtle.


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FS19 – Claas Jaguar 800 Pack V188.8.131.52
Changelog V 126.96.36.199
– adapted driving behavior should now fit (with 40 around the curve but you should not do)
– Pendulum axle pendulum swing reduced should no longer strike in the wheel arch
– Hubs are now dark gray (Thanks Diego for the tip)
– adapted driver\'s position and movement of the joystick (thanks Diego for the tip)
– Helper now runs with Direct Disc (Thanks da-hoffi for the tip)
– Logos added by configuration
– License plates installed with Spec and Normal and configurable if no sign with engine variant or another
– Horn made a little louder
– Seatcam installed with Sitzfederung and everything that belongs Display\'s adjusted and so on
– Fire extinguisher processed (weggeschitten and exchanged)
– color choice for pickup PU 300 for rims and hubs adapted font PU 300 is dyed with the main color (Thanks Percy for the tip)
– all colors now available in metallic colors (thanks to Percy for the tip)
– Pickup height adjusted when lowering
– Reallights realigned (light cone)
– Adblue blue colored cover complete with blender to assign the material (Thanks Percy)
– Material adapted for outside mirror in the exterior (Thanks Percy for the instructions)
– Material reworked in the cabin should now look a little better (seats with fabric and leather armrests)
– fixed cylinder at the feeder (thanks da-hoffi)
– Script installed which indicates the utilization of Schnedwerks, unfortunately, it works only with the pickup and the Orbis why the other not the error did not find
Utilization is indicated by means of a bar in the display as well as a value in Hilfefester F1 (thanks da-hoffi)
The first thing unfortunately was the modder MB3D modeling of the Jaguar built in 17er unreachable so I decided after a long struggle the Jaguar
to ask the DL, if the said modder sees this here but he should please contact me for release. Thank you
Pack consists of the following equipment:
Claas Jaguar 800 in the versions 840, 850, 860, 870
Orbis 750 corn header working width 7.50 m
Direct Disc 610 in 3 versions Standard, one that can only divorced grass and one for wheat, barley, soybeans, oats and rapeseed (idea of a team member)
Chop the Pickup 300 HD into a swath
Cutting unit carriage for transport from the Direct Disc 610 cutting unit NOTICE The cutting unit must be fastened with tension straps
So now to the emergence of the Mod since I did not find a nice Jaguar in 19s (just so MB bombs) I decided to convert one myself and got myself
grabbed the 17er 800 Jaguar from the modhub.
Jaguar and the Orbis are from the 17er convert but completely revised adapted to LS 19 texture system as well as the XML are on the 19er Stand.
The Direct Disc pickup and cutter carriage are all Krone devices from the game which have been adapted to the Claas design. By a color choice stands
Everyone is free to customize the vehicles and devices themselves.
The cutting unit carriage is a bit cheaper because it has broken something and now you need to attach the Direct Disc me straps.
For Jaguar something he has a configurable GPS which also fades in and out with the Wopster also works together so has a function
REQUIREMENT GPS mod from Wobster is availableFS19_guidanceSteering. Furthermore, I missed the Jaguar a swing axle :).
The Direct Disc is hinged so you can see it was edited in Maya.
In addition, some features are installed which you can discover yourself.
If you do not like the Jaguar Pack, do not load it! I know that not everything is the same and the LS is still a game.
Zetor6245 - von LS 17 in LS 19 konvertiert und Pack so aufgebaut wie es jetzt ist
Sardor Percy - 3D-Schrift, Crawler färbbar Material anpassen
da-hoffi - Texursystem für LS 19 erstellt
Ifkonator - ChangeModTitle Script Freigabe liegt vor
Pixelfarming - Die schönen Bilder vielen Dank dafür
und andere die ihre Ideen eingebacht haben
Danke an alle
Download FS19 – Claas Jaguar 800 Pack V18.104.22.168 - www.modsup.com
Download FS19 – Claas Jaguar 800 Pack V18.104.22.168 - modsbase.com


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Cal Poly will host the American Marketing Association's (AMA) 2016 Marketing and Public Policy Conference Thursday through Saturday, June 23-25. The event is expected to attract marketers, academics and public policy makers from around the world to the Cal Poly campus, representing a wide range of universities, agencies and organizations.
With the theme "fostering change for communities and societies," speakers will explore how policy on large and small scales can ignite change and impact the quality of life for consumers. Cal Poly alumnus Peter Feldman (Business Administration, '89), global product general manager at Amgen, will give the keynote presentation at an awards luncheon Friday, June 24.
AMA will also host an intensive workshop and doctoral seminar prior to the event June 20-23. The workshop is intended to increase the number of scholars and the quality of research in the marketing and public policy domain by providing doctoral-level education and mentoring sessions from accomplished senior researchers. Participants will have the opportunity to hear talks, receive feedback on research, interact and socialize, and identify new research ideas and directions along with these researchers and mentors.
The event is co-chaired by Brennan Davis, associate marketing professor in Cal Poly's Orfalea College of Business, and Beth Vallen, assistant marketing professor at Villanova University.
Registration and conferences details are available at www.ama.org/publicpolicy.


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Women's Center & Shelter of Greater Pittsburgh and other generous community groups host events throughout the year to ensure that the needs of the women and children we serve are met. Check out information on past and upcoming events. We hope you will join us at a future event!
Upcoming Events
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RANCHO MIRAGE, Calif. – There's a new carrot in women's college golf, and the reward is major. The Annika Award – presented by the Annika Foundation and Haskins Commission – will honor the most outstanding player in NCAA Division I golf. The winner receives an exemption into the Kraft Nabisco Championship.
"We all want to encourage young girls to play the game, to stay in the game and to develop in the game," said Sorenstam. 'I think this is one way to do that."
The prestigious Haskins Award, honoring the late Fred Haskins, has recognized the top player in men's college golf the last 41 years. Winners of the Haskins Award include Ben Crenshaw and Phil Mickelson, both three-time winners, as well as Tiger Woods (1996), Luke Donald (1999) and Graeme McDowell (2002). This marks the first time there's a female equivalent.
The award will be presented in the fall of 2014 at a soon-to-be-announced college tournament in Orlando, Fla. Golfweek is the official media partner of the Annika Award and will organize the college event.
Sorenstam, winner of the 1991 NCAA Championship, played college golf at Arizona and won seven tournaments. She turned pro in 1992, after finishing runner-up at the NCAAs. She was an eight-time LPGA Rolex Player of the Year and is the host of this week's Kraft Nabisco Championship.
Sorenstam learned about golf in Arizona while playing alongside a Wildcat in a tournament in Japan. At that point, she'd only been to Miami and had to consult a map. When she arrived in Arizona the following August for the start of her freshman year, it was her first time in the desert. She got off the plane in 1990 with two suitcases; her roommate, Leta Lindley, showed up with a U-Haul.
"I didn't look at any other schools," Sorenstam said.
It worked out nicely.


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Yes, I went totally phatic (props to Kevin for the term) with twitter this morning. In case you missed it — it was like my own version of JAY — behind the music:
Jason Adam Young: was leavin' — but got sidetracked by Sunny Sweeney — leavin' itunes NOW Jason Adam Young: IMDB left out the best Mike Burton quote ever: "it's a mysterious world, Ed, and I'm a curious man…" Jason Adam Young: (path to Ed all via wikipedia): "Jackon" -> June Carter Cash -> Johnny Cash -> Vivian Liberto -> Ginnifer Goodwin -> Ed ( … Jason Adam Young: got out with only the Bruce Hornsby version of Fortunate Son/Comfortably Numb — whew — now browsing IMDB for quotes from the tv show "Ed" Jason Adam Young: NOT impressed with the Ricky Skaggs and Bruce Hornsby version of "Mandolin Rain" Jason Adam Young: Impressed with Flynnville Train's "Nowhere Than Somewhere" Jason Adam Young: i'm completely out of touch with the new music since all I listen to is NPR and talk radio. Some of this is pretty good. Jason Adam Young: Marc Cohn's "Walking In Memphis" is clearly one of the greatest songs ever Jason Adam Young: browsing the itunes music store and avoiding making purchases
Which probably had all my twitter followers hoping and praying I don't bring my trademark verbosity back to twitter for a while.
P.S. bonus del.icio.us link — Essential Viewing — Women of Country Special


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No Sympathy for Shelly Sterling
I couldn't understand why Rochelle Sterling, the wife of deposed racist owner of the Los Angeles Clippers Donald Sterling, was sitting courtside for the Clippers dramatic game 7 victory over the Golden State Warriors. After all, Donald Sterling, as NBA Commissioner Adam Silver said, wasn't just being banned for one set of recorded comments, however offensive, but for a "pattern of behavior." Silver did not spell it out, but it was assumed by everyone with a working cerebrum that by "pattern of behavior," the commissioner was referring Sterling's years as a slumlord. After all, he had been cited repeatedly by the Justice Department for violating the Fair Housing Act and, according to court testimony, spoke about black, Latino and Asian people in a manner that would make Archie Bunker blush.
If this "pattern of behavior" cemented Silver's resolve to ban Donald Sterling, then why is Rochelle aka "Shelly" still courtside? After all, she was also named in these lawsuits and accused of similarly abusive racist language as her husband.
Ms. Sterling denies ever trafficking in racial slurs, but far more damningly, has also been captured on video illegally entering the homes of people in the Sterling tenements by impersonating a health inspector. As "health inspector," she asked for and recorded the ethnicities of their tenants. (The Sterlings were big on racial quotas for their housing projects.) Even if she was an actual health inspector, and not just playing one on the Internet, this is illegal.
Given Donald Sterling's demonstrable misogyny, I'm sure these 60 years of marriage have not been easy for Ms. Sterling. But these personal travails don't excuse business practices that are racist and beyond the pale.
So, once again, why was Shelley Sterling courtside? Why was she leading cheers, embracing players and playing the role of embattled but brave cuckqueen: a veritable "Good Wife" of the hardwood? It turns out that this was the doing of Clippers coach Doc Rivers.
Following their victory over the Warriors, Rivers said:
Recommended Articles
It's a tough one for Shelly, really. She didn't do anything wrong. You have compassion for her. I kept hearing about the girlfriend, and Shelly's the wife. You know what I mean? I talked to her today, and she's been through as much as anyone as well. She asked if she could come, which I thought was a very nice gesture, and she just wanted the players to know that she loved them, and she told me to tell them. I thought, why not?
Rivers has been praised effusively throughout this whole process for his class and grace under pressure, keeping his team together amidst the swirl of distractions. Yet this embrace of Rochelle Sterling is a mistake, painting her as a tragic figure is obscene. It is not as if Doc Rivers, at this point, is unaware of the Sterlings' history. He said earlier this week that he "probably should have" researched more into Donald Sterling's past. He should also know more about Shelly Sterling's hands-on tenement management techniques, as they've received extensive coverage this week in the local LA media. By coddling Ms. Sterling, Doc Rivers sends a message that the hounding of thousands of the poorest residents in Los Angeles is a lesser crime than being caught on audio being a racist jackass.
Rivers should read and reread the section of the 2006 justice department lawsuit that reads, "Defendants Donald Sterling, Rochelle Sterling, and their agents and/or employees have engaged in a pattern or practice of discrimination on the basis of race, national origin, and familial status in connection with the rental of dwellings owned by the Korean Land Company, the Sterling Family Trust, and Donald and Rochelle Sterling, in violation of the Fair Housing Act."
It is still possible that Rochelle Sterling will end up as owner of this team. Adam Silver left that loophole open in his press conference by not guaranteeing that the team would leave the clutches of the Sterling family. One wonders if the highly litigious Donald Sterling would dangle a transfer of the team from himself to Shelley as a compromise to keep 30 years of NBA dirty laundry out of open court. But in the short term, her presence courtside is like a looming reminder that when the smoke has cleared, one Sterling has been merely replaced with another.
Ironically after the Game 7 victory, Doc Rivers gave a passionate speech in which he said, "We needed that. The adversity is good for us." If adversity is what they want, then coddling Rochelle Sterling guarantees more of the same.
Dave Zirin
Edge of Sports


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At the start of a meeting with NATO Secretary Jens Stoltenberg at the Pentagon today, Acting Defense Secretary Patrick M. Shanahan said he is encouraged by NATO's operational progress its efforts to increase burden-sharing.
The North Atlantic Treaty Organization ensures transatlantic security and, Shanahan reiterated President Donald J. Trump's pledge to be with NATO 100 percent, which, of course includes the Article 5 collective defense guarantee.
NATO's European allies have increased their contributions to the training mission in Afghanistan and to efforts in Iraq to establish a training mission aimed at ensuring the Islamic State of Iraq and Syria does not reestablish itself in that country, Stoltenberg said.
Increased Spending
Shanahan praised Stoltenberg for his work in reaching an equitable division of the security burden. "Since President Trump took office, America's NATO allies have stepped up defense spending by a total of $41 billion," Shanahan said. "Allied defense spending increased by more than nine percent from 2016 to 2018 – the largest increase is 25 years. By 2020, our NATO allies are projected to increase defense spending by approximately $100 billion."
This is money that goes directly to deterrence and defense. The increase means larger exercises, mobility and infrastructure improvements and investments in the alliance's advanced response force and the revamped command structure. "This has allowed us to increase our force presence on the territory of our most vulnerable allies," the acting secretary said.
"A few years ago, achieving these improvements and funds might have seemed impossible," he said. "A few years from now, we will write the same success story on readiness. I'm encouraged that we are moving forward on our readiness initiative – 30 battalions, 30 air squadrons and 30 warships ready to fight in 30 days or less."
More needs to happen, but the work is well started, he said. "We need to move from theory to practice, and from practice to results," Shanahan said. "And results come from real changes to posture."
Security Talks
Shanahan discussed Russia's continuing violations of the Intermediate-Range Nuclear Forces Treaty. "This is unfortunate," the acting secretary said. "After our collective efforts to return Russia to compliance, we've kept our part of the deal; Russia did not. Moscow refuses to honor its international obligations, eroding trust and security not only in Europe, but far beyond as well."
Stoltenberg and Shanahan welcomed the recent talks with the Taliban in Qatar. The secretary general said the talks, led by U.S. Ambassador Zalmay Khalilzad, the special representative for Afghanistan reconciliation, have the potential to work. "We are encouraged by what we see now and the progress in the talks with the Taliban" he said.
Stoltenberg noted that the alliance will "not stay longer than necessary," but will not leave until there are assurances that Afghanistan will not become a haven for terrorists.


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Step 1: Launch a Windows Server Amazon EC2 instance
To deploy the Hello World application with CodeDeploy, you need an Amazon EC2 instance running Windows Server.
Follow the instructions in Create an Amazon EC2 instance for
CodeDeploy. When you are ready to assign an Amazon EC2
instance tag to the instance, be sure to specify the tag key of
and the tag value of
CodeDeployDemo. (If you specify a
different tag key or tag value, then the instructions in Step 4: Deploy your Hello World
application might produce unexpected
After you've launched the Amazon EC2 instance, return to this page, and continue to the next section. Do not continue on to Create an application with CodeDeploy as a next step.
Connect to your Amazon EC2 instance
After your Amazon EC2 instance is launched, follow these instructions to practice connecting to it.
In these instructions, we assume you are running Windows and the Windows Desktop Connection client application. For information, see Connecting to your Windows instance using RDP. You might need to adapt these instructions for other operating systems or other RDP connection client applications.
Sign in to the AWS Management Console and open the Amazon EC2 console at https://console.aws.amazon.com/ec2/
In the navigation pane, under Instances, choose Instances.
Browse to and choose your Windows Server instance in the list.
Choose Connect.
Choose Get Password, and then choose Choose File.
Browse to and choose the Amazon EC2 instance key pair file associated with the Windows Server Amazon EC2 instance, and then choose Open.
Choose Decrypt Password. Make a note of the password that is displayed. You need it in step 10.
Choose Download Remote Desktop File, and then open the file.
If you are prompted to connect even though the publisher of the remote connection can't be identified, proceed.
Type the password you noted in step 7, and then proceed. (If your RDP connection client application prompts you for a user name, type
If you are prompted to connect even though the identity of the remote computer cannot be verified, proceed.
After you are connected, the desktop of the Amazon EC2 instance running Windows Server is displayed.
You can now disconnect from the Amazon EC2 instance.
Do not stop or terminate the instance. Otherwise, CodeDeploy can't deploy to it.
Add an inbound rule that allows HTTP traffic to your Windows Server Amazon EC2 instance
The next step confirms your Amazon EC2 instance has an open HTTP port so you can see the deployed webpage on your Windows Server Amazon EC2 instance in a browser.
Sign in to the AWS Management Console and open the Amazon EC2 console at https://console.aws.amazon.com/ec2/
Choose Instances, and then choose your instance.
On the Description tab, under Security groups, choose view inbound rules.
You should see a list of rules in your security group like the following:
Security Groups associated with i-1234567890abcdef0 Ports Protocol Source launch-wizard-
N22 tcp 0.0.0.0/0 ✔
Under Security groups, choose the security group for your Amazon EC2 instance. It might be named
launch-wizard-. The
in the name is a number assigned to your security group when your instance was created.
Choose the Inbound tab. If the security group for your instance is configured correctly, you should see a rule with the following values:
Type: HTTP
Protocol: TCP
Port Range: 80
Source: 0.0.0.0/0
If you do not see a rule with these values, use the procedures in Adding Rules to a Security Group to add them to a new security rule.


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Historians consider the Renaissance one of the outstanding periods of genius in world history. The Renaissance began in Italy about the 14th century, and reached its height in the 15th century. In the 16th and 17th centuries it spread to much of the rest of Europe. The word renaissance, which means "rebirth" in French, refers to the rediscovery by scholars, called humanists, of texts containing the achievements of the ancient Greeks and Romans. In fact, however, the Renaissance was a period of discovery in many fields - of new scientific laws, new forms of art and literature, new religious and political ideas, and new lands, including the Americas. Nevertheless, the recovery and the fuller appreciation of the writings, arts, and attitudes of the ancient Greeks was perhaps the most distinctive feature of the period. New ideas of grace, harmony, and beauty were inspired by the sculpture and other artistic remains of classical Greece and Rome. (Compton's Interactive Encyclopedia)
In 1453 the fall of the Byzantine Empire was marked by the capture of Constantiople by the Turks, who had already overrun the rest of the Empire, including the Balkans; to cap this achievement they returned south, to capture the capital city of Constantinople. This event is said to have contributed greatly to the progress of learning in the West, according to Compton's Interactive Encyclopedia. Many Greeks entered Italy and brought with them manuscripts of Greek literature. This contributed to the process of modernity by reviving classic learning of ancient art and science. (This interpretation is disputed by many historians, among them George Sarton.) Men began once again to exercise their minds, so that they became less servile, and their ideas became clearer and stronger. During this period, men abandoned the medieval features of indistinctiveness of thought and instead began to cultivate Pure Mathematics and Astronomy.
The 16th century was a period of increased intellectual activity. Germany was the leading country in new scientific thought; the Germans brought great productivity in the sciences, mainly due to the country's commercial prosperity. Specifically mathematical activity was largely centered in the Italian cities, and in the central European cities of Nuremberg, Vienna, and Prague. The first great Renaissance contributions to the mathematical sciences were made in Italy and Germany. In Germany advances were made in astronomy and trigonometry, while brilliant contributions to algebra were made in Italy. (Cajori) Among the various Renaissance scholars, two significant mathematicians are worth special mention because of their important contributions to the mathematical field of algebra: the French mathematician of the 16th century, Francois Viéte; and the Italian mathematician Girolamo Cardano.
François Viéte is known as " [t]he greatest French mathematician of the sixteenth century... ", (Eves, p.277) and the " [f]ather of modern algebra", (Catholic Encyclopedia). Perhaps Viéte's importance to the mathematical society is because his mathematical investigations are characteristic of the "new" science at the turn of the 16th century. Viéte was the first to formalize mathematics; which allowed for a simplification of algebraic manipulations. In my opinion, without Viéte's contribution of symbolic algebra mathematicians would be significantly handicapped today. Viéte was born in 1540 in France, the son of Etienne Viéte, an attorney in Fontenay and a notary in Le Busseau. His mother was a first cousin of Barnabé Brisson, President of the Parlement de Paris. Evidence places the Viéte family among the most distinguished in Fontenay. By the age of 20 at the latest, Viéte had already earned a degree in law at the University of Poitiers, in 1560. He soon returned to Fontenay to take rank with the leading barristers at the province, and at age 24 he became a legal advisor of the Huguenot Antoinette d'Aubeterre; who remained his life long confidante. On the side he tutored Catherine, the daughter of Antoinette. Throughout Viéte's lifetime, he gained the acquaintance of highly respectable clients and friends such as the Huguenots, Coligny, Condés, the Queen of Navarre, Henry Navarre, and Francois de Rohan; all significant political figures. At times, Viéte's association with such clients hindered his career. For instance, Viéte was a Huguenot sympathizer at the time of their religious persecution. "Thus Viéte was a victim of political enemies who succeeded in having him banished from court in 1584 to 1589" (Calinger)
His recognized political career began in 1573 when Viéte went to Paris and was appointed by Charles IX to the parliament of city. During the 6 years that Viéte held a position in that parliament, he was also a personal assistant to the King himself. In 1589 he worked for the French state as a parliamentary councilor. The in 1590, during the war with Spain, Viéte assisted Henry IV of France as an interpreter of intercepted Spanish codes.
Along with his notable achievements in the political arena, Viéte also made a mark in the field of mathematics. Viéte wrote numerous works on trigonometry, algebra, and geometry such as the "Canon Mathematicus Seu Ad Triangula" in 1579, the "Artem Analyticem Isogoge" in 1591, the "Supplementum Geometriae" in 1593, "De Numerosa Potestatum Resolutione" in 1600, and "De Aequationum Recognitione Et Emendatione". His most famous work was "In Artem" because it contributed greatly to the development of symbolic algebra. Symbolic algebra is one of three types of algebra. This is the type of algebra that we use today. In symbolic algebra which all forms and operations are represented by a fully developed algebraic symbolism, i.e.: x2+ 13x + 9. In my opinion, it allows one to express his mathematical ideas in a formalized way, and it is much more convenient to read and understand. For the first time in mathematical history, Viéte had introduced the new notion of using vowels systematically to represent known quantities, and consonants for unknown ones. The main significance of this notation is the use of letters instead of numbers in the theory of equations.
Like many other Renaissance mathematicians, Viéte was a student of the ancient Greek literature produced by great mathematicians such as Euclid, Pappus, and Diophantus. He did not recognize at the time what the "analytic art" or new algebra meant for the field of algebra, which will be later discussed. Viéte developed this algebraic notation with the intention of a simple means to the end. He said "Behold, the art which I present is new, but in truth so old, so spoiled and defiled by the barbarians, that I consider it necessary, in order to introduce an entirely new form into it, to think out and publish a new vocabulary, having gotten rid of all its pseudo-technical terms, lest it should retain its filth and continue to stink in the old way ..." (Klein, p.153) His main goal was to understand the ancient Greek ideas of Euclid, Pappus, and Diophantus, rather than the later ideas of the Hindus and Arabs. Viéte was particularly interested in the notions of analysis and synthesis, thus according to Viéte his new algebra was merely " a rediscovery of ancient Greek mathematical methods which would lead to a true mathematics, basic to the search for a universal science, a search later continued by Descartes and Leibniz" (Struik). He thought that his new algebra was simply a new tool for understanding the ancient Greek notions of analysis and synthesis. He believed he was merely a preserver of the ancient Greek sciences, not neccessarily an innovator of modern algebra.
In "In Artem", Viéte refers to the ancient Greek sources. He took the ideas of Euclid, Pappus, and Diophantus and wanted to explain them further so that others could have a better understanding of the their works. Thus, he constructed a calculation with "species" rather than with numerical calculations, to make things more clear and organized. Without his systematic algebraic notation, he would not be able to efficiently explain those ideas of analysis and synthesis. (Struik) Viéte wanted to clarify the ideas of analysis and synthesis. "Analysis is the assumption of that which is sought and the arrival, by means of its consequences, at something admitted to be true"(Heath, "Euclid's Elements") While synthesis is " assumption of that which is admitted and the arrival, by means of its consequences, at something admitted to be true" (Heath, "Euclid's Elements") An example of an analysis is as follows:
An example of a synthesis is the opposite line of attack:
In the first chapter of "In Artem", Viéte discusses a type of analysis which he refers to as "rhetic". He claims that the zetetic art applies logic not the numbers but species. The zetetic art is important because it is successful in comparing magnitudes with one another in equations. In the proceeding two chapters, he uses the ideas of Euclid to establish his foundation for his algebraic notation. He takes postulates from Euclid's Elements such as "the whole is equal to the sum of its parts" (Appendix to Jacob Klien, p.322) and "things that are equal to the same thing are equal among themselves"(Appendix to Jacob Klein, p.324) He also refers to the laws of homogeneity such as " homogenous quantities must be compared with homogeneous quantities." (Appendix to Jacob Klein, p.324) In the first couple of chapters, Viéte was emphasized to pay attention to units (i.e.: inches or gallons) when using his algebraic notation, you cannot just throw all types of units into one equation and expect to understand it. Basically he is laying out the rules of using his notation, to avoid confusion and misapplication of his innovation.
In chapter 4, Viéte describes the four rules for calculation of species. Rule One is "to add a magnitude to a magnitude" (Appendix to Jacob Klein, p.329). In this rule, Viéte states that one can only add homogenous magnitudes; quantities with the same units. For example, according to Viéte's rules for species you cannot add apples with oranges, you can only add apples with apples and oranges with oranges. Viéte uses this rule to make sure that the addition sign is used correctly and not just arbitrarily. The Second Rule is " to subtract a magnitude from a magnitude". This rule is similar to the first rule, except one is subtracting. The 1st and 2nd rules are not appropriate for numbers today. Numbers are abstract entities, adding 10+5=15 is mathematically correct regardless of what units are being added The third and fourth rule, respectively, "To multiply a magnitude by a magnitude: Let there be 2 magnitudes A and B. It is required to multiply the one by the other. Since, then, a magnitude is to be multiplied by a magnitude, they will by their multiplication produce a magnitude heterogeneous in relation to each of them" (Appendix to Jacob Klein, p.332-338) and "To divide a magnitude by a magnitude" (Appendix to Jacob Klein, p.332-338). These two rules basically say that when a magnitude is multiplied (divided) by another magnitude, the solution will always be heterogeneous (different in kind) to the original magnitudes that the process is performing on. Apparently Viéte's claim is logically correct. Multiplying any 2 kinds will always give a new kind that is different form the original two. For example, a side multiplied by a side is a plane (not another side).
Viéte's "In Artem" dealt with variables (species), operators, and units. His laws introduce variables (species) to a certain power, the law of homogeneity, and the idea of denoting unknowns by vowels. Without his accomplishment, people would not be able to work easily with equations. In my opinion, if Viéte had not constructed such a formal original algebraic notation system, the level of mathematical development possibly could have reached a standstill. During the times of the Renaissance, it was hard for people to conceptualize mathematical problems and ideas. Unknowingly, Viéte set up the building blocks for people to use later. Apparently he was successful in creating a language that allowed mankind to express their ideas, logic, and problems in a systematic and organized way. His new algebra was something that could stand on its own, it wasn't merely a tool for understanding analysis and synthesis, instead it was a whole new way for people to look at mathematical problems and notions. Thus as Viéte would say "[We will] leave no problem unsolved."
In contrast with Viéte's respectable reputation and dignified family background, the controversial and enigmatic Italian mathematician Girolamo Cardano led a stormy and unstable life with many ups and downs, twists and turns. "Cardano's character was an enigma to many of his contemporaries...He is a man who has been praised and vilified; by some he has been called a genius, by others a poseur, some have presented him as a benefactor to mankind, others frankly believed him to be an evil spirit, indeed a monster." (Ore, p25)
Girolamo Cardano was born in 1501 in Milan, in northern Italy. He was the illegitimate child of Fazio Cardano and Chiara Micheria. Fazio was a man of universal interests; he was a lawyer in Milan but was also deeply involved in the medical sciences and was an expert in mathematics. In fact, even the great Leonardo da Vinci had consulted with Fazio many times in respect to geometric questions. At a late age Fazio met Girolamo's mother Chiara, who was much younger than Fazio. Chiara did not come from high society and thus was not socially acceptable in Milan. She was a young widow with three children from her past marriage when Fazio met her. Eventually, Fazio married Girolamo's mother.
While growing up, Cardano was an assistant to his father much like a servant. Cardano became anxious to receive an education, despite his father's wishes for him to merely receive home schooling. After a long struggle with his father, Cardano eventually received his father's consent allowing him to attend his father's old university in Pavia to study medicine. However, after only one year war had broken out between Spain and France; thus Cardano had to transfer schools to the University of Padua. At Padua, Cardano showed some of his remarkable abilities. He was a brilliant student and often he would hold his own in disputes with the members of the faculty.
While Cardano attended the institution, his father passed away. As a source of income Cardano resorted to gambling. His knowledge and understanding of probability is thought to have assisted him in his numerous successes in games. However, his gambling became a fault that lasted throughout his life and robbed Cardano of valuable time, money , and his reputation. At the age of 25, Cardano finished his studies at Padua, thus he applied for admission to the College of Physicians in Milan. His application was denied due to his reputation for aggressiveness and critical opinions. Thus, Cardano decided to become a country doctor in the little village of Sacco.
In Sacco, he married Lucia Bandarini, the daughter of the local innkeeper. Realizing that he could not support a family in Sacco, he made efforts to relocate. He tried again for admission to College of Physicians in Milan, and once again his admission was denied. His luck became worse when he had to move back to Milan into a poorhouse with his family. Once he was back in Milan, Cardano's luck changed. Milan's nobles were deeply interested in scientific inquiry. Due to the respectable reputation of his late father Fazio's name, Cardano was appointed to his father's position as a public lecturer at the Piatti Foundation, a reputable medical institution in Milan. At the Piatti Foundation he was not only a lecturer but he was occasionally allowed to treat patients. During this time he had discovered many cures, resulting in an enhancement of his reputation as a physician among his colleagues.
Finally in 1539, after several unsuccessful attempts for admission to the College of Physicians in Milan, Cardano gained admission into the College. Within a few years, Cardano became the most prominent physician in Milan. "The pope and Europe's royal and imperial heads with their princely families were convinced that no physician could better safeguard their health than Cardano." (Ore, p.13) In addition to his step to success, Cardano began publishing mathematical books such as "The Practice of Arithmetic and Simple Measuration". At this point in time Cardano was at the height of his fame, as a practicing doctor no other could compare, and his books were read everywhere by intellectuals.
Cardano's wife Lucia died in 1546, but Cardano apparently was not effected by this event. He was too busy writing best sellers, and indulging in his scientific studies. He was at the height of his fame. He was treated like royalty and he was the world's leading scientist.
Cardano's fortune once again took a turn for the worst. His eldest son Giambatista poisoned his wife with a cake mixed with arsenic. Cardano supported his son in every way; he hired the best lawyers available, wrote petitions, and appealed for clemency through all his friends and influential patients. Despite his strongest efforts, Giambatista was sentenced to death. This tragic event continually haunted Cardano even until his own death.
In 1570, Cardano himself was put into jail on the charge of heresy (according to one tradition). In some of Cardano's writings, there were statements that could be construed as being impious. It is said that he cast the horoscope of Jesus Christ, and wrote in praise of the Emperor Nero, known in his day as the tormentor of martyrs. In a work entitled "Subtility" he wrote a dialogue about the pros and cons of Christianity. However, because of his powerful and influential friends Cardano was only kept in jail for three months. Upon his release Cardano was forbidden to be a professor and was denied the right to lecture publicly, but worst of all he was denied the right to publish any further books. Cardano decided to travel to Rome, and the reception in Rome was favorable. He was immediately invited by the College of Physicians of Rome as a member, and was granted a pension by the Pope.
Gerlamo Cardano died on September 20 1576. Cardano left his entire estate to his grandson Fazio. His books and manuscripts were left to his friends. His lifetime accomplishments are especially highly regarded in mathematical circles. "...[T]he significance of his contributions to mathematics suggest that he ranks with Copernicus (astronomy), Versalius (anatomy), and Paracelus (alchemy and medicine) as one of the founders of that revolution. He displayed a mastery of calculation and a confidence in dealing with algebraic equations in his work." (Calinger, p233)
"Artis Magne" was Cardano's most widely recognized work, because it contained the first published account of general solutions for cubic and quartic equations by means of radical expression. In addition, this was the first book that paid some attention to computations involving square roots of negative numbers. The notion of imaginary roots was left incomplete until Raphael Bombelli laid out the foundation of a more detailed account of imaginary entities. "The `Artis Magne' has always been highly praised as a milestone in the history of mathematics...Nowadays, the `Artis Magne' would be characterized as a text on algebraic equations. To Cardano's contemporaries it was a breakthrough in the field of mathematics, exhibiting publicly for the first time the principles for solving both cubic and biquadratic equations, giving the roots by expressions formed by radicals, in a manner similar to the method which had been known for equations of the second degree since the Greeks or even the Babylonians."(The Great Art, Forward p.7) Before and during the Renaissance era there was a great deal of interest in the solution of cubic, thus the book and its contents was a great victory in the mathematical field.
Neither the solutions to the cubic and quartic equations were his own discoveries. The former was first discovered by del Ferro and rediscovered by Tartagalia and the latter by Cardano's disciple and son-in-law Lodovico Ferrari. In 1535 Tartagalia was challenged to a problem solving match with Fior. Fior gave Tartaglaia problems concerned with cubic equations. On February 12, 1535 Tartagalia discovered a method of solving cubic equations. For reasons unknown, Tartagalia did not want publish the method yet; so all mathematicians from around the world strived to construct the method yet all failed. Tartagalia tried to keep his method a secret but Cardano persistently begged him to show him the method. Cardano made a solemn promise to Tartaglia that he would not publish the method until Trataglia had himself published it : "I swear to you by the Sacred Gospel, on my faith as a gentlemen, not only never to publish your discoveries, if you tell them to me, but I also promise and pledge my faith as a true Christian to put them down in cipher so that after my death no one shall be able to understand them." (p.77, Ore)
Not surprisingly, Cardano took advantage of his knowledge of the cubic equation's solution and immediately started working on the proof of Tartagalia's rule. Cardano knew that there was more that could be done with this knowledge of the cubic solution. "After I was in possession of this rule and had found the proof for it, I [Cardano] understood that here many other things could be discovered, and with my confidence thus already increased I found such results, partly by myself and in part through the work of Lodovico Ferrari, my former pupil." (Ore, p. 85-86) He and his student Ferrari, made efforts to solve bi-quadratic equations. Although Cardano was able to solve an equation such as 32 = x4 + 2x3 + 2x + 1 by a process employed by Diophantus and the Hindus, he failed to find a general solution. His brilliant pupil Ferrari made the discovery of the general solution of bi-quadratic equations. Cardano was so elated by these two discoveries he had in his own possession, he knew no better way to crown his achievements than by writing Artis Magnae with the rules for solving cubics and quadratic equations. Thus Cardano broke his solemn vow to Tartagalia and went through with his own desires for praise and recognition.
Therefore "Ars Magnae" appeared in 1545 and won immediate acclaim by all prominent mathematicians. "From the mathematical publications of the second half of the 16th century one can see that the book exerted a direct and profound influence upon the rise of European mathematics (p.84, Ore) This was a immense achievement because for centuries mathematicians were in search for a solution of cubics, and many believed that it could not be found. Starting from as early as the Babylonians, mathematicians were concerned with equations of higher degree. Some claim that the Babylonians were the first to solve quadratic equations. They developed an algorithm for solving problems that would lead to a quadratic equation. They used the method of completing the square. A limitation of the Babylonians was that all their answers were positive quantities because the answer was a length. About a century later, Euclid constructed a geometrical way of solving quadratic equations, which later became useful method in the cubic solution found in Cardano's "Artis Magnae". However, Euclid like the Babylonians had no notion of equation or coefficients. He merely worked with geometric entities. Therefore the discovery of solution to cubic and quartics was an accomplishment long awaited.
Since the Renaissance era did not have an efficient algebraic notation available, Cardano had to list a multitude of equation types. Because of his notational difficulties, he bases most of his proofs on geometrical arguments, using the ancient Greek mathematician Euclid's style of reasoning. Nowadays, modern mathematicians would not find a need for such methods, but at that time "Euclid's Elements" held the best position for logical thought. Euclid solved second degree equations by constructing squares, thus Cardano expressed the same logic by using cubes to solve cubic equations of the type x3+ px = q.
In addition to Cardano's magnificent display of the cubic solution in "Ars Magnae", he is also recognized and distinguished from other mathematicians for acknowledging the use of imaginary or complex numbers to get real solutions. ".[H]e calculated formally with imaginary numbers but did not accept them." (Calinger, p.234) Unlike other mathematicians before him, he does not avoid or brush imaginary numbers aside. He found something strange when he applied his formula to certain cubics. He found negative numbers under the radical sign. Nobody before him had learned how to take the square root a negative number. In "Ars Magnae", Cardano does give a calculation with complex number, however he did not really understand his own calculation. " In his `Ars Magnae', he takes notice of negative roots of an equation, calling them fictitious, while the positive roots are called real. He paid some attention to computations involving the square root of negative numbers, but failed to recognize imaginary roots. Cardano observed the difficulty in the irreducible case (case when a cubic equation has roots that are expressed by the difference of 2 cube roots of complex imaginary numbers) in the cubic, which, like the quadrature of the circle, has since 'so much tormented the perverse ingenuity of mathematicians'. But he did not understand its nature" (p.135, Cajori). Cardano calculated formally with negative roots but he did not really accept them. Clearly, Cardano used imaginary numbers when it was convinient for solving cubic equtaions, but he did not understand what they actually were. Since he did not understand them, he does not further discuss him in his work.
Perhaps the main obstacle in Cardano's understanding of imaginary roots is that in his search for a solution to cubic equations his "cause was to preserve the purity of the Euclidean tradition" ( Tanner) Cardano solved the cubic equations with geometrical conceptualization (Euclidean logic) , thus the notion of negative roots ( or magnitudes) was not easy to understand of visualize. Who would ever think of a magnitude, such as a side of a square to be negative in length? It is difficult for people to conceptualize this notion of negative roots now, and thus it must have been even more difficult for people of the time of the Renaissance. "Cardano and his age were not less conversant with abstractions and intangible reality..." (Tanner, p.177) In "The Great Arte", Cardano indirectly admits that he does not have a full understanding of complex numbers and that he merely uses them for calculation. ".[S]ince such a remainder is negative, you have to imagine -15-that is the difference between AD and 4AB.namely 5+ 25-40 and 5- 25- 40, or 5+-15 and 5-15. Putting aside the mental tortures involved, multiply 5+-15 and 5-15, making 25-(-15) which is +15. Hence the product is 40" (Cardano, p219) Cardano uses the word "imagine" to indicate that he is not comfortable enough with complex numbers to explain exactly what they are, but for the reader to assume that they exist so that one can perform the necessary computations for cubic equations. Thus a reason for Cardano's blindness in understanding negative roots was that "... Cardano's mind still ran on his geometrical arguments...of Euclid's Elements Book 2. Prop.7" (Tanner, p.169) . "Cardano's other cause, in defence of Euclid, is not to be underestimated, despite its negative and retrograde appearance. It underlines a hiatus that mathematics meets at every breakthrough, and is most familiar today in its 'applied' aspects. In the step from static to dynamic theory, when inapplicable rules for matter at rest are used to derive properties of matter of motion, in their classical treatment. It was also the basis of many ancient paradoxes, which admit as arguments against such a step would have halted advance at the start, but whose serious consideration is a source of unexpected insights even today." (Tanner, p.178) His knowledge of Euclidean methods was both a blessing and a curse on his studies of cubics. At the same time it allowed him solve certain cubics, but also handicapped him in understanding the true notion of imaginary roots which could have allowed him to advance even further in his mathematical accomplishments.
Cardano and Viéte's individual contributions were major stepping stones toward further mathematical discoveries. Cardano provided a tool for solving equations of the 3rd and 4th degrees. He began the crusade for understanding the notion of imaginary roots and complex numbers, which led to higher worlds of mathematical thought and abstraction. His contributions ignited European mathematical development. Viéte's new systematic algebra opened doors for further mathematical development. He created a tool which assisted other mathematicians to engage in detailed mathematical discoveries. He allowed people to express their thoughts mathematically with a higher degree of detail and precision. Both these accomplished Renaissance mathematicians contributed to the foundation of elementary algebra. Without Viéte and Cardano, algebra would still be as underdeveloped as it before and during the Renaissance period.
Primary Sources
Secondary Sources


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DNA is destiny. Or is it?
Nell Donahue was born an echo witch — a weak witch with just enough magic in her to read the tea leaves of bored suburban housewives. Nell's spent her life envying her more gifted sister and chasing magical powers she could never attain until an unexpected trip to hell increased Nell's abilities ten-fold.
Now Nell has more powers than she ever dreamed of. She's also being haunted by the ghost of a slain college student, threatened by a pack of semi-human demon-worshipping ghouls and harassed by a brawny detective who's awakened something in unlucky-in-love Nell that she'd much prefer remained dormant. Too late to return to her status as an echo witch, Nell must learn to harness her enhanced powers before she loses everything, including her heart.