Since, then, the spheres by which the planets themselves are moved (Λ) are eight and twenty five, and of these only those by which the lowest situated planet is moved need not be counteracted, the spheres which counteract those of the first two planets will be six in number, and the spheres which counteract those of the next four planets will be sixteen, and the number of all the spheres those which move the planets and those which counteract these will be fifty five.