OpenType features include numerators/denominators, fractions, ligatures, scientific inferiors, subscript/superscript. However, these rates are ratios that fail to reveal their numerators and denominators. The denominators are listed in , while the numerators are all 1s. From the second, the numerators of the first column are the denominators of Euler's formula. Then "bd" is a common denominator and the numerators "ad" and "bc" can be compared. Proved by expanding the numerators and using the half angle formulae. This equation of the numerators is an absolute identity, true for all values of x. Consequently, we will get the numerators grouped by the end digit. The days in the numerators are calculated on a Julian day difference basis. The sum of the numerators is formula 59. The numerators of the second line are preceded by 0. Then we solve for the numerators, A and B.