Miscellanies 6.11.85

In another way, too, the number one hundred and twenty is triangular, and it is made up, by way of equality, of sixty-four, whose partial sums generate squares: 1, 3, 5, 7, 9, 11, 13, 15; and, by way of inequality, of fifty-six, the seven even numbers starting from two, which generate the oblong numbers: 2, 4, 6, 8, 10, 12, 14. According to yet another meaning, the number one hundred and twenty is made up of four numbers: one triangular, fifteen; another square, twenty-five; a third pentagonal, thirty-five; and a fourth hexagonal, forty-five. For in each kind the fifth is taken by the same proportion: of the triangular numbers counted from the unit the fifth is fifteen, of the square numbers twenty-five, and of the following ones proportionally. Now the number twenty-five, being the fifth from the unit, is said to be a symbol of the tribe of Levi; and thirty-five belongs to the arithmetical, geometrical, and harmonic diagram formed from double ratios, 6, 8, 9, 12, whose sum makes thirty-five. In these days, the Jews say, children born at seven months are formed. And forty-five belongs to the diagram formed from triple ratios, 6, 9, 12, 18, whose sum makes forty-five; and in these days likewise, they say, children born at nine months are formed.