noncuple

36 vnto 4 is a noncuple proportion.

To proue that a trilater equilater Pyramis, is noncuple to a cube inscribed in it.

If for duple we had substituted triple, quadruple, quintuple, &c. the action would have come out noncuple, sedecuple, 25ple.

In the following odd multiples above the ſeptuple arc, the mean arc may be greater than three quadrants: Thus, for inſtance, in the caſe of the noncuple arc, in which the three equidifferent arcs are the quintuple, ſeptuple, and noncuple arcs, ‛tis evident the greateſt magnitude of the ſeptuple, or mean, arc, or that which it has when the noncuple arc is equal to a whole circle, is ⁷⁄₉, or ²⁸⁄₃₆, of the whole circumference, which is greater than ²⁷⁄₃₆ or ¾ of the whole circumference, or three quadrants; and ſince this is true in the noncuple arc, it follows a fortiori that it will be true in all higher multiples.

In the noncuple series, each term exceeds the octuple of the sum of its parts, by unity.