Posts tagged 'separando'

G.197 separando (separation of ratio)

Separation of a ratio means taking the excess by which the:term:antecedent <G.181> exceeds the consequent in relation to the consequent by itself.

G.198 magnitudes proportional componendo

If magnitudes be proportional componendo, they is proportional separando.

G.199 magnitudes proportional separando

If magnitudes be proportional separando, they is proportional componendo.

G.201 whole whole part

If, as a whole is to a whole, so is a part subtracted to a part subtracted, the remainder is to the remainder as whole to whole.

G.207 magnitude ratio fifth

If a first magnitude have to a second the same ratio as a third has to a fourth, and also a fifth have to the second the same ratio as a sixth to the fourth, the first and fifth added together will have to the second the same ratio as the third and sixth have to the fourth.

G.345 numbers continued proportion

If three numbers in continued proportion be the least of those which have the same ratio with them, any two whatever added together is prime to the remaining number.

G.368 many numbers please

If as many numbers as we please be in continued proportion, and there be subtracted from the second and the last numbers equal to the first, then, as the excess of the second is to the first, so will the excess of the last be to all those before it.

G.386 segments proportional square

If four segments be proportional, and the square on the first be greater than the square on the second by the square on a segment commensurable with the first, the square on the third is greater than the square on the fourth by the square on a segment commensurable with the third. And, if the square on the first be greater than the square on the second by the square on a segment incommensurable with the first, the square on the third is greater than the square on the fourth by the square on a segment incommensurable with the third.

G.389 there unequal segments

If there be two unequal segments, and to the greater there be applied a parallelogram equal to the fourth part of the square on the less and deficient by a square figure, and if it divide it into parts which are commensurable in length, then the square on the greater is greater than the square on the less by the square on a segment commensurable with the greater. And, if the square on the greater be greater than the square on the less by the square on a segment commensurable with the greater, and if there be applied to the greater a parallelogram equal to the fourth part of the square on the less and deficient by a square figure, it will divide it into parts which are commensurable in length.

G.390 there unequal segments

If there be two unequal segments, and to the greater there be applied a parallelogram equal to the fourth part of the square on the less and deficient by a square figure, and if it divide it into parts which are incommensurable, the square on the greater is greater than the square on the less by the square on a segment incommensurable with the greater. And, if the square on the greater be greater than the square on the less by the square on a segment incommensurable with the greater, and if there be applied to the greater a parallelogram equal to the fourth part of the square on the less and deficient by a square figure, it divides it into parts which are incommensurable.

G.498 square rational segment

The square on a rational segment applied to the binomial segment produces as breadth an apotome the terms of which are commensurable with the terms of the binomial and moreover in the same ratio; and further the apotome so arising will have the same order as the binomial segment.

G.590 equilateral triangle inscribed

If an :term:`equilateral triangle <G.13>` be :term:`inscribed in a circle <G.148>`, the :term:`square <G.63>` on the side of the :term:`triangle <G.12>` is triple of the square on the radius of the :term:`circle <G.10>`.