Posts tagged 'componendo'

G.196 componendo (composition of ratio)

Composition of a ratio means taking the:term:antecedent <G.181> together with the consequent as one 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.236 parallelogram parallelograms diameter

In any parallelogram the parallelograms about the diameter are similar both to the whole and to one another.

G.410 rational segments commensurable

If two rational segments commensurable in square only be added together, the whole is irrational; and let it be called binomial.

G.411 medial segments commensurable

If two medial segments commensurable in square only and containing a rational rectangle be added together, the whole is irrational; and let it be called a first bimedial segment.

G.448 segment commensurable major

A segment commensurable with a major segment is itself also major.

G.491 segment commensurable minor

A segment commensurable with a minor segment is minor.

G.557 pyramids height polygonal

Pyramids which are of the same height and have polygonal bases are to one another as the bases.

G.589 circle diameter rational

If in a circle which has its diameter rational an equilateral pentagon be inscribed, the side of the pentagon is the irrational segment called minor.