Posts tagged 'invertendo'

G.182 invertendo (inverse ratio)

Inverse ratio means taking the:term:consequent <G.181> as antecedent in relation to the antecedent as consequent.

G.183 equal magnitudes ratio

Equal magnitudes have to the same the same ratio, as also has the same to equal magnitudes.

G.202 there magnitudes others

If there be three magnitudes, and others equal to them in multitude, which taken two and two are in the same ratio, and if :term:`ex aequali <G.174>` the first be greater than the third, the fourth is greater than the sixth; if equal, equal; and, if less, less.

G.204 there magnitudes others

If there be three magnitudes, and others equal to them in multitude, which taken two and two together are in the same ratio, and the proportion of them be perturbed, then, if ex aequali the first magnitude is greater than the third, the fourth is greater than the sixth; if equal, equal; and if less, less.

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.376 commensurable magnitudes ratio

Commensurable magnitudes have to one another the ratio which a number has to a number.

G.377 magnitudes ratio number

If two magnitudes have to one another the ratio which a number has to a number, the magnitudes is commensurable.

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.425 find the second binomial segment

Find the second binomial segment.

G.431 find the fifth binomial segment

Find the fifth binomial segment.

G.552 circles squares diameters

Circles are to one another as the squares on the diameters.

G.556 pyramids height triangular

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

G.563 cone part cylinder

Any cone is a third part of the cylinder which has the same base with it and equal height.

G.565 cones cylinders height

:term:`Cones <G.561>` and :term:`cylinders <G.562>` which are of the same :term:`height <G.209>` are to one another as their bases.

G.570 similar cones cylinders

Similar cones and cylinders are to one another in the triplicate ratio of the diameters in their bases.

G.578 spheres triplicate ratio

Spheres are to one another in the triplicate ratio of their respective diameters.

G.601 set out sides

To set out the sides of the five figures and to compare them with one another.