Posts tagged 'third-apotome'

G.469 third apotome

But if neither be:term:commensurable <G.372> in length with the:term:rational <G.392>segment set out, and the:term:square <G.63> on the whole be greater than the square on the annex by the square on a segment commensurable with the whole, let the apotome be called a:term:**third apotome** <third-apotome>.

G.470 find the third apotome

Find the third apotome.

G.479 area contained rational

If an area be contained by a rational segment and a third apotome, the “side” of the area is a second apotome of a medial segment.

G.485 square apotome medial

The square on a second apotome of a medial segment applied to a rational segment produces as breadth a third apotome.

G.496 medial area there

If from a medial area there be subtracted a medial area incommensurable with the whole, the two remaining irrational segments arise, either a second apotome of a medial segment or a segment which produces with a medial area a medial whole.