Posts tagged 'first-apotome'
G.454 first apotome
Given a:term:rational <G.392>segment and an apotome, if the:term:square <G.63> on the whole be greater than the square on the annex by the square on a segment:term:commensurable <G.372> in length with the whole, and the whole be commensurable in length with the rational segment set out, let the apotome be called a:term:**first apotome** <first-apotome>.
G.455 medial segment there
If from a medial segment there be subtracted a medial segment which is commensurable with the whole in square only, and which contains with the whole a rational rectangle, the remainder is irrational. And let it be called a first apotome of a medial segment.
G.462 apotome medial segment
To a first apotome of a medial segment only one medial segment can be annexed which is commensurable with the whole in square only and which contains with the whole a rational rectangle.
G.467 find the first apotome
Find the first apotome.
G.477 area contained rational
If an area be contained by a rational segment and a first apotome, the “side” of the area is an apotome.
G.478 area contained rational
If an area be contained by a rational segment and a second apotome, the “side” of the area is a first apotome of a medial segment.
G.483 square apotome applied
The square on an apotome applied to a rational segment produces as breadth a first apotome.
G.484 square apotome medial
The square on a first apotome of a medial segment applied to a rational segment produces as breadth a second apotome.
G.494 rational area medial
If from a rational area a medial area be subtracted, the “side” of the remaining area becomes one of two irrational segments, either an apotome or a minor segment.
G.495 medial area rational
If from a medial area a rational area be subtracted, there arise two other irrational segments, either a first apotome of a medial segment or a segment which produces with a rational area a medial whole.
G.584 rational segment cut
If a rational segment be cut in extreme and mean ratio, each of the segments is the irrational segment called apotome.