If a rational (straight line), which is commensurable in square only with the whole, is subtracted from a(nother) rational (straight line) then the remainder is an irrational (straight line). Let it be called an apotome.
An apotome is a straight line whose length is expressible as
\[1 -\sqrt{\delta},\]
for some positive rational number \(\delta\). See also [Prop. 10.36].
Proofs: 1
Corollaries: 1
Definitions: 2
Proofs: 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
Propositions: 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58