And if the attached (straight line) is commensurable in length with the (previously) laid down rational (straight line), and the square on the whole is greater than (the square on) the attached (straight line) by the (square) on (some straight line) commensurable (in length) with (the whole), then let the (apotome) be called a second apotome.
The second apotome is a straight line whose length is \[\frac{\alpha}{\sqrt{1-\beta^{\,2}}}-\alpha,\]
where \(\alpha,\beta\) denote positive rational numbers.
Corollaries: 1
Proofs: 2 3 4 5 6 7 8 9 10 11 12
Propositions: 13 14 15 16 17 18 19 20 21 22