And if neither of the terms is commensurable in length with the rational (straight line previously) laid out then let (the whole straight line) be called a third binomial (straight line).
The third binomial is a straight line whose length is \[\sqrt{\alpha}\,\left(1+\sqrt{1-\beta^{\,2}}\right),\]
where \(\alpha,\beta\) denote positive rational numbers.
Proofs: 1 2 3 4 5 6 7
Propositions: 8 9 10