Editing Euclidean geometry (section)

===Infinite processes===
Ancient geometers may have considered the parallel postulate – that two parallel lines do not ever intersect – less certain than the others because it makes a statement about infinitely remote regions of space, and so cannot be physically verified.<ref>Nagel and Newman, 1958, p.&nbsp;9.</ref>

The modern formulation of [[proof by induction]] was not developed until the 17th century, but some later commentators consider it implicit in some of Euclid's proofs, e.g., the proof of the infinitude of primes.<ref>Cajori (1918), p.&nbsp;197.</ref>

Supposed paradoxes involving infinite series, such as [[Zeno's paradox]], predated Euclid. Euclid avoided such discussions, giving, for example, the expression for the partial sums of the [[geometric series]] in IX.35 without commenting on the possibility of letting the number of terms become infinite.