··

rrxiv is an open protocol. Specification · API · Pulse · AboutMaintained by the rrxiv working group · Privacy-respecting analytics

Source — Euclid's Elements, encoded as an rrxiv paper — rrxiv

Browse/Euclid's Elements, encoded as an rrxiv paper/source

Source — Euclid's Elements, encoded as an rrxiv paper

58 files·489.1 KB···Download archive (.tar.gz)

Reader · live HTML Source files · 58 files · loading…Rendered · PDF

← Claims Full view

VII.19 Proposition VII.19

If four numbers be proportional, the number produced from the first and fourth will be equal to the number produced from the second and third; and if the number produced from the first and fourth be equal to that produced from the second and third, the four numbers will be proportional.

Proof

Discrete analogue of VI.16: cross-multiplication preserves and detects proportionality. Use VII.17 in one direction and the converse argument (proportion from equal products via VII.14) in the other.

lines 74–74 in main.tex

58 files·489.1 KB·

· 58 files

← Claims Full view

VII.19 Proposition VII.19

Proof

Discrete analogue of VI.16: cross-multiplication preserves and detects proportionality. Use VII.17 in one direction and the converse argument (proportion from equal products via VII.14) in the other.

lines 74–74 in main.tex