Submit Spec API

//

··

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

··Download archive (.tar.gz)

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

58 files·489.1 KB·

· 58 files

Files

texpaper/main.tex2.8 KB
texpaper/books/book01.tex22.4 KB
texpaper/books/book02.tex20.7 KB
texpaper/books/book03.tex34.3 KB
texpaper/books/book04.tex12.3 KB
texpaper/books/book05.tex14.4 KB
texpaper/books/book06.tex21.5 KB
texpaper/books/book07.tex19.0 KB
texpaper/books/book08.tex14.5 KB
texpaper/books/book09.tex17.1 KB
texpaper/books/book10.tex49.5 KB
texpaper/books/book11.tex22.8 KB
texpaper/books/book12.tex10.3 KB
texpaper/books/book13.tex12.3 KB
texpaper/common-notions.tex765 B
texpaper/definitions.tex27.6 KB
texpaper/figures/fig-i-1.tex702 B
texpaper/figures/fig-i-32.tex1.2 KB
texpaper/figures/fig-i-47.tex1.8 KB
texpaper/figures/fig-i-5.tex1.1 KB
texpaper/figures/fig-ii-11.tex1.3 KB
texpaper/figures/fig-ii-14.tex2.4 KB
texpaper/figures/fig-ii-4.tex1.8 KB
texpaper/figures/fig-iii-20.tex1.2 KB
texpaper/figures/fig-iii-31.tex1.0 KB
texpaper/figures/fig-iii-36.tex1.5 KB
texpaper/postulates.tex1.1 KB
clspaper/rrxiv.cls12.7 KB
•CITATION.cff729 B
•LICENSE-CODE1.3 KB
•LICENSE-CONTENT1.0 KB
•README.md4.7 KB
imgpaper/figures/fig-i-1.pdf2.4 KB
imgpaper/figures/fig-i-1.png14.5 KB
imgpaper/figures/fig-i-32.pdf2.8 KB
imgpaper/figures/fig-i-32.png8.7 KB
imgpaper/figures/fig-i-47.pdf4.5 KB
imgpaper/figures/fig-i-47.png10.9 KB
imgpaper/figures/fig-i-5.pdf2.9 KB
imgpaper/figures/fig-i-5.png11.4 KB
imgpaper/figures/fig-ii-11.pdf3.0 KB
imgpaper/figures/fig-ii-11.png7.9 KB
imgpaper/figures/fig-ii-14.pdf2.8 KB
imgpaper/figures/fig-ii-14.png7.0 KB
imgpaper/figures/fig-ii-4.pdf3.6 KB
imgpaper/figures/fig-ii-4.png6.6 KB
imgpaper/figures/fig-iii-20.pdf3.7 KB
imgpaper/figures/fig-iii-20.png14.0 KB
imgpaper/figures/fig-iii-31.pdf2.5 KB
imgpaper/figures/fig-iii-31.png10.3 KB
imgpaper/figures/fig-iii-36.pdf2.7 KB
imgpaper/figures/fig-iii-36.png11.0 KB
•rrxiv-meta.json3.4 KB
•scripts/build.sh834 B
•scripts/extract-cir.sh2.6 KB
•scripts/merge-sidecar-edges.py4.5 KB
•scripts/render-figures.sh3.6 KB
•scripts/verify.sh3.4 KB

paper/figures/fig-i-1.pngimage · 14813 bytesRaw

Binary file — open the raw URL above to inspect.

← Claims Full view

I.27 Proposition I.27

If a straight line falling on two straight lines make the alternate angles equal to one another, the straight lines will be parallel to one another.

Proof

Suppose the lines meet; I.16 gives a contradiction. By Definition I.23 they are parallel.

lines 74–74 in main.tex