# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00067971:0042
# Permalink to this reading: https://leibnizlegible.com/page/00067971:0042?run=39
# Title: Leibniz-Handschriften zur Mathematik LH 35, 1, 12
# Folio 21v, page id 00067971:0042
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 20r); this page is its left half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00067971&page=42
# Source image: https://digitale-sammlungen.gwlb.de/content/00067971/jpgs/default/00000042.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 39, 2026-08-27T09:55:26Z — 29 lines, status machine
# Lines: 29 recognised, mean confidence 0.91
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line: the recognised lines in reading order, one per line.

pro positi
eorema 1 Triangula similia sunt aequiangula
per
fin
Nam qu sint triangula similia ABC. DCF erit ang. A ert
anguli A: B: C:: D. E: F. Ergo per pr  per prop. 2. A: D: : AF BH d
jam A+ B +C aequ. D + E + F per prop. 1. Ergo A aequ. D eodemque modo 
B aequ E et C aequ F. triangula itaque aequiangula sunt. Q: E. d.
Theorema EI. Tiangula aequiangula sunt similia
sint triangula aequi angula AB CpsD EF. sit recta dH aego DE.
et sit fiat sint aliae q H9 (et 88) ad D H, ut BC, (et C A) ad AB. Lx
per ax. 2 datur triangulum dHG per prop.  4 latera habens
proportionalia ex coustuct. lateribus ipsius ABC, proportio nalia ex constuct
ergo per ax. 1. simile est Triangulo ABC. (ergo per theor. 1 aeydiampe
ei aequiangulum, jam ABC et DEF aequiant
espondens
DEF aequiangula; et et latus hrmolegum habent aequale. DE. Ipsi a dH. ergo
hec hi per ex hypoth. ergo triangula DEF. dH _ congrua sunt
per  prop. 3. jam DF  dH8 et ABC similia sunt, ut ostendimus
Ergo tria e triangula aequiangula ABC. DEF similia sunt. Q. E. D.
suit duo vel (quanquam eodem redrat) seut duo triangula
aqu esse similia. Nam si ipsi ABC simile fieri potest  super latere 5
Ninnion  1b4 D
aequali DF. D id erzo aequiangula sunt per praecedentem. Ergo DEF et Sug eliam aequim
aequianusa
gula sunt, sed habent latus aequale DF et 59. Er ex constructione Ergo congrua sunt per
aprop. 3. Si autem unum congrnonum terto simile est, Ectiam alterum ei simile erit
2
Ergo ABC. et DEC similia sunt