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# Title: Leibniz-Handschriften zur Technica LH 38
# Folio 289r, page id 00068537:0579
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068537&page=579
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 42 lines, status machine
# Lines: 42 recognised, mean confidence 0.89
# 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.
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# After the first blank line: the recognised lines in reading order, one per line.

e
Sit 2. planum trianquer FDC
eum
plano equatoris. Luio ergo duo pluna
24
0D, 6IN, se mutuo secantia per rectam 6NV, parallela
2. prop. 10.)
b. 16. 11. E.)
C. prop. 13.
d. 9. 11. E.)
sunt duobus planio se mutuo secantibus
per rectam A0, plano scilrcet aequatorio,
et plano ABO, parallelae erunt comunes
ipsorum sectiones, nempe aecta ON, X
radino aequatorio AO.  nod est propontum.
Simili prorsus modo demonstaabitur
luadem radcum A0, = cum ee ad rectam
FM. Zuod erat 2. loco probandum.
ropoo. 14.
Si duo puncta punotu FN, vel C, M,
recta linea connectantur, utracis EN, vel
CM, producta occurret subotyeari in puncto
intersectionio equodem subitylario eum
linea aequinoitiali, hoc est in puncto, O.
secet enim, si fieri potest, recta FN pro
ducta substylarem in alio puncto quam un o,
v. 9. in Z, ita ut FNZ sit una linea recta
ducatur que a punctoz, ad apicem stgei
A, recta ZA. Cum igitur planumtruum
rectarum AZ, AF, F. WZ, se cet duo plana bTN.
ABZ quae ostensa sunt parallela, erunt
proinde coues sectioneo, ON, AZ, parallelae inter
se; sed raduio AO, eidem bN, fuit quoque
ost enous parallelus; ergo rectae AO, AZ quae cons
currunt in A, sunt et ia inter se = quod est absuro.
Ca dem est demonstrad. de recta, CM.
a
s
ns
7
a. prop. 10,
b. Lems. 3.