# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/898203430:0239
# Permalink to this reading: https://leibnizlegible.com/page/898203430:0239?run=74
# Title: De Locis Solidis Secunda Divinatio Geometrica (shelfmark Leibn. Marg. 151)
# Folio 47, page id 898203430:0239
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=898203430&page=239
# Source image: https://digitale-sammlungen.gwlb.de/content/898203430/jpgs/default/00000239.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 45 lines, status machine
# Lines: 45 recognised, mean confidence 0.90
# 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.

ORBTHATAAVM POTEATINM EIUT. LIB. II.
cinatam quam cumque D F incer puncta C, B posse difterentiam inter lui
inam quaeratOrUm AD, DB, Se rectansulum ADB.
EX CENITO C dUCaEuT AlymPEOTOS C C vertica-
lein consentem ad F. secans in L, de ad alteram
parcem descripra oppolita Sectione NL, ad eam
PrOduCatr FD in L.
Tam, quum Cic A B lecta bitariam in C, de non
bitariam in D, difterencia quadrarorum AD. DB
super rectangulum ADB, eric quadratum AC cum A
eriplo quadrari C D (per Lerrima praecedens) sed
quadratum A C aquatur C F. (ob positam laterum
aqualicatem) vel recrangulo L. G F ipsi quadrato
CF aequalis 2 de triplim quadrati C D est quadra
cum DC (nam quum policum sic semitrantuersum
CF triplum sui lemireeci, eric e quadratum C F.
eriplum semiaris coniusati PP, adeoque, de quadratum GD criplum qua-
drati DC, ob triangislorum similiudinem) ergo differentia inter quadras
ca sinuI AD, D B, _ rectangulum AD B est rectangulum L. G F vna
cum quadtato DC, hoc est vnicum quadratum D F: de hoc de sinoulis
similibus ordinatis _c. Ouare convexum praedictae FIyperbolx CA LoCuS
propolia Ordinationis. Ouod crat dec.
LEMMA. IX. PROP. IXX.
T recta AB secta sit bifariam in C., eigue adald ua
directum quaedam BD. Dico quadratum AD ex
data, (5 addita; cum quadrato additae BD, aqua
esse quadrato C. D ex dimidia, es addita una cum
rribus quadratis AC ex eodem datae dimidio, Cs cum
rectanoulo ADB sub data cum addita in additam.
M
Z PTOdUICCA C A sumatUE A F xqualis addiexe BD: quumque siE A C
L aequalis CB, erit TOta F C aequalis CD, adeoque F. D eric secta Bi
tariam in C, et non bitariam in B; quare, per Lemma prxcedentis, qua
Oraca siniul E B, B D aqualid erune quadraco dimidix F. C. cum cribus
quadraris incerpolici segmenti C B, ud cum
rectangulo E BD; scd duo F B, BD aquan- F.
tur duobus AD, D B; _ quadratum F. C
aequatur quadrato CD, de tria Cunul C B
aequantur iribus simul AC, atque reCtanGUIUm EBD RGHaTuIE RCCLanBU-
I0 ADB, ergo d duo quadrata AD, D B simul aequalia sune quadrato
CD, vna cum iribus quadratis AC, et cum rectangulo ADB. Duod
erac demonstrandum.
PRO
a EI. PecUM
di COnic.