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# Title: De Locis Solidis Secunda Divinatio Geometrica (shelfmark Leibn. Marg. 151)
# Folio 24, page id 898203430:0052
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=898203430&page=52
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 33 lines, status machine
# Lines: 33 recognised, mean confidence 0.87
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
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# After the first blank line: the recognised lines in reading order, one per line.

VINCENTI Vilam PLOCIS
C C
Le eu 
Olligitur hinc, in qualiber Coni-sectione, quacratum cuiulcunque
rami à verrice ducti aequale semper esse rectangulo sub composica
ex luxe ordinatae segmento initer axem, e regulatricem, cum sesmento
abscissi axis, in hoc idem seBMENEUM.
ORensum enim est quadratum rami BFT aequale rectanguio sub LM (qua
constac ex L. I inter axem, _ regulatricem, et Cx IM, sive ex YB segmento
axis ip(I IM aequali, ob angulos lemirectos ad M, B) in MI, sive in idem IB.
PROP. ZV. L E M M A II.
r. C rectos angulos ad verticem ABC, DBF. subten
dant rectae AC, DF, ita et primo, AC ad DF
sit et AB ad BD; Dico AC. ips DE aequidistare.
Vum enim sIF DE A C ad DE, ita A B ad B D, permurando erit
CA ad AB VE FD ad DB, anguli aurem ad B sunt recti, ac ideo
reliquorum veerque minor est recto, ergo per seprimam sext
Elemene triangula A B C, D B F. sune xquiangula, de angulus B A C
aequalis alterno BDE. Ouare A C aequidictat ipsi DF..
B.
Si vero AC ad DF. maiorem habuerit rationem
quam cele in e. sonausat bst sebando rdau
etam L ondbn bdm etdacibelo C. Lf clt Pat 1bd L3+L.
Y enim negatur hoc, vel D F ipsi C A aequidictabit, vel ipsae simul
a convenienE 2d parteS COnrariaS D, C. Non primum. Ouia A C.
ad D E esset ve A B ad BD, quad est contra FIypochelum.
Non secundum. Cuia DF, ducta ex D ipsi AC paralleta, necerario
caderet intra angulum F. DB, aeque ita AC ad DF rationem haberee
eam, quam A B ad B D, scd ratio A C ad D F. Ponitr maiOF F2
tione A B ad BD, ergO _ A C ad D E: maiorem haberee rarionem
quam ad DF: quare D E. minor esset DF, quod es Falsum, quum sIE
maior (opponitur enim D E obtulo angulO DFF, DF VerO aCUIO DEF)
erso producta DE convenit necellario cum C A ad Partes F, A.