# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/898203430:0218
# Permalink to this reading: https://leibnizlegible.com/page/898203430:0218?run=74
# Title: De Locis Solidis Secunda Divinatio Geometrica (shelfmark Leibn. Marg. 151)
# Folio 26, page id 898203430:0218
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=898203430&page=218
# Source image: https://digitale-sammlungen.gwlb.de/content/898203430/jpgs/default/00000218.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 38 lines, status machine
# Lines: 38 recognised, mean confidence 0.93
# 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.

VINCENTM VIVIANI DE LOCIS SOLWDIS
LRMMA. II. PR OP. ZXXIZ
I recta linea inaequaliter vtcunque secta fuerit, qua
Ddratum tocius, duobus simul rectanculis (ub tota, ea
minori parte, ona cum differentia inter quadrata par
tium aequale est.
PF data AB vecunque secta inaequalitet in C, ita vE DC sic pars mis
D NOT. Dico quadratum AB duplo rectanouli ABC, cum differentia
inter quadrata parrium AC, C B aequalo eAe. Fx A C sIMatUr A D
aequalis CB.
Jam quadracum AB constac ex dupio
rectanouli A C B, e ex quadratis BC,
C A, Sed quadratum C A COnSTat CX Gua-
drato AD, _ ex lui ipsius disserentia su-
per iptum quadratum AD, vel super quan
dracum CB, ergo quadra un AB constat.
vel aequale est duobus rectanoulis A C B
vna cum duobus quadraris B C, AD, ee cum praedicta differentia, sedt
duo rectanoula AC B cum duobus quadratis B C, AD consiciun duo re
ctangula ABC (quum AE B C aequalis AD ex constructione) eroo idem
quadratum AB aequatur duobus rectansulis ABC via cum ditterentia.
quadratorum AC; C B. Ouod erat demonstrandum.
PROPOSITIO XXXK.
Ocus Ordinatarum potentium differentiam inter qua
dratum datae. C5 differentiam quadratorum partium.
est ad concauum Parabola, cuius vertex sit occursus
datae cum parte assumpra, axis ipsa data, rectum vero
latus datae sit duplum.
IT data AB vecunque inaqualiter secta in C, Ita ve C B sie pars m
 nor, et per verticem B circa axem B A delcribatur Parabola, cuius
sem rectum latus SIc data AB. Dico eam
esse Locum propositum: hoc est ordinatam
C F posse ditterentiam inter quadratum.
datae AB, _ disterentiam quadratorum
Parrium AC, CB.
Nam (per lemma praecedens) quadratum
datae AB aequatur duplo rectanguli ABC vnâ cum dister etsd inter quar
dxdlb