# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/898203430:0226
# Permalink to this reading: https://leibnizlegible.com/page/898203430:0226?run=74
# Title: De Locis Solidis Secunda Divinatio Geometrica (shelfmark Leibn. Marg. 151)
# Folio 34, page id 898203430:0226
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=898203430&page=226
# Source image: https://digitale-sammlungen.gwlb.de/content/898203430/jpgs/default/00000226.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 42 lines, status machine
# Lines: 42 recognised, mean confidence 0.92
# 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.

34
VINCENTA VIVIAME DE LOCIS SOLIDIS
AC, sed rectangulum sub AD, AC aequale cst rectaneulis sub AD, F. C, e
TUb AD, AF, quorum primum, nempe re
Cranouum sub AD, F C RQUaTT FCCLAN-
sulo sub AD, DC ( quum CF, C L
sinc xequales) alterum vero, nempe sub
P.D, AF aequatur rectangulo (ub AD.
DB (cun iteim AF, D B sinc Xequales)
eroo quadratum A D aequale est duplo rectanguli sub AD, DC vnâ
cum rectangulo ADB. Ouod erat demonstrancum.
P R OPOSITIO LIMI.
Ocus Ordinatarum potentium differentiam inter re-
ctanculum sub inaequalibus partibus inteerantibus
datae, eo quadratum maioris seementi, est ad conca
num rperbolae, cujus vertex sit punctum bisecans
datam; axis vero transuersus sit dimidium datae, quod
superest ex maiori seemento, rectum verd larus ipsi da
ta sit aequale.
IT data AB, secta bitariam in C. Tam patCE quadEAtIM A C aequan
D lc esse rectangulo A C B, at s eadem data inaequaliter secetur in D
inter C, B, patet quoque quadratum AD maius esse rectangulo ADB.
AIis praemonitis. Si per verticem C, circa axem C B, cum axc transverso
A C, e recto lacere ipsi datae A B aequali fac HIy PerbOla C B. Dico
hanc esse Locum propolitum: hoc est ordinatam D C porse disterenciam
inter quadratum maioris legmenti AD. et rectangulum sub sesmentis
inae qualibus ADB.
Ouoniam enim rectangulum ADC ad
21. Primi quadratum DC eA ve 2 transuerlus axis
AC ad rectum lacus AB, vel in ratione
subdupla, eric rectangulum AD C di-
midium quadrari DC, siuc duo simul xe-
etangula AD C aequalia quadrato DC,
sed duo ADC. Per Lemma praecedens.
aequantur disserentiae inter quadratum
AD, de rectangulum ADB C quia AB
secta est bitariam in C, e non bitariam
in D) ergo e quadratum ordinata DC praedictae difterentia sequale CAt:
de hoc de qualiber simili ordinata ad C B. Ouare concauum huiusmodi
Hyperbolae est Locus proposuae Ordinacionis. Ouod erat ec,
COniE.
Lemina