# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/175905688X:0243
# Permalink to this reading: https://leibnizlegible.com/page/175905688X:0243?run=74
# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 221, page id 175905688X:0243
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175905688X&page=243
# Source image: https://digitale-sammlungen.gwlb.de/content/175905688X/jpgs/default/00000243.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 50 lines, status machine
# Lines: 50 recognised, mean confidence 0.84
# 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.

1
icc
ade
M
cun
ie
1
c
CDMMERHX AHL EN LIDRUnTI.
22. L
EEc ad inquirendum, utrum pro-
prietas circuli, quae declarat, qua-
drata ordinacim adplicatarum ad
diametrum esse aequalia rectangulis
sub segmentis diametri, cum circu
B LO SIE RCCIPIOCA NEC nC: SupPONatuY
recta AB, d in cam perpendicula-
ris CD, hanc habens proprietatem, uc quadratum luper ipsd lix
aequale rectangulo sub segmentis AC, C B. Quaritur qualis sIE
linca ADB.
Ad quod investigandum, secta A B bitariam in F, PONAEF
AEveIEB DA, C E DK, _ CD D y: CTIEGuC A C ∞ a =X
d C B∞ a- F x. Jam cum AC mulciplicatâ per C B proreniat
a a = X X, prO rectangulO A C B; hocque ex data proprictate
aquetur quadrato ex CD: erit a d = X X ∞ y y. Deinde, quo-
niam, linea CD perpendiculari existente super AB, quadratum
ex ED, per 47 Primi Elementorum Fuclidis, est aequale duo-
bus quadratis ex F C _ C D. erit quadratum ex F D ∞ X X L yV.
Ac proinde siin hac Cumma pro yr Tubrosetur a a - x X, habc
bitur quadratum ex F D ∞ aa, hoc CA, P D ∞ a. Id quod osten-
dic, rectis AF,. F. D, X F B lingulis iph a ae qualibus existenti-
buS, lineam AD B esse circulum, CujUS CenErUM F, ac idcirco
proprietarem allesatam cum circulo esse reciprocam. Ouod
iplum ee hoc modo cognolci potest. Adrertendo scilicet, utrum
proprictas propolita sine necessariâ subjecti inclusione demon-
Arari porsienecne. Si enim ea ab sque necestaria subjecti inclu-
sione demonstrari nequeat, proprietas erit reciproca; lin secuS,
proprietas communis.
EIc ad ceselsaum, num proprietas
haec cum criangulo rectangulo sic reci
proca, nimirum: eres angulos simul lum-
Peos aequales esse duobus rectis: adver-
tendum tantummodo est, utrum de-
monstracio illius criangulum rectangu-
lum praesupponat necne; ac proinde cum
ipla absque ulla discretione in quolibet
triangulo locum obcineat, concludendum
E. C 3
e
mo