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# Title: [Geometriae Pars Universalis, Inserviens Quantitatum Curvarum transmutationi & mensurae] Geometriæ Pars Vniversalis, Inserviens Quantitatum Curvarum transmutationi & mensuræ (shelfmark Ms IV, 377a)
# Folio 117, page id 1047377675:0133
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1047377675&page=133
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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 0.86
# 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.
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# After the first blank line: the recognised lines in reading order, one per line.

pi
ve Dsi  2d C; eodemq: modo arcus RL CC ad AveM ABUTH
AE CuOLUEA DE Ps CE ad C _ idcOvcarCUS BC ad rectum PL
ita arcus Ce ad axem Egurae AE cuolura, de permurando, re
arcuS BC ad arcum L B iEA reCCA FI ad axem AgurA AF cvo
luca, ae racioarcus BC ad ArcuM LP eA Compolica ex ratione
arCHS BC adBID de ex ratianc arcus BD ad arcum L F scureCtE
CA ad rect EEA, Se ideo recta FI CH ad aXem AGurE AB evOlU.
te inrarione copoliea exracione arcus BC ad AECUM BD SE CX
racione rectae C A ad rectam F A; Ced rariO C A ad F A eAt imul.
ciplicara rarionis BC ad BD in racione P ad O, de conuerten-
dos componendo de rursus converrendo, racio AC. ad AB Peu
IXadCHIeA malciplicata illiusracionis (quae componieur
exracione arcus BC ad arcum BD de ex racione recte C A ad
reCtaM E. A) nempe rarionis rectae llad axem AgUTE AE CuO-
lurae in racione P adP. 2. Sed rarioTK ad G: FI est mulcipli.
Cata rationis FI ad FCin racione P ad P O; a proinde F. C
esaxiS ASurA AF cuolutaes Puncque FA, CiHI, aequales; e idco
(cum hoc semper Hac) manifectum est ex huius r4 e eius
consectario Aguram FFIKI eNC Aguram AE C crolucam, quod
demonctran dum eraE.
Figura FITKI est illa descripea in huius 5 q, cumque pore-
ric inreniriresta illam cangens in puncto dato ope huius 73
porerie quoque (exconfectario huius 18) recta duci spira-
lem AEC. tansens in puncco daco: Caepisime criam (VEDaTCE
ex hViuS 58) inveNIEUFRECEA aequAIIS CUEVA FHIK, quae eciam
aequalis eA spirali CurVa AFC.
Ope huius +5 vel 26 nullo negorio probatur secrorem
BAC esse ad spacium spirale AEC UC 2P F Pad.
P R O P. 65. F IZ F O R E M A.
Ic circuli secror C AB includens spiralem AF C caliSMAS
cura, ve (ducrrecta quacunque AF producta arcum le.
CanECin D) rasiO D ad BA SC mulsiplISaTA raTiONISC. D ac