# Leibniz Legible — https://leibnizlegible.com
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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 57, page id 1047377675:0073
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1047377675&page=73
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 39 lines, status machine
# Lines: 39 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.
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# After the first blank line: the recognised lines in reading order, one per line.

51
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FGuex XYL cirCA axEM VSInPATIONO COMPORCA; ex PFOPOPA
tione suverficiei eronci inferioris 34 C D ad superhciemerui
ei inferioris 567 Y X2 e ex proportioneradiirocacionis F L.
ad radium rocacionis Ter, quod demonstrandum erat.
HIoc Theorema ctiam locum habee eodemque modo de
monstratur in supertciebus rorundis genitis a rotatione li-
nex vellinearum quarum cunque tiguram non comprehen.
dencium.
P RO P. 29. Y HI E O R F M A.
Si super qualibet sicura circa axem intelligatur exlindricus rectus.
ita sectus a plano in duos truncos, ve planum per oppositarum cy
lindrici bascum axes ductum, siat plano secanti normale: truncus
onus erit ad truncum alterum reciproce, ut partes radiirotatio.
nis resecta a centro eranitatis ficura.
Vver qualibet ABUFR L RM cirCL LXeM K N sic cplindri-
a CUS RECtUS ABDMLK sECtUS IN ErUNCOS ABDZYZ, ZYZ
XLM, 3plANO E TV C ad planuM ACNK, per oppolicarum
exlindrici balium axes AC, RN, ductum, normali: AINEP, O,
cenera gravicacis balium oppolicarum, quae iunsantur recta
PO. Producatur planum (ecanSi dOnCCAXES AC, RN (A OpuS
eA) productos incersecet in punctis F,S; de in co(dem axes
(E OpuS CH) produstos line perpendiculares FL, SO; mani.
Feccum eA FIS Desse Parallellogrammum rectangulum, icem
FPesse cylindricialcicudinem, ee IS rotationis radium, quip.
Dead incerfectionem plani secancis ec ba (cos L. RE MI nemDC
rectam TV es perpendicularis, quoniam ducieur in plano F
2ST, quod verique plano ee sccanci dc b2 (c05 L. ICM est nOr.
male. Dico eruncum ABDZ Y Z eNC ad cruncum 2 YL
MLK re reciproce IO ad 05. amediis punctis rectarum
FI, IS, nempe H, R, ducantur rectA HIS, RF, necnon
TR sCCANS O P in X; crune icaque inter se Parallella d
aequa