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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 15, page id 1047377675:0031
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1047377675&page=31
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 56 lines, status machine
# Lines: 56 recognised, mean confidence 0.79
# 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.

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erunci, sed differeneia inter reccilineum inPeriprum ee cir-
cum lcriptum minor est quantitare x ex suppolirione; d ideo
differentia incer superticiem erunci ee figuram mixcilincam
muleominor est quam a, quoniam earum urraris demonstra
cur maior reccilineo inlcripeo ec minor circum scripron quod
hieri non pocele, bonicur enim x difterencia incer superte.
ciem erunci de mixcilineum; nulla igitur ele differentia incer
Eguram mixtilineam ee superticiem erunci, ee proinde lunt
aquales, quod demonstrandum exae.
eildem poliris, Remixcilineum V Y BD2 3E talis naturae,
UEs a quolibet puncto currae FO nempe C ducta parallella
rectxe LEnempe C2, incercepea recta B 2 incer duas curras
VD, DE. Hac aequalis cangenticurram proxolicam in puncto
EPEOEFACEA ad reCEam A D, nempe receX Cu. dico mixei-
lineum VXBD23E aquale esse superficicirrunci superio-
ris ciuldem prioris cylindrici polica ejus alcitudine recra
AV. FECLE M Cu in punCEO O RE rectanormaliS C7 reCtam
R V secans in puncto7. ob similicudinem criangulorum S7)
GKII _E GS ad C7 ita GK ad OFT, _ VE OK ad OTTITASV ad
GM rel SB, _ SR ad Ouu rel BZ; de id co CS est ad G7 uERV
ad Se eodem modo demonstrari pocelt IT eNe ad lB uERV
ad T3: cum que hoc hac in omnibus punctis currae E O, mani-
Fectum eA ex huius 2 mixcilineum R D 2 ZEV esse aequale su-
perticiei cxlindricirectiinAistenei currae EO, cuius alcicudo
RV; acque luperkicies crunci interioris xe qualis est mixcilineo
RV YBD, e proinde sperticies crunci superioris equalis
est mixtilineo DBYVE 32D, quod demonstrare opor-
cuit.
Elinc eriam manifectum est superficiem crunci inferioris
de mixtilineum RV XBD ehe quancicoces magnirudine
de sraritace analogas, quoniam endem aequalicas quae de
monltratur de inccoriss eodem modo demonstratur de par
cibus earum proporcionalibus. Manifectum quoque elt lu
verticiem erunci superioris e minsilineum V XBVZ3E elle
quam