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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 8, page id 1047377675:0024
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sed eriam demonsrrarum ele, nec esse maius, superticies ige
tur cylindriei recri super curva 7D cuius alcicudo e(c X,
aequalis esc mixrilineo P NL. H82, eciam quando cangens
7A recEa 78 ese perpendicularis, quod demonserandum
eraL.
Fix demonseratione manifeltum ese mixtilineu PHLFISL
e superticiem exlindricam super curra 79C. D esse quanci-
racesmagnieudine e grarieace anal09as, quoniam eadem
aequalicas quae demonseratur de inceoris, eodem modo de
monteratur de parcibus carum proporcionalibus; de ideo
earum cenera aequilibrii eodem modo diridune receam 28:
Ted ipla curra 7D ele magnitudine e gravitare ana loga
cum superticie cxlindrica; de ideo curra elc eriam magni
cudine e graricare analoga cum mixtilineo idem cumre
liguiscenerum habens aequilibrii in recea 2 8. perspicuum
quoque estmixcilineum PHL. FIS2 eAe ad rectansulum X. in
25, UE Curua 79CD ad recram 28.
P ROP.
3. T H F O R F M A.
IIdem potieis quae prius; supponatur praedicca (uperf.
 cies cylindrici recei super curra 79DC Cccari a plano
perrectam 2d transeunte, de in angulo lemirecro ad planum
Od2 inclinane. inferiorem superticiei cylindricae partem a
plano secram apellamus trunci superticiem. Dicotrunci su-
perticiem aequalem ese mixtilineo RSPVSZ. LUPPONAEUT CX
cendicurra 79C D in rectam sibi aequalem e  0 a, de iuna
acurrecra ax aequalisrecta L, uE compleAEUE rCCTANSU.
Jum Bx a R, quod necellario aequale esc eam (uperhiciei
exlindrici quam mixtilineo PNL. HS2. Sic R it aequalisre.
CTK 273 de a puncco  ducatur curra t   St calis NATUEX3
uc sumpea recta quacunque F Z Equalicurra particulae cui
cunque nempe 79. perpendicularis ad reCEaM R. A CK
DUMCTO Z in curram  St, nempC _ , AaF ae qualiS DErPeM
dli.