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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 12, page id 1047377675:0028
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e 2
Ted excelsus mixtilinei maioris Xk o Z Se a R supra mixrili.
neum minusRSTVsZ eAtminor dicco excelsu reccilinco
rum, quoniam mixtilincum maius estminus receilinco na-
iore ee mixeilineum minus est maius rectilineo minore; de
ideo excessus mixcilinei maioris supra minus minor est di-
etis receangulis limul Tubloco excelsu reccilinei RESNTudE
suprarectilineum ti  o u 58_ R; sed dicca recrangula
Simul, exhypochesi, minora lunc quam a; de ideo dictare
ccongula simul sublaco dicro excessu muleo minora lunE
quam a; e proinde mixrilineum maius excedie minus mul-
tominore exce lsu quam ae, quod est ab surdum, ponitur enim
a excessus mixcilinei maioris supra minus; non elcergomix-
cilineum fF o 2 st a R maius mixcilineo RSTVSZ, Ced de:
monstrarum es eriam nec esse minus; sunc igitur mixrilinca
 o  St AR, RSTVS2, incer sC aequalia, quod demonstran-
dum CraE.
Sune eriam alii huiuscheorematis caTus, quibus omnibus
pores opplicari haec secunda demonstrario; volui tamen
priorem ceiam adhibere, quoniam mihi apparer simplicior.
etiamsi non Acgeneralis; lectorem tamen admoneo illam
priorem poreodhibere in calu maxime ordinario, nempein
Aicuris prioribus, reliquis manencibus dum curra RV in
prooressu ab R ad V magisa recta 2 d elongaeur.
Fx demonstrarione manifectum est mixrilineum RSTVSZ
ee superficiem crunci esse quancicares magnicudine de gravi.
eacc analosas, quoniam endem aequalicas quae demonstra.
cur in inceoris, eodécciam modo demonstracur in parribus
carum proporcionalibus; de id eo earum cenrra aequilibrii eo-
dem modo dividune rectam d2.
Nonexitimo opus esse Lectorem admonere, quod data
haerna trunci superficie, deneur omnes alixe, quorum plana
secantia, balem (A opus est) producte in eadem recta secant,
cales enim cruncorum superticies incer se lune uc carum al-
cicudines, vel ur rangentes inclinationum planorum secan
ciuI