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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)
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culum e diameeri quadratum; huic obiectioni respondeos
posito circuli diamerro b, erit ipse circulus terminatio seriei
convergentis, cuins primitermini sunt b, b2, e secundi
Yqua
264
e proinde quadratum diameeri est ad
2 b2 f. v92b4
circulum ut b2 ad praedictam terminationem, quae torminario
nobis nullo modo est magis incornita quam radix sur desolida
numeri 40. dicune alii non bene esse demonstratum (in scholio
prop. 5) sectorem AB IP eundem esse cum terminatione seriei
conversentis, cuius primi cermini (unt crianculum ABP O
trapecium ABFP, D socundi rectilinea ABTP, ABDL P:
ex proinde plenam demonstrationem hic subiicio: si sector 
praedicta terminatio non sunt aequales, sir inter illas differen-
tia Z; er producatur series convereens donec termminorum
conversentium (nempe P e Q) differentia sit minor quam
Z euidens enim est (ex prop. 6.) hoc fieri posse; hisce positis,
patet cam sectorem quam seriei terminationem consistere inter
e
terminos P e ; e proinde quatuor sunt quantitates,
quarum maxima ex minima sunt P e Q intermediae au-
tem sector e terminatio seriei, erit que differentia intermedia-
rum nempe Z maior quam differentia extremarum, quod
est absurdum, nulla erso est differentia inter sectorem e serrei
terminationem, er proinde aequales sunt, quod demonstran-
dumerat. Alii obiiciunt contra prop. TT. ita; si addatur
23 termino 23 F a2 b (er, termino b 22 ++ b2 2, enerverur vis
utriusque demonstrationis; respondeo 23 esse quantiarem in-
defi-