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# Title: [Vera Circuli Et Hyperbolae Quadratura] Vera Circvli Et Hyperbolæ Quadratura (shelfmark Leibn. Marg. 98)
# Folio 90, page id 834940469:0174
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quad LCCC_ X AE duplum suxerheiei crunci exie Xra
dius circuli aequalis superticiei sphaeroidis genita aroratio
RE CUrHEFFT circa axem FY, quod demonstrare oportuic.
Ilinc ceiam paret quod superticies sphaeroidis sc magni.
cudine se craricace analoga cum leomeneo elliprico F D Fo
RP, idem enim quod demonaratur de inceoris, non dictimile
mechodo demonttratur de parcibus carum proportiomalibus
v.9. eodem modo demonstratur superticies genita exroca-
tione curuae FN aequalis circulo cuius ractii quadracum dun
Dlum est Pcemenci clliprici FkPO, quo demonstrata est prae;
lens propotirio; quod criam in cribus lequencibus est incel-
ligendum, cum eadem sic racio huius ee illarum, me enim
ex dec cadem (eMperrepeTerE.
PROP. 48. PROBLEMA.
inmenire circulum aequalem (aperficiei spharoidis latae
Ic sphaeroislaea genica ex rocarione FemiellipleosM C
Rcirca axem breniorem M R cuius superticiei oportee
ainvenire aequalem circulum. In verricibus M, R, elliplem
eangane recta MA, RD, aequales lemith laceris recti. Dein-
de centro P, verrice C, per puncta A, Cd, ducarur hyperbola
ACD, de Seomenco hyperbolico ACDRM AAC ae quale qua-
dracum cuius diamerer recta X. dicoz esse radium circuli
aequalis superticiei sphaeroidislaca propolice. Sic hyperbolae
alymptota PF rectam DR sccans in F, Scque hyperbolam
cangens in verrice recta B C C, Q iVBSANCUF RCCAX FD, PC70
ex quoliberellipseos puncto l in onem MR sic perpendicula
ris IO rectasC C PD, PF, PC interlecans in punctis FB Kd
OLicem hyperbolam incerlecans in E. Sic recta CN aequa
lisrectae DIE; manifecstum est (ex commentarius Firancilc. a
Scorten in Carrelium p28. 224) rectam NI ellipsem cangen.
tem in punctol normaliter (CCorC. Quoniam PF eAhyPerbO
1∞