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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 90, page id 1047377675:0106
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quadrarum recra X he duplum superticici trunci erie X r4
dius circulixequalis superticiei sphaeroidis genica arocario
ne curue FFT circa axem F.F, quod demonstrare oportuie.
Hinc eciam parer quod superticies spharoidis sic magni
cudine e graricare analoga cum lesmento elliprico. L D F
RT, idem enim quod demonstratur de inceoris, non dissimile
methodo demonstratur de parribus carum proporcionalibus
v. 8. Codem modo demonstratur superticies genita ex rota-
tione curua P N aequalis circulo cuius radiiquadracum du
plum est CcemenciellipriciFRPO, quo demonstrata est prx
lens propolicio; quod eriam in cribus lequentibus est intel
ligendum, cum eadem sic rario huIuS de ilLaRUI,ME CNIM
eader eadem lemperreperere.
DROP. 48. PROBLEMA.
invenire circulum aequalem superficiei spharoidis lata.
Ic sphaerois laca genita ex rocatione Pemiellip(eosMC
Rcircaaxem breviorem MR, cuius Cuperticiei oxortee
invenire aequalem circulum. In verricibus M, R, ciliplem
tansane rectae MA, RD, aequales lemissilaceris recti. Dein-
de cenero P, verrice C, per puncta A, D, ducarur hyperbola
ACD, _ Legmenco hyperbolico ACDRMhac aequale qua
dracum cuius diameter recta X. dico X esse radium circuli
aequalis superticiei sphaeroidis laex propolire. Sic hyperbola
alymproca PF rectam DR sccanS in L, licque hyperbolam
tangens in verrice recta BC. C, d IUINBAnEuF TCCtX PD, PC.
ex quolibec ellipseos puncto I in axem MR Sic perpendicula
ris IO rectASCC, PD, PF, PC incerlecans in punctis II h
O Licem hyperbolam incerlecans in E. Sic recta CN ae qua
lisrectae OKi manifectum eA (ex commenearius Franci(c. a
Scorrenin Carrelium Pa8. 214) rectam HI elliplemtansen
rem in puncto lnormalirer secore. quoniam PF est hyperbo
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