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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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2
ius
ersqualesecta FO, IH; cumque hoc semperhnr in om-
nibus punctis curux ellipricx MCR, manitepum cA ex huius
3 Teomencum hrpertiolicum AC IdR M esse xquale FuPerR.
cieierunci super curua elsiprica M CR lcAx plonoper recta
Mcronscunte, se in ansulo semirecto cum hase erunci in-
clinante; ec igitur cum quadracum rectae X sic duplum super-
hcicierunci, eric X radius circuli aequalis superticiei sphaeroi
dis lacx genitx exrocatione curux cllipeica MC R CIrCA aXE
BR, quod demonstranduM CTAE.
PROP. 49. PROBLEMA:
Invenire circulum aequalem suverficiei conoidis byperbolica.
Tcconoishyperbolica geniea ex reuolurione lemihyper-
a bola FST circaaxem LS, cuius superticiei oporret inve-
nirc aequalem circulum. In vertice Fhyperbolam rangac re.
eta FFI aequalis semisi lacerisrecti. Deinde describaturhy-
perbola crantions punctum HI, idem habens cenerum nempe
Idec eundem semiaxem coiugatum nempe DF cum hyper-
bolapropolca LST; Erque hyperbola descripes BHIR ordi-
nacim applicatom ST productam secans in R; de Pcomento
hyperbolico FHRS Aacaequale quadrarum, cuius diameter
Ridico X esse radium circulia qualis superticiei conoidis hy.
perbolicae propolica. Sic hyperbola propolicae a(ymptoca
DV, rectom FH productam secans in R, licque hyperbolae
invencae a(yMpEOcA D Y, F H eriam productam secans in C3
e producacurrecta D HI. Ex quoliber hyperbolae propolira
puncto Laxi applicetur ordinacim recta JC, quae produc
rectas DF, DV, D Y, incerlecet in punctis 2, O, L, de hyper.
bolam invencam in puncto P; licque e A aequalis rectae CZ)
manifectum est (ex Fran. a Schoccen commeneariis in Cor-
celium pa8. 216.) iunctam rectam OA tangentem hyperbo.
dam in puncto AnormaliEer (CCALC. Guoniam reca F.K hyPEx=
Bola