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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 100, page id 1047377675:0116
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25
jus4 lemihyperbolam BKL. eNe aequalem superAciei trunct
supercurua parabolica DB I sectx a plano perreccam DB
transeunee e in angulo semirecto cum balc erunci inclinan.
ec; e ideo, cum quacrarum recea X sic duplum superticiei
trunci eric Xradius circuli aequalis superficiei genitx aro
huius carione curuxe parabolicx cirea rectam D B, quod demon
Arandum Crac.
Fx hac propolitione pater Pemihy perbolam DKL. eNe ma-
enicudine ee granicare analosam cum Cuperticici: ex haC,
ancecedente e huius 38 non difticile est invenire centrum
Gravicacis curux parabolicx rel eius portionis cuinscunque
datae, guod admonnisse CuHciaE.
PROP. 53. PROBLEMA.
Invenire centrum gravitaris semicylindri recti oblique secti.
IE circulus BC OOcylindribasis, cuius diamerer B,
a lirque recta B A circulum eangens in A semicrsindriat
sicudoxequalis rectae BC, perinde enim elt cum omnes Pemi
cylindri luper eadem balc unc analogi, quae producarurad
parces Bindehnire, sicque ei parallela ee indetinire longa
recta PE; AAnECTIAM AP, CR, DT, parallela dimetroB)
ee dueotur AZ recta reliquis le habencibus ve in Agura. Sit
Sigura CRM ealis nacura, ve (dueta rect a quaCUnque EYKMI
paralLela rectae PC) FY SE Ad FY DE OT ad RM: ABUTa CRM
eM analoga maenieudine et gravicare Cemicylindro; acque
huius fipura scu semierlindri cenerum aequilibrii ita invent
EUT: AnEC R, RS aequeles reliquis se habencibus re in figu
ranhacque tigura DOT ealis nacurae, re (ducta recta quacun-
que F XKMNC) EY HE AAKL VEK Mad NO; de Agura DOI
circum scribatur rectansulum DV: sic deinde re figura CRM
ad siguFAM DO T ita F. Y sCu R C ad C Z, manifectum est ex
hnius 37Q eAC CBMrum aguilibrii ABUrX C. M Ri ABurA AII
EC