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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 51, page id 1047377675:0067
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it
C
A
PXOP. 24. THFOAPMA
.
Eildem positis, quae in antecedente: superficies trunci erit ad super
ficiem soliditorundi orti ex ejus baserotata circa communem (e-
etionem baseos siopus est) productaees plani secantis, et altitua
docylindrici d circumferentiam circuli cuius (imidiameter est
paratio int eadem sicur in ancecedentes did
co supcenciem erunciR ODC esse ad superticiem solidi
rocundi orti en LOEDEIONE AGUrR DE FC CIFCA TK AXCM FOCA-
tionis, et oP alcicudo cylindrici ad circumferentiam circuli
edus lemidiamrecer estradius roracionis L. P. in anteceden-
ce demonutoum est OP esse ad circumterenciam circuli cu.
justemidiumeler PL., ve IIE ad circumferentium circuli cu-
jus lemidiaer FV: acque haec proporcio eodem modo
deonstracur de omnibus rectis in superhcierrunciR ODC
ed darem BL FC perpendicularibus, ad omnes circumteren.
cias circulorum ab earum punctis intimis in circumrocacio.
ne descriptasi atque ex omnibus illis rectis condatur ipsa su-
perticies trunci, e ex omnibus circumterenciis circulorum
ab intimis rectarum punctis seu a baseos ambiru descripeis.
consarur superticies Colidi rocundi orri ex rotatione baleos
circa exem IK; ee ideo verna ancecedencium ad vnam con-
lequencium, nempe OP alcicudo crlindrici ad circumteren.
tium circuli cuius lemediamerer elt LP radiusrocationis, ica
omnes ancecedentes, hoc est, luperticies crunci RQDC, ad
omnes conlequentess hoc est, luperticiem Colidi rorundi or-
ei exrocatione ba(eos DEFC circa axem rotarionis IK, quod
erac demonstrandum. Hoc eriam cheorema demonstrarur
eodem modo de rrunco superiore s Agura AB conCiPIATUE
rocari circa rectam MII.
Pacet ex demonstracione superticiem trunci RD C de
superticiem Colidirorundi orri exrocarione baleOs D E FC
CITCa
radiusrocationis.
SUra _ pE