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# Title: [Vera Circuli Et Hyperbolae Quadratura] Vera Circvli Et Hyperbolæ Quadratura (shelfmark Leibn. Marg. 98)
# Folio 52, page id 834940469:0136
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circa dLCH Tocacionis PK, ese quancieaces magnicudine
prouicare analogas, quoniam eadem proxortio qua demo
Aratur esse incer eocas, eodem modo demonstracur ese ins
cerparces carum proporrionales.
P R O P. 25. EH F O A E M A.
Fisdem positis, supponendo anculum inclinationis, Plani secantis
cum base cylindrici (Riopus est) producta, esse semirectum: Dico
quadratum semidiametri circuli aequalis superticiei (olidi rotun
di duplum esse suxerficiei rrunci.
Sc enim ex praecedente, re alcicudo cxlindrici ad circu
La Ferenciam circuli cuius lemidiamerer est radius Focan
cionis, ita superticies crunci ad superticiem Colidirorundi.
in hoc aucem calu, quando angulus inclinacionis e lemire.
etus, alticudo cxlindrici est ae qualis radio rocationis; e ideo
in nostro casu, ve semidiamecer ad Cui circumferenciam, ica
superticies crunci ad superticiem Colidi rocundi; re aucem
Temidiamerer ad circumterenciam ica Pemissis quadrari le-
midiametri ad circulum; de ideo re lemissis quodraci Pemi-
diamerri ad circulum, ita superticies rrunei ad superticiem
Folidi rocundi; de conuercendo d permutando, circulus est
ad superticiem Colidi rocundi ve lemissis quadraci lemidii
metri ad superticiem erunci; se d circulus lupponitur xqua-
lis superticici solidi rocundi; ec igicur Pemiltis quadeaci lemi.
diamerri illius circuli aequalis ett superticieierunci; de ideo
quadracum Cemidiamerri elt duplum superticiei eruei, quod
demonstranaum erac.
Duxe praecedences proposiciones eodem prorsus modo
demonstrantur de superticiebus rorundis genieis Cxroca
tione rnius vel plurium linearum quarumcunque sive recta-
rum curuarum vel mixtarum, Rsuram non claudencium 5
semper enim ad supexkicies ey lindrisi recti super linca vel li.
neis