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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 111, page id 1047377675:0127
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FIL
ad. consideratis considerandis demonstracio non dittert
ab huiu556.
PROP. 62. ZHEORF M A.
Ildem suppolicis exlindricis, qui in ancecedence; lc d
L cum alcicudine BF, de suppotiro cylindricum Cuper II
AEFH secari a plano ipsi bali seminormali ee cam secance in
recta AII: dico parallelopipedum super ABF F esse ad inte-
riorem eruncum cylindrici superHIAEFE in racione 2Q = L
ad9. Sic primo Pminor quam 9. lirque re AB ad C C ita B
Dad DRprorractam verlus A E, d compleatur quadeueum
ABFO ex parre A tis icem ex omnibus punctis R imaginctur
curua BRO: Pacet ex constructione rationem BD adDR eNC
mulciplicatam racionis BD adB Finracione P ad G, de diui-
dendor ratio DR ad B F, nemperatio D R ad FO, estmulei.
plicataracionis BD 2d BFin racione O= P 2dC, d ideo qua
dracum NB FO est ad Aiguram BR O Finracione 2 Q= P ad huiuss
B AEVEABFE ad NBFO ica EF seu AB ad OF sCu BF, _ id eo
rectansulum ABFF est ad figuram BROFinratione compo-
lica exratione 28 P ad O ee exracione AB ad BF. Ouoniam
eA VE AB ad CC It2 BD ad D R, eric rectangulum AB in DR
aequale recrensulo BD in C6, ac reccansulum aB in DR CA
communis incerleccio crlindricirecri super BROF alcicudi-
nem habensis AB cum plano secance super R D ad basem
normali, ee recrangulum BD in C C est incerseccio eiuldem
prioris plani producci cum erunco inferiore cxlindrici super
ATAEFM; cumque hae incerlectiones semper coneingant ellé
aequales manitestum est inferiorem eruncum cxlindrici su
DeAHIAEEH equalem esse cylindrico super B R OF alcicudi.
nem hrabenci AB; et ideo parallelopipedum super ABF F
cum alcicudine AB cC ad cxlindricum (uper BROF scu EruM-
cum inferiorem exlindrici luper IIAEFH ve balis AB FF ad
batem BHOF, hOCCH in PationS CompOHICAEX FaFIONE Z
E