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# Title: [Vera Circuli Et Hyperbolae Quadratura] Vera Circvli Et Hyperbolæ Quadratura (shelfmark Leibn. Marg. 98)
# Folio 15, page id 834940469:0029
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PROP VIII PROBLEMA.
Sint dua quantitares data A. B, ex ratio quaelibet data C ad D:
oxertet invenire aliam quantitatem, ut ratio eins
ad A sit multiplicatarationis Bad A im
ratione C a L.
Tr primo ratio C ad D commen-
a Curabilis, seque inTer C QED
FDC. Atis
communis mensura Fis eEquories F. Continetur in D cories sIE
rario Fad A lubmulciplicaca rarionis B ad A; _ quories. P
continetur in C tories sicracio ( ad A mulciplieaea rarionis
Fad A: dico C esse quancicarem illam quaesicam. racio C ad
2d a es mulciplicaca rarionis Fad A in rationCC adF, XCP2-
eio F ad. R estmulciplicaca rationis B ad A in rarione P ad. I;
eisitur ex aequalitare, racio C ad A est mulciplicara ratio-
nisB ad A in rarione C ad D, quod demonstrare oporruit.
Onodhrario C ad D sic incommensurabilis, geomerri-
Cam huius problemacis praxem esse impossibilem mihi per-
Juadeo; approximationecamen hieriporest, alsumendo ra-
tionem commenturabilem eius loco, quae quam proxime ad
illam accedat.
Sit Ceries conversens, cuius
primi termini convergentes
TInEA, B, Secundi C, V TerEII F,
: Tinrque secundi cermini ica
Facti a primis, veracio B maio-
ris ad Aminorem sc mulcipli
cararationis Cad A inratione dara maioris inaequalicatis
Mad NI. de veratio B ad A Eic mulciplicaca rarionis D ad A in
ratione daca maioris inxequalicaris M ad O: AnEG: FerEI; EeT
minieodem modo facti ex secundis quo secundi facti lune
Exprimis; deque ica concinuecur leries.
ti