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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 20, page id 1047377675:0036
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2
SIC nacurX uE duCTA YN quae cunque AO reccae perpendicud
laris aequiraleat porencia urrique IL, IM; cric recransulum
MIKaquale mixrilineo IA FL: Rnon AFica ducatur curra
AVY calis nacurae uc rectangulum M IV Aac aequale mixtili
neo IA FL, e demonstrabitur secundum cenorem huius
propolicionis rectas (qua curras AX, AG cangunt in pun
etis V _K) Cse incer se parallelas, quod est absurdum conz
era propolicionem praecedentem.
Hluius eriam propolicionis rarii sune casus, (ed hocincel
decto, in reliquis nulla rectat ditticuleas.
PROP.
7. PROBLEMA.
Rectam ducere datam curvam tangentem in ejus puncto dato
s modo curva sit ex earum numero, quas C arte siuts
appellat Ceometricas.
IEcurra BHI C hyperbolas cuius diameter recta AK _
ordinacim applicaca FHI, IEC, calis naturae, uc Colidum
ex quadroco a B E in AF sC ad solidum ex quadraco a BI i
AK AE cubUS AB F II ad cubum AKC. Sit AB daCa a BF b, ee
rario solidi ex quadraco a BE: in AF ad cubum ab FFI uE a3 a0
c3: Oporcet invenire punctum F, re ductarecta FHhyperbo
lam eang ae in pucto HI. ex dacis AB, BE, dacUT AF arFb _E PTB
VC (ab 2c3rk b3C3). SiEF FZ _ D L nihil leu PeruMO; et
proinde erie BDb -08C A D a rf. b - 0,F D Z -0it CM DC VC
C3 a b2 = 2c3 a b0 rta c3 a02 fC, b3 - 3c3b20  3C3b02 (303)0
quoniam supponimus ordinacim applicaram DC incidere
in curram in eodem puncto C vbirecta FH eidem (simodo
Domibile HC) Curra OcCUErIE CrIE UEFHI ad EF ita DC ad DF;
e ideo rectangulum ex D F. in E FLnEMPC VC (b2C3 a23-