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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 503, page id 1815201908:0560
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6
P A R A B O L. A.
PROPOSITIODCCOXV.
InE A B C ellip(eoSares AC, BD; de Super A C minore ave, vedia
merro, descriprus lic circulus AIEC, quem in IY Secent linex F G, p2-
rallelae axi B O: junctisque punctis FTKE, ponantur F. L. normales ad axeM
BD, RancqueF, L, M xquales TTK.
DicoB, M, Mt puncta eAcad parabolam.
Demonstratio.
BOnancur TTN, ParalICla FL.: Xx P Cen-
rrum, sic commune circulo e elliphierie
igitur ve B F, ad H Fs siC FC ad FTO, id est
LF ad N R, e pertnucandove BV ad L F,
sICR F ad NB; quarEd HF dd NK, CA
ve BF ad TB, ec perrmucando DE BF ad
RF, Sic BF ad RN, _ BL est ad BF,
VEKN ad RN: SCd CADE R N adRN, SC
HK quadratum ad quadracum FIK, id est
perlirpocheuim ve MT. quadracum ad qua-
dearum MT; igicur re BT lincaad lineam
BP3 SIC MT quadracum ad quadracum
ML. quare B, M. MI puncta Cunc ad parabo.
lam.
PR OPOSITIO, CCCXYI.
Vper ABC ellip(eOS aXC A C qua-
Ddracum constieuatur AF, cuius
diaeFer C D OcCurEaE rectis
FG, HI, LK laceri AB paralle.
lis, in MI, N, O. Hac aurem AC
quadrato, aequale rectangulum
GFAS d AIguadraco aequale
rectangulum SHII, dein de qua-
draco AL. aquasc rectangulum
TAI.
DicoD, R, SsI puncta esse ad
Barabolami. . FIl aic
assumiur in propositione ellipsis; ob se-
quentes propositiones.
Demonstratio.
Tsde
2 Fctangulum R F C est ad Fectan-
guIUm SAT DE RF ad SHL; &
STII rectangulum est ad rectanou-
lum TKL ve S ET linca ad lincam F R: ivitur sc quadrata AC, AI, AL, id clt
Ot, D FL. DR, camincer le concineneracionem, quam lecta RL, dHL, ER. qua-
re D, R, S, Y puncta ead paFab ola (UNE.
2 292. bml 13
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10
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