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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 658, page id 1815201908:0715
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DROPOSTTIO CCXLII.
Aca sc parabola ABC, et eiusdem alcicudinis hyperbola A DE,
habenres communem arem AF, ad quem ordinarim polirx sinc
B, FD
AIY PE R BOL A.
Dico quadraca BFs. Ltur cumpla producere hyperbolam.
LXCOn
bLX29
buius.
rab
Demonstralto.
rsacor. DOnatuT ex A linea AG OCCurrenS F D lineis in C C,  A C paraIICIAFH, ve
LFCIT rectansula aequalia sinc quadracis F.D: Parec: HFL eAe in directum. Rane
icerum F B quadracis a qualia rectangula GFP: conat qusque IY eNc rectam
lincam. deinde IK rectae aquales tiane F. C; patel u RK elle rectam lincam, re-
aangula igitur IX F aequalia sunc quadraris BF. _ IK L H rectangula aequalia
quadracis fi D. ondc IK HIrecangula aquancur quadialus BP. LD. liaucemIKII.
perbolam. uouctaedemerandum.
rectangulis aequalia ponancur quadraca RI, puncta KL I ad hyperbolum lunc, igi
cur ( B F, F D quaclacis a Guatia Pertanul suacaca, paret illa quoque ello adhy.
Onacurellipleos axis maior AB, Cs CentoD, potitis quoruis diame
ErIS DE, hanE F F PAallela DC diametro coniugaca AB: e Ranc
Dico CG eAc ad casdem Hy perbolam cuius cenerum D.
Demonstratio.
PROPOSITIO CCXLIII.
Glane rectis FC aqualeS FK
describatur circulus luper
axc AB, _ PerhciaC
quadra
cum NFI, cricicaque rectangu
lum IF L ad IRL,
rellansa
lum quemadmodum cstc rectan-
sulum 2FP ad O R P, rectan.
eulum hoc estrequadratum FL
2d F F. quadracum. vnde re est
FF quadracum ad quadratum
FF, ica smilicer est ET GHI re-
aangulum ad rectangulu FTON
cum ex constructione DF An
quales L LL VEL X H, et alCeL
QuadTaTUM
aquales F C Vel FK, _ DI
rectis DL, a Guales P, FC.
ut   ss  ee e  pe es et et t e et  et e e e t e  t  e  e    s. t  e se s  s e e  te e e  te e e t e e   s ti  e  e t te et  s ltt