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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
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Coroil.
eccd
olis
AZPERBO L A.
Demonstratio.
DOIcaPet C linea CF, hyperbolis occura
rac in C e F. purictisi ex quibus ordinarim
ponaneur linea CFT, TL: quonium BD diame.
cer in C bisfecta est e CR oppolicis occurrie
sectionibus, rectae HIC, FT ordlinacim ad com-
munem diamerrum BD a Policx x quales lunc:
quare _ TD, BFT quoque b xquales lunc: sed
ex typochesi rectae GD, C:P aequantur, aequa
lesiixicur lunc CI, C HI, undereliqua C C quo-
que reliquae C F aequalis cst.
Vocetur aurem punctum C centrum hyper-
bolarum: recto vero BD. C F carundem diame.
eri tranluerla qux in C cenrro bitariam divi-
duneur.
PROPOSITTO VI
Tinc ABCD parallelogrammi dia.
amerridux AB, CD, delcripeis aurem
super singulis parallelogrammi laceribus,
circulis, ferancur circa illos linea, AB,
CD, FOranEeS qUATUOE OpPOLICOS CO-
nOS quorum axes FO, III. FaCtAQ; Pet
axes sectione, parallelosrammum émer.
SaC, AC BD cui aequidistans tac lectio,
exhribens in conicis (uperkiciebus lineas
NOP, TVX, RLM, ORS.
Dicoillas essc hyperbolas.
Demonstratio.
beanc in balibus opposicorum conorum li
neaS NP, S, TX, RM quae (cum lectiones
illa x quidister parallelosrammo AB C C quod
eformacur sectione Facta per axes conorum op.
polirorum) aequidistane diametris AC, CB,
BD, D R: 3deoque e incer se: divisis igitur
AC. NP bitariam in Z X Y, duCaTuT LL, Pet
quam, vei de P verricem conorum planum du.
cacur, exhibebicillud eriangulum per axem, cu-
DLAnA NOP, TVX, RLM, ORS exti-
Enti jus lateribus, exera conum occurrene sectiones NOP, TV X: chyperbolx igitur
De _DP,FVX. Cmituet ocu hyperbolE XLM, OR 5.
PRC
aS