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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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M A X F R I A R V M.
secundae ad terriam tories mulciplicet rationem prime ad secundam, quoties superst
cres conuexa hyperbolica inceriacens inter secundam ex terciam parallelam multi-
plex est superficiei concaua interiacentis inter primam es secundam. Pas. 611.
pr. 157.
Deduabus hyperbolis inter eosdem asymptotos sectis per parabolam. 611. pr. 158.
159. 160.
Duas praeterea, quae adhanc materiam spectant, sed locis suis excidere, vide 631.
pr. 189. 190.
Ostenditur quod hec materia vereat ad inventionem duarum mediarum proporciona-
lum.
S1q. in Schol.
De hyperbola inter asymptotos constituta, e secta per duas parabolas, quarum axes
sint asymproti, es vertex sit punctum concursus asymprocorum, ac in primis inue-
niuntur tres es quatuor continue proportionales.
614. pr. 163 164.
Ex puncto concursus eiusmodi parabolarum, ad a symptotos dimittantur duae parallela
habebuntureres superficies aequales, duae quae inter vnam parallelam, unam parabo-
lam Ss hyperbolam interiacent, alia quae duabus parabolis es hyperbola continetur.
616. pr. 166.
Icem aliae supersicres residuae ad paralleloerammum quod ex parallelis dictis, e asym-
peoco fic, aequantur inter se. aliae praeterea comparationes ficurarum a (sienantur. 616.
pr. 167. 168. 169. ∞48. 618. pr. 171. 172. 173.
P A R S SE Z F A.
Solutio variorum problematum, aliaque theoremata ad pleniorem
hyperbolae coenitionem spectantia.
atarum conuexarum hyperbolarum exhibetur ratio.
Elyperbola ad eandem applicatae diametrum, ex communem habentes diametru
transuersam, eandem habent inter se rationem, quam ordinatim posita ex eodem
puncto diametri.
Datarum hyperbolarum concauarum exhibeturratio.
Fyperbola communem habentes diametrum transuersam, habent ordinatim positas ex
eodem puncto proportionales.
Explicatur in quo consistat similicudo hyperbolarum.
Darae huperbolae similis exhibetur.
624. pr. 178. 179.
Dux hyperbola, diversae magnicudinis axem habentes reducuntur ad duas similes, ean-
dem diametrum habentes.
625. fr. 100.
Daris asymprocis exhibetur hyperbola, quae per datum inera asymptotos punctum tran-
seat.
625. pr. 181.
Datae hyperbola alia aequalis datur, cujus asymproti datum contineant anculum. 626.
pr. 182.
Problemata circa divisionem linea rectae, quae per hyperbolam absoluuntur. 627. pr. 183.
184. 185.
In omni cono sectiones hyperbolicae parallelae similes hyperbolas exhibent. Pac. 628.
pr. 186.
In parabola pars diametri à x ercice erusdem es concineence intercepta, aequalis est ills
4XH 2
linea
620. pr. 174.
621. pr. 175.
621. pr. 176.
622. pr. 177.
623. in Schol.