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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1045, page id 1815201908:1102
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SP HI AE R O IDF 3.
e ROPOSIFFO CXVII
Aci Sphaeroidisaxem exhibere.
Constructio es demonstratio.
IE sphaeroides ABC, cuiuS AXEM OPOE-
Dcear exhibere. Aac sectio quaecunque
E. DB. cric ea a aue circulus, aue ellipAS. In-
vento huius sectionis axe F B, per R B, AaC
sectio AB C ad angulos rectos sectioniFDB.
eric ea rursus ellipsis. Inueniatur denique se-
ctionis ABC axis AC. DiCOA C aXeM
quoque Fore spheroideos. cum enim sectio
ABC ad angulosrectos consticura sic lectio.
ni F D B cran(ICNS PeF aXCM F B, eric b in
plano AB C axis spheroidis, ac proinde
ABC elliplis eric Facta peraxem à qua sphe-
roides Formacum elt; axis orvo cAt A C spha-
roideos ABC. Duod crar demonstrandum.
PROPOSTTIO CXIZ.
Aci Sphaeroideos cenerum altisnare.
Constructro e demonstratio.
Nuentus axis AC diuidacur bifariam in F. DicoF, punctum eNe guxesitum, est
enim hoc ipsum cenerum ellipseos ex qua sphxeroides Formarum est per quodom-
nis linea in sphiaroide polica bisecaTur.
PROPOSITIO CLL.
ainislectto per cenetum crantsens
oblique ad axem, elliplin exhibee
dissimilem illi gux per axem facta est.
Demonstratio.
Arcuto ABC per ceneru sphaeroideosD ob-
ligua ad aRcm. DicoA BC MHe cllipum disti-
milem P FC sectioni quxe Facta est per axem
Duod aucem limilis non ie Caca lec
Duod ABC Sic ellipSIS PATCE CX IFZ. huiuS.
amibo recta sune plano F FG, erie per 19.
ondecimi communis corum sectio BD recta
planOF FC, ac proinde pex detin. Z. H1. eriam
ABC sectioni F F C sive FB C, Sc ostendo.
Tc B F C sectio per axem sphaeroideos recta
plano AB C Cheri enim id PorcHt peF 11O.) PeF
cenerum aurem hac sectio HIB L ad axem F. C
recta, (per 18. undecimi eriam recta erit plano
FF C) Faciens cum plano AB C communem
sectionem BD: cum plano aucem R F C+ TC.
etione D F. quoniam igicur planA ITBF, ABC
104
X13. huitos
BColligirur
pXI
recta
a ooeao