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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1049, page id 1815201908:1106
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SPH AROTDLd.
e R OPOSLTIOBAKVII
Aeae sectioni in spharoide alceram
in eodem aequalem constiruere,
quae datxe ellipsi sic similis, habenci inter
luosaxes non maioremrationem quam
axesinter se habeane lectionis per axem
spheroidis.
Constructio ex demonstratio.
lem oporreac exhibere e similem dacaD.
hac per praecedencem guxdam sectio per cen-
crum spheroideos BFC Similis D. Deinde
Aac a FIIK sectio parallela BF Cnque adiplam
FF C sectionem eam habeac rarionem quam
ABC ad sectionem candem P. F G, crieque
pertectum problema ve per semanifectum est.
PROPOSITIO CZXVIII.
D datum punctum in sphaeroidis
Lsuperticie concingens planum po.
RetE.
Constructio e demonscratio.
deos AB C, ad quod oporreat planum ad-
ponere quod sphaeroides concingat. invento
baxC C B, agatUT per C B, _ A punctum pla-
num ABC, perque ca quae libro de ellips do-
CniuS, POnAEuE AD in planO AB C, con
cingens sectionem in A, crecta denigue AF
normali ex A ad rectam AD, qua OCCUTrAE
axiin F. AaC Per AD planum rectum ad se-
ctionem ABC. Dico illud sphaeroides con-
tingere in A. Ouoniam F A linea recta est
ad D A, e simul ex constructione planum
Per AD rectum ad planum AB C, isicur et
iam R A recta eA ad planum per AD posi
cum. Cum igicur linea F A breuissima AC
octensac ad ellipsim AB C, _ limul breuim-
ma ad planum orchogonum per AD, necet-
Pario planu per AD normalicer planO ABC
in sistens, concinsic sphaeroides in A erBOPYG.
Ricimus quod Eueracre quilium.
P)Aca lic sectio in sphaeroide AB C cui xequa
Ie A punctum darum in supersicie spharoi-
2E
t. ho
B. Bai
C232 ellips.
    e tie p  pi   t e e s      t   pu .     u                 e  n   p   u