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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1046, page id 1815201908:1103
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1046
B PHI A R O IVL S
ans hulus. recta ad AC, qux axisa cA sectionis AB C. ergo BD alcer axis eA sectionis ABC.
IHe.
Smilicer perspicuum cAt F D, D F axes Cu CIlipleos PF C. quoniam vero HBY
Bur. hu. b circulus eAt, aequales sunc D F, D B. hispositis propolicum ica concluditursmon est
axis F.D 2d axem D F, vraxis AD adazem D B, hoc eAt DF. Duodcamen iuxra
definicionem z. requiricur ad elliplum Cindilirudinem.
Corouur.
Spharoideherum, edelectio per axem minorem minima.
Demonstratio.
Ineduo axes pheroideos AB, C D et sectio
Per illos Facta exhibeac cllipum ACBD.
Dreo illam elle Maximam omnium sectionum
quae in sphaeroide heri postunt. Prigatur HIF
normalicer ad planum AC B. Deinde PeF
quamlibet lineam ITF in plano ACB, 8
AMCaM LL Rectio Ponacur L. FC. Dico illam
eAC mHIOrem plano ACB. Per rectaS AB.
(IF AaC sectIO AF B, cric sectio A F B xequa.
islectioni AC B, sed A F D sectio est maior
lectione FFC cum linca AFFEC maior axis
ac proinde maior quauis diametro ITF. Pgieur
eriam e C B maior est sectione P L G. Igitur
sectio per axemmaiorem maxima est omnium
Cectionu quae in sphaeroide heri postune, mini-
mamaurem ese CF D manifectius eA quam
redemontrari debeat.
PROPOSITIO CXAII
ctionibus ellipricisper cenerum Factis.
X demonstratis pacec axem minorem sphaeroideos elte communem omnibus le.
PR O POSITIO CXXI.
Ectioperaxem maiorem maxima eAt omnium sectionum, quae in
aurem axc minore ciluem, peccdemplin extribere in (phaeroide
cuius axisaequaIS LICdata Ca LLL.
Aca quavis TR linea que Sirminorare maiore spheroideos, maior
Constructio es demonstratio.
rlentoaxe spheroideos A CB odacr ex Cencto ealac cireuus interuallo al
midio aala LR. Occtens lecclont AC. I Petaremtacta in puncco L, aiungan-
cur F. II. Denlgue per rectam LHlG lectio hac LFC recca ad planum AC B. Di-
COF FC ese quaelicam secrionem. cum enim secriO R F G, recca sic ad planum
aihns. E GuoaDet ancheli icarcleccionis LCCais ell L. C. qui cum exconltiu
etionedalatio ut Dala Lhtalet Delleclum ee Gudaslobtemutequtebula
eRO.