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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1005, page id 1815201908:1062
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NGVLA CXLINDRTCA
Demonstratio.
1007
GREca CxCenrO LMI normali ad K F diamecrum, inscribaeur lemicireulo qui est
balSrnoula parabola KM I axem habens LM. Demonstracum est a cylindro a Vide2s.
paraboliooabe balim parabolam KM I e alcicudinem lemidiameeri L pT ~. huins.
quari rngulam super baA lemlcirculari INM K, d alcicudino dlametri R L. sedeciam
peaecedenci propolicione ostensum est eidem eylindro parabolico aequari prramidé
cuius alcirudo sic IM, basis vero rectangulum quod sub KI de dupla alcicudinis
cylindei parabolici, sub dupla nempe ipsius P. MI, hoc est rursum sub KI, concine-
tur. erso prramis, cuius alcicudo est semidiamerer L MI, balis vero quadratum, dia-
metri KI, aquacur exlindro parabolico, hoc est veiam ostendi, aequatur vngulx. se d
CEIA COEPUS L GTTEC D A L B xequatur prramidi cuius balS sc aequalis quadeato B62 huins
RI ex alcicudo lic LM. ergo corpuS L. OHFCD AL. xquale elt ingulari magnir
cudini. Duodtuir demonstrandum.
LR 5
A R T A.
Comparatio onula cylinarica cum sphaera es aliis corporibus.
Ac parce maxilr incendimus symbolizationes ingulx cylindricae
acum sphaera nocas reddere, canta enim est similiendo incer vngulam
ex sphaera, veomnes spllaea proprietares, unsulx communes sinc, quem-
admodum exiis que dleinceps demonMraturi Cumus cognolcipoterir.
PROPOSITIO LX VII.
Aca Cierngula C D Na cplindro recto abscisti, alcicudinem parem
Phabens diameero BaLCB CM, ex hac relectum SIEB ADC Cegmen-
cum plano peraxem eflillari cranscunce, cuius communis lectio cum
ba(I olliprica sIc recta B D. Circumscribatur aurem polrgonum
CF F C A arcui AF. C, X lecundum lacera polyooni tiant plana axiparal-
ela qua extibeant in platto ellipeico comunes lectiones CHI, HIK, IED.
ec ponacur AL. comc Ct, xequidistans suc normalis diamerro
N
Dicc
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