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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 160, page id 1815201908:0217
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ESSTONE S
23+. onde draro AB in alcitudine linex O, aequale est a parallelepipedo super quadrato A3
n
in alciendine AK; cum habeane bales ex constr. e alcicudines reciprocas. Ouare
cumpyramisB L. K sic rna certia paralle lexipedi super A G in alcirudine AK (est
enim A K alcicudo pramidis, quia AK vE ex construct. precedencis proposicionis
pacer, est normalis ad A P.) itemque parallelepipedum saper quadraco A G in alci-
cudine cerria parcis rectae 9. Cc eiuldem parallelepipedi cerria pars; crune preamis
ee dictum parallelepipedum aequalia. Juare cum prramis maior sc inscripea cubica
prramide, etiam dictum parallelepipedum nempe luper quadearo AB in alcicudine
Tertie parris recte O, crit maius parallelepipedo quod prramidi, cubice equale Fece-
ramus. Fadem isirur erie pyramidis includencis ee inclula qua horum parallelepi.
pedorum disterentia. extibuimus ergo, ecc. quod perebatur.
PR OPOSITIO CLXX.
Aexe seriei liudauldi cubica, prramidem super F quadrato da-
co, aequalem CxMIBCTC.
b7. vna
cimi.
165. huiu.
Construco demonsratio.
leterico cubocum aM. Ba. C. aec. de aacum quadra
eum SIE F, ec hac ve quadracum E ad quadracum AB, ica
linea aequalis serici rationis AB ad D F ad lincam O. Dico
prramidem cuius balis sic guadratum F, alcieudo aurem cri-
plaiplius O serici cubicx x qualem eAe. Nam parallelepipe.
dum cuius balis sic quadracum F alcicudo  aequatur c Pa-
rallelepipedo, cuius basis sic quadracum AB, alcicudo rero se.
ries racionis AB ad D F, hoc cs oseriei cubicxe. Ergo pacal.
lelepipedum cuius basis sic quadratum F ee alcicudo cripla
recta Oeriplum crie serici cubica. atqui c idem parallele.
pipedum eriplum cAprramidis habentis basm F, alcicudinem
verorriplamrecta O. ergo pyramssilli seriei cubica aequalis
ric. Lactum isItHF elt quod perebatur.
F
t u  s n    p   t  p e ete  ete   e  u  A pt     i ut et a s  e  t t  ta    te  p i t  .    n  ptl ts. 1