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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 739, page id 1815201908:0796
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F6
PL ANV N
Demonstratio.
retistineis A F, DH patallelis ad BC, inscribaneur planis B AC, DD C in:
ACTECtAnGUL R F, RF :K HI, K TI. ductis irem lineis R C AGUITX BF C in
Anica Grnilicer rectangula inseribANEHE R G, X G. Rectanoula RF, ducta in re-
ctangula KFT, corpori quod sic ex ductu plani BAC, in planum BDC in-
scribune infinira parallelopipeda, quorum bales lunc rectangula ARD, alci
EDdines verO AF, AF sive DFI, DII. Similicer rectangula RG, R C+ ducta
in se corpori quod sc ex ductu plani BF C in scipsum inscribune infinica pa-
rallelepipeda, quorum bases sunc quadraca RP, K P, alcicudines R, GP
Acqui ex hypochesi rectangula AKD semper aequalia lune quadracis RB. ErBO
Parallelepipeda inscripea corpori facto ex ductu plani B AC in planum BDC X
quales bales habene basibus paralleloxepedorum inseripeorum corporigenico ex du-
ctuplani BF C in Cciplum. sunt aurem ex alcicudines A F alcicudinibus F. C Xqua-
les. Frgo omnia parallelopipeda inscripea corpori genito ex ductu muruo planorum
B A C, BDF, aequalia sunc omnibus parallelopipedis inleripeis corpori producto
ex plano BF C ducto in sc. Cum ipicur in propolicionibus proxime praecedencibus
demonstrarum sic parallel oxipecta illa ita posse mulciplicari ve corpora ipsa quibus
inscribuneur exhautiane, hoc est re ex iis ablaca relinquane quacicacem daca qualibee
minorem; ipls eciam corpora inter se aqualia csenecese cA.
rlteriorem huius rei demonstrationem peritus Ccometra non requiret. Vi tameit rieori
Geomerrico per omnia sarissiat id ipsum accurarius demonstrabimus hunc in modum
Si corpusgenitum ex murno ductu planorum B AC, BD F, non sic X quale COr-
pori quod sic ex plano B F C in se ducto, necelse est alcerutrum ese minus alcero
Ponatur primo id quod Rc ex ductu plani B I C in seipsum ese minus alcero quan-
cicare aliqua quam vocemius Z. Bieviraris criom caula corpus nacum ex ductu plani
BP C, in SC VOCCUS COrPUIS RF C, ex COrpuS Factum ex ductu mucuo planorum
BAC; BDC, cOrpuIS AB CD appellerur. Ex propolicionibus proxime praeceden
cibus parec sruris B AC, B DC cocInsCribi pONC rEEtaNGUIA RK, RP, IEFL, RFL, Ve
ea in lemuruo ducta inscribane corpori AB C D parallelopipeda, qua deticiane ab
ipso corpore, cui inscribuneur, qulancieare minori quam sir daca quanTICAS L. Cr∞O
parallelopipeda inscripea corpori ABC D malora lune corpore BP C: led paralle.
lopipeda inscripea corpori A BD C supra demonstranimus aequalia semper ese eo:
tidem parallelopipedis inseriptis corpori BF C. ergo parallelopipeda inletipta corpo-
ri BF C eciam maiora sune ipso corpore BP C, pars coros quod est absirduri. Nois
isirur corpus BB C minus est COrpOrE ABD C. Eodem modo demonstrabime
CorpuS, AVDC non ese minus corpore BB C. Neucrum isicur alcero minus est,
aequalia ixicur sinc necesse est. Ouod erac demonstrandum.
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