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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 156, page id 1815201908:0213
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DROGRFSSL
E S
g.
seriei Cao Caneeae nem, quam habec R S ad lincam quae aque di-
stabic a prima R S, _que cubus a cuboprimo AM. Duo lerac demonctrandum.
Corollarium.
Vohuccheoremata eidem terdaca demontratione, ael omnia limilium corpo.
inonae
b80. buiu s
AVBuS AME ad cubum D P, est in eriplicaca a racionis AB ad D E, hoc eA per
constructionem rationis RS ad ST. Aeguicciam RS ad quarram V Z, elt in
eriplicata racione eiuss quam habee R S id ST: ergOVE R S ad V X. Se cubuS
AM ad cubum D P. Simili raciocinacione ostendemus cubum primum, ad quemuis
rum genera liccor eke.
DROPOSITIO CLAI.
lonsicudinis R. Cuper quacracis aurem lingulis, exstructi line cubis
Constructio es demonsrato.
Ata sic quadratorum leries, habens bales in direetum, ex terminum
Pecitur seriei cubica aquale paralle lexipedum exhiberi.
Eriei racionis primae ba-
seos A B, ad qUATEAMDP,
Tac. b Xequalem AF; _ (UPCL
LL alcicudinc AB, rectan-
sulum AC: deinde (uPCF
rectanoulo A C in alcicudi.
alcicudine linex, aqualis le-
ne AB; construe parallele.
pipedun Leccangurum. BCo
hoc seriei cubicae aequari.
Vel siper quadraro AB in
riei Pacionis AB ad D F, Fac parallete PpCC. DBHOVEHC GuLMCMI. PTaCCMUL
BF aequalis D F. Ononiam igitur ex constructione seriei rationis A B ad B I, sue
=82. Bains. AB 3d D F, aqualis est A F, CrICC A F ad BF, ve AB ad BL, hOC CA vE AB
d22. sexci. 2d D F: quia aurem quadraca ex hypochesi lunc conua,  CL AB, BC,
F33. Dnc. C D, DF, _c. in conrinua analogra; vnde de cubuSC AM ad cubum BN, VE AB
ad D F, hoc est (sicucoltendi) ve AF ad BF: Onare cu palatteteppe a
Cic ad parallelepipedum B C, Erebalis AC+ ad ba BC C H IL L alt BL,
ime
F25. Vnde.
ii
51 fexri. crie cubus AM ad cubum BN, ve parallelepipedum AC, ad parallelepipedurm
BC: Aequi cotan scriescubica MK, cA ad feriem cubicam NTK, ve cubus A M ad
huins. CuBum BI, C180 Palanetepecuus AC, Ci se palaserepipecum B C, ve series
pipeduim den decubus idem AM, 2d leriem cubicam NK; (cum enim parallele.
Pipedta AC, BC conttructaline lupra bales A C, B C in communi alcicudine AR.
Dacet cubum AMI eAc excessum parallelepipedi A C: luper parallelepipedum BC.)
leaqueleries cubica NK de Parallelepipedum BC, erunc equalia; communique
addico cubo AM, cora seriescubica, es paralle texipedum A Ci aequalia erun. Fa.
tum igicur est quodpccebatur.
cubica MR, ad leriem cubicam NR: ergo dividendo cubus AMI, es ad parallele.
Corol.
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