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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 165, page id 1815201908:0222
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# Lines: 39 recognised, mean confidence 0.87
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lB
edi,
is
adep
Tan
20
AB
M
GF OM L lRIC A:
163
ciem parallelepipedi L, rebalis ad balim, nempe vecompolica ex quadrupla
AIN ee dupla NYO, ad composicam ex quadrupla OR ec dupla RS. REqui vE
quadrupla MN cum dupla NO; ad quadruplam 9 R cum dupla R S, (C NN
cum dimidia NO ad O R cum dimidia RS; eroo suporticies parallelepipedi
MP, est ad superticiem parallelepipedi OT, hoc. est ad suxerticiem prramidis
cubice, re MN cum dimidia NO, hoc cst ve series racionis AB ad I) F cum
dimidia AB, ad OR cum dimidia RS, hoc est ad seriem rarionis AB ad CD
u ea AB: quoderac demonttrandum.
EROPOSITIO CLXXVII
Roportionem exhibere qua cuperctes prtamtais Habet aa MM-
serpea libe pslamtals cublea superticiem: eo modo incelligendo
superete leriei cobica, quo in praecedenei propolicione.
Constructio es demonstratio.
Sumemus hoc loco prramidem isosceliam, Facilicatis Grati2. sIC C19O pyF4-
LLnis OLM R N isoscelis, cnins basis sic quadratum OMI, cur prramis cubi-
La AB, CD. ecc. inscripra incelligatur, Factogue quadrato OR aequali quadrato
LB reperiatur linea OFI aequalis seriei racionis AB prime ad cerriam F L; ex (UpeF
Juadraro OK in alcicudine CFI, Fac parallelepipedum, cuius superticies aequabi-
asuperticiei prramidis cubicae. Dico verectangulum super dupla I N et L. N 2175. Ian
camquam vna recta, in alcirudine LM, est ad rectangulum liper quadrupla CFI
et dupla AO camquam vna recta, in alcicudine HO; lic prramidis includencis
superticies, ad superticiem inclusa preamidis cubicxe. Ducatur enim ex verrico
Pramidis N ad I. M normalis NP, quae ve ex datis Facile colliges, bisecat L MI
in L. Icclans msu NVC.eaupium cit trianguli rectanguli L. P N. ve patel
sulcm NL. M duplum elt crianguli L. MH. crxo rectanoulum sapet alplaLN,
IM alcicudine L. M, eAt quadruplum crianguli L MHI, hoc cs aeguacur coci (upCrH-
iet Pstumiais PrEcet balim: quare rectangulum supet dupla L.N ee L M CaM.
Gllam
ex cremmemis; elso recanoutum AL P, aquale est criangulo LNN. _ rectan-