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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 160, page id 845634801:0166
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 56 lines, status machine
# Lines: 56 recognised, mean confidence 0.89
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FH E O R E M A S YS P A FIC U N
Lqualitatum quarundam cubicarum adfectarum, in quibus pote-
stanisonea est sub latere.
60
tus lubtensus à perpendiculo primi, lic tripsus ad angulum acurum sub.
cenlum a perpestunculo secundi: cubus ex dupla bale secundi, Mmuasson
dolib Eriplo quadFaEOtYDOTCNMLRII CALTCICMLDALHIL CIPLALLLCCUIICI a qua
bitur Colidob quadralohs porenula, in cuptam balin primi.
di, contractast proctactamre longitudine ejusrecta, qua porest quadrato
eriplum perpendiculi ejuldem, minus ejuldem balisiFa COnErACLX PTOETa
ctaere cubo; aequabitur eidem Colido lub quadraco hypocenula communisi
inbalin duplanprimi.
IuS F A B, ErIPIUS aHGIHI C A B. PrImL igicur crianguli balIS SIEF A, perpendicolum FB. (WB
in analyricis constiturum est.) Secundibasis C A, perpendiculum CB.
Dicoprimo; cubum ex dupla ipsius C A, minus lolido sub eriplo quadcaco ipsus B R in
duplam ipsus C A, xquari Colido sub quadraco B A in duplam ipsuS F A.
cripla est ipsus OB peripheriae. Si
sccetur peripheria C F bitariam in
K, crune legmenta B C, G K, K
aequalia. ducatur jam recta A R
Frir isicur ex demonstratis a nobis
Theoremare seo ad Sectiones AN
Gulares, ur semidiameter ad rectar
AG, ita recta A C ad compolicam
ex AB, AK. Sc plomdeur diame.
ter A B ad duplam ipsIuS A G, ic3
AC dupla ad duplam compolicani
ex A B, A IE. Igirur A G quadea
cum quateF, aquaBITUT ABGTCBAEC
quadrari dupli a diamerro, de rectangulrtub diamerro AB, _ A R bis.
agoregacum rectangulorum AB in A CbIS, AB In ALbis, aequabicur rectangulo quare
sub AC, AH. _ adhibica in priori a qualicare congrua antiche (, AC quadratum quater. mi-
nus AB quadearo bis, aequabitur AB in A R bis. Ouate adsumpra comimuni alcitudite A R
bis, eric AG quadracum quater, minus A B quadraco bis ad rectangulum quarer sub AC.
AK; id est ad rectangulum sub A G bis in A K bis; vel ex secundx aequaliraris analoeil
mo, ad aggregarum rectanoulorum AB in ACbis, AB in AFbis, ur AB ad AC bis. est au
rem _E A B quadracum ad A B in A C bis, ur A B ad A C bis: eroo (i à similibus similia au.
Ferantur, nempe ab AC quadraro quater minus A B quadrato bis, ablato A B quadrato, et
ab 2gereBacO AB in AC bis, AB in A F bis, ablaco A B in AC bis. R elinqueneur; illic quidé
AC quadratum quacer minus AB quadraro cer; hic vero AB in AF bis, quae inter se crunEuI
AB ad AC bis: quare AG cubusocties, sive cubus duplx ipsius A C, minus AB quadcare
rec in AGBis eguabIu A B guuutaro in A FOs. GuouCat poIoco gemoneranou
Secundo: 2 puncto B educatur reela DI. Hguc lcomencum B l incer B punctum, et
rectam A C incerceprum, aGuale ipsius B C duplae: OcCurTac aurem ip sa B L produca
rectangulo CVl, lacus BI rectoe alieulo, adplum elelareris B C. cric anguu
Dicoisicur Colidum sub a B quac et M A l. inas cubo ipluis A l, 2guar1 1010
CTtueruce duo triansula rectansula aequalis hyporenusae, e angulus ac
Rurlus. Colidum sub guiadrato erip lo hyporenula, in balin simplam (e cun-
CEr cieaas cujus diamerer A B, eique inscribantur urcunque duo rriangula rectan-
sula AFB, AG B, quorum communis hyporenula erit ip (a diamerer: ex sit angu-
Ouoniam eniim peripheria F B
Tcerum: estur AB ad AC bis, ica AIC bis ad duplam compolicam ex AC, AF, ac proinde
circumterenciae circuliin epitele a aalu lecta AO. Quomam isitur in criangule
GBIduarum Cectratum antusecti, live eriens adoe secotum, et lacus GL Poterii
triplum laceris G B. Perpeneccet Marou A6 B.
Cub AB quadrato in AF bis.