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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 33, page id 845634801:0049
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 53 lines, status machine
# Lines: 53 recognised, mean confidence 0.89
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# After the first blank line: the recognised lines in reading order, one per line.

l0Y A L K1OA L d.
quadraro in B gnadracum 6, - A in B cubum 4, = B quadraco. quadraro. LlinC aUIEeM OF-
dinacue
lidum, plus lacere lecundo in idem solidum, minus quadraro quadeato lareris primi-
minus cubo laceris primi in lacus secundum quadcuplum, minus quadraco laceris primi
in laceris secundi quadeacum sexruplum, minus larere primo in laceris se cundi cubum qua-
druplum, minus quadearo quadracolaceris secundi, aeguatur plano- plano ex adoreento
lacerum in coefficiens solidum, adFectomulca quadrato quadcati absaderesaco praedicto.
Ainsere.
inD, = A quadrato- quadraro, = A cuboin B+, = A quadraco in B, quadratum 6,  A
in B cubum 4, =B quadraro. quadcato. Flinc itaque ordinabicur
cundi, xequarut plano. plano ad ceficience longicudine de cubo adgresari laterum, ad-
tecto mulca quadcaro quadrari abs aderegaro eodem.
Porro monitum se cupio, singula haec Theoremata gene seos seu syntheseos potestarum adfectarum or-
dine respondere singulis analy seos pocestarum earundem Problematis; quae sol vuntur in eruduisimo ope-
re de numerosa pocestatum resolutione. Duod quidem adnocare necessarium.
A in DColidum, = Bin DColidum, = A quadrato quadrato, = A cubo in B +, - a
2
Situerine duolarera, et platerea coeficiens Colidum. lacus primum in coesticiens lom
OPOSTZFO XLIV.
PLano-planum sito cudo,  a=CO-quadrati à bino-
Miaradice, adlcita congeun un   n et
SuradXbinomia A - + B, Subcubica coetficiens D longirudo. OpOreAC IONaUII abS
A - + B cabO e ipsa D, adFectum mulca quadraco. quadcari abs A -F B, componerc. la
A - t B cubum ducatuED = A = B. eF cientur singularia plano-plana,
A cubus in D, -+ A quadcaco in BFerIH D, -+ A in B quadratum cer in D, - + B cubO
E O R E M A.
Si Fuerine duo latero, e praecerea coefficiens longicudo: cubus lateris primi in coef-
Aciencem longitudinem, plus Tolido sub guadearo lateris primi ee lacere secundo criplo
in candem oncudinem, plus solido lub lacere primo ee lareris secundi quadraro criplo
in candens lonsicudinem, plus cubo lareris lecundi in eandem longicudinem, minus
quadracc quararo laceris primi, minus cubo laceris primi inlatus lecundum quadru-
plum, minus quadraro laceris primi in laceris lecundi quadracum sexcuplum, minus la-
cere primo in laceris lecundi cubum _HddtaDIaM, Mos Quadento quadraro laceris le
F. N F 5I5
TRIANGHLOR I
R OPOSTFFO ZLV
TRiangulum rectangulum a duabus radicibus, eHingere.
Suneo duxe radices A, B. Oporreat ab iistrianeulum re CEanonlUM, CFINOere EF VerO
docente Pythagora, quadrarum laceris subrendentis angulum rectum, aequale est quadea-
eis laterum circa rectum. Larus aurem lubrendens solet per excellentiam vocari hypo-
chenula. Latera vero circa rectum, perpendiculum e balis. Foisiturrecidieres, uc a
duabus radicibus poliris, efingenda sineeria quadrata, quorum unum aequatur duobus
reliquis, ec maximilatus altimiletur hyporhenule. R eliquorum vero latera perpendicu-
lo e bahi. Ordinarum aucem jam ance est, quadracum adgreesri duorum lacerum, ae qua-
ri quadraro differentix corundem, de quadruplo sub eildem laceribus rectangulo. Oua-
Lead expolicas radices A, B, Subjiciatur terria propotetonanS ESH SAII CA-
=B quadraco
Trematum, hyPOThenUCA CONSIEIRTUE a- I. B auacraco. Di Ferenria earundem, balis, nempe
Perpendicularis exir, B2, cujus videlicet quadratun aequatur rectangulo
sub excremis. Omnia in A, ur ad idem DCHS AAIPHTCACIOMES TAICLA GHA GUE LCVOCCHEII: CLIC
hypochenula A quadrarum, + B quadcaco. pespendicularis A in B 2. Balis A quadcat
Etinc