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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 34, page id 845634801:0050
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d SFL C
Elinc efingere est a duobus laceribus, erian-
gulum rectangulum. Fnimvero hypochenusa AC
limilisadereoaco quadrarorum, balis differencix
corundem, perpendiculum duplo rectangulo.
Aque efingere est a proporrionalibus eribus,
criangulum rectangulum. Enimrero hypoche-
nula tir similis adgregaro exrremarum, basis dit-
ferenrix carundem, perpendiculum medix du
PIX.
ON S E CF A R E Y M.
Perpendiculum crianguli re ctanguli mealum proporrionale eA incer adoresarum ba
DPOSFTFO XLVI.
Duobus triangulis rectanscilis certium eriangulum rectangulum ef
Sunco a a . Scilicet,
Fiac cerrii hyporenusa similis ei quod fC ex
hyporenula primi in hypocenutam secundi,
nempe Z in X. Plana igicur similia Ba( _ per
Pendiculo ducta quadratice, Faciene Z. quadea-
cum, in X quadrarum, id est per incerprecario-
nem, id quod AE ex B quadrato, L D quadraro
in C quadratum, -= F quadrato: quod Factum
constat quacuor plano planis, nempe B quadra-
eo in G quadrarum, + D quadrato in F quadra-
tum, ec B quadraco in F quadratum, D qua-
draro in C quadrarum. Binis primis ad daturpla.
no. planum duplum quod sic conrinue absB, D, F, C, et auteratur binis postremis; vet
conversim, auterarur binis primis, ex ad datur binis postremis. Nihil Factis deperiir vel
accesie, quominus facta plano. plana, plato. plano ex Z quadc. in Z quadracum ad X-
quencur; bina porro illa plano. plana adlciro vel demprobis communi illo plano- pla
Primo calu, prima eAt BinC, F D in F, al
cera Bin F= D in 6: secundo vero calu, prima
eA Bin C, = -D in F, alcera B in F, + D in 6.
Cleriulque casus, prima adlimilatur perpendi.
culo, secunda ba(.
Ergo hac vel illa methodo a duobuseriangu
lis rectangulis effingere cAcerrium criangulum
rectangulum. Enimvero hypocenula cerrii Aec
Similis facto sub hyporenusis primi ee secundi,
perpendiculum adoresato tacti à bale primi in
perpendiculum secundi, et Facti reciproce à
bale secundi in perpendiculum primi; balis
difterentia, incer factum sub balibus primi de
secundi, etactum sub eoruudem perpendicalis.
Vel, perpendiculum adsimilatur differentiae
Factorum reciproce à bale unius inperpendicu-
lum alcerius. balis vero adgregato facti sub b2
Bino libus, et Facti sub perpendiculis.
Friangulum aurem rectangulum à duobus
aliis triangulis rectangulis primo exposiromo-
do deductum, roceturrriangulum synareleos.
secundorriangulum dixreleos, ob cautam (u0
exprimendam loco. Hinc
LHEO
Aineb.
ETC
(cos de hyperetula, a eteutiam carundem
Angere.
no conrinuetacto absB, D, F. C, planas habentradices, quarum
BinC
Din F