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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 250, page id 845634801:0256
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E L L E M E N X V ~
PROPOSFTTO XVII.
Si duo triangula fuerinexe quicrura singula, _ ipla alcerumalteri crurI.
duobusrectis, lic criplus anguli quen ae vampriu: Loap
baleprimi e cruris communis quadrato, minus cubdebale puu, aequale
criangula aequicrura a
BC, EDC, ec ipsIS AB,
BC cruribusaqualibus
primicrianguli, aequalia
TUnEDF, DC crura (c-
cundi criansuli. Oua-
lium aurem ilterque an-
gulorum BAC, BC A
est parsuna, angulus A
BC est duolum recto-
rum minus duabus cali-
busparcibus, e angu-
lus exrerior anguli AB
C duarum est illarum
reriori aeglatur ansbilus
ADC: quoniam sune
concinuaram u, pit uoque l’e agaticur palanera , k, lecances cale
perpendicularicer in L, K. Suncisirur AI, LC aequales, e ideo hc A C ip sius A L du
Pla. leaque sunc quoque aequales AB, BHI, _ Fc A HI iplius A B dupla. A quales qu
eAt AB ad id quod tir lub HlB. HD, id est, ad criplum quadrarum ex AB, minus qua
drato
bus xequalia, angulus autem, quemis qui est ad basin secundi relinguite
est Solido luobase lecundi  cruris commuss uactal.
Sicprituum eriangulum ABC, habens crura AB, B C aequalia. FF quia angulus quel
quilibet eorum qui lune ad basin secundi relinquir e duobus recs. pus est ipic
anguli B A C, ∞ major sirrecto necesse elt. Ideo ett qoepiorum BA C, BC A qu
sunc ad balin abgulorum contequener masor ulee ecu, alisde adeo angulus ad ved
ricem AB C est minor recto. Ouare in AB ponatuT C D, iphi A B aequalis. Deiric
ex D in C A productum, POnacUE DF. ipsi quoque AB equalis. Sunt igirur dua
parrium, cui angulo ex-
aequales abguli DBC.
C DB ob aequalicarem
quoque ccurum C B.
CD. Ex anguIO aUrEM AD C _C D AC, composicus est angulus exterior anguli L
C. A. Seclindum icaque triangulum est C. D L. Iplu a Guetucut, le clura llabensa
qualia crutibus primi ABC, et urrumque angulorum quem anguli ad ba(In D C F. r
DE C relinguu c duobus rectis, criplum ansIB X C Vet BC A. DCos iplu
deato et D C (Cu AB.
Centro enim C incerrallo C B vel CD describatur circulus, de aearur diametet
FC G (CCanSE A, uri continuatur, perpendiculariter in C, iplam vero AD quoque
solidum sub AC de quadrao ex  , sat 1  L C e qua
que E. li, RC, aticL. C dupla ipHS L. R
Oladratum aurem ex C H, aequale est quadrato ex C F, id est AB una cum co qudu
tic sub 1I F, II C, et Conrettendo quadrarum ex C FLmUS QuaaFaIO ER AB, a Guale et
ci quod sic sub HF, H C, hoc est ei quod tir sub HB. HI D. Iplum porro quadcacum
ex C HI, aequale es quadFAEO CL A LLHHIUS GUAOTaTO ex A C. d quadratUIM CX A IL ct
quadruplum quadrati ex A B. Lriplum isitur quadrarum ex A B minus quadrato
A C. aequale est ei quod Ec sub BH, HD. Sed cAHIB ad HD, Sicur C I ad CR,
CA CI ad CR, licuE C A ad C F: cum sinc hx illaTM AMPIX. OLAFCSICUEC A a
CE, ita HB ad HD, _E COnSeqUentEF SICUE C A ad C E, ita quadrATuM ex FLB,
1d1De