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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 255, page id 845634801:0261
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al
COM
EF L O M E F R E A.
PROPOSTZTO XXIII.
lelquialterutriulque ansulorum qui lunt ad balin, e a termino balis duca-
tur ad crus linea recta ipsi cruri aequalis, unde hac triangulum rurlus cru-
rum xqualium, quorum unum est educta (ecans; alterum crus primi non
lectum: erit in ilto lecundo erranoulo uter que angulorum qui sunc ad balin
criplus religui.
Sit Erianoulum AB CHaBenSErUrA A B, A C aqualI2, C HIF AHSIIuS B A C se (quial-
cer uriulque angulorum ABC, ACB, e a C basis cermino ducatuF MCLUS A B Fecta
C D ipsi AB vel AC aequalis, unde criangulum
AC D curlus sE ae quicrurum habenS CrUTA CD, CA
aequalia. Dico in eriangulo A C D urrum que angu-
lOrum AD C, D A C ese criplum anguli D C A.
Ouoniam enim anoulus B A C sesquialcer est anouli
ABC, vel AC B, ideo qualium parrium angulus
A B C elt duarum, ralium B A C est erium. Sed de
carundem angulus AC B est duarum cum (iC angu
l0 A BC aequalis, acque adeo eres anguli er
ABC, id est duo recti, estimantur seprem.
ccuri C A aequale, ideo qualium angulus D A C caxacus est erium parcium, talium exiero-
dem angulus AD C, atque adeo angulus A C D parsuna, cum calium duo recti sincle
prem. Tucriangulo igitur AD C urerque angulorum D AC. ) ADC est criplus reliqui
AC. D. Ouod erar ostendendum.
PROPOSTL1O XXIV.
Sic datus circulus cujus A cenerum, diamerer B A C. Oporcec in daro circulo hepla-
Bonum aequilarerum e aequiangulum describere.
Diamerer C B continuetur in
O ica ue D B adD A CIC, uc quadr2-
EUM ex A B ad quadraTUIM ExDC.
de in circumterencia pOnaCUED F.
aequalis semidiamerro. Dico F B
esle arcum heprosoni, id est, lep-
cimam parrem coctus circumteren-
IX.
Secer enim DL iplum quoque
circulum in F, _ junganeur semi
dIAMeERI A E, AF. ER ioicur eri-
angulum D E A aequicrurum X ira
constirueur, dc difterentia balis
_ cruris ad balin eA, (icur quadra-
tum cruris ad quadratum compo-
Ergo in dato circulo inlcriptum eltheptasonum aquu et dseat t.e
ueete oporrebat.
Si Fuerie criangulum aGuCruTuM, Cusus aSuu Qdi existir in verticeliE
Duoniam aurem de quicrurum quoque H Cansutat A C D, habens videlicet CruSDC
In dato circulo heprasonum aequilarerum, dt xequiangulum describere.
lIEX ex crure _ balC. Ouare recta
AF ips cruri aequalis sccacbitariam
angulum ad balin, ideoque qualium duo recti sune parcium seprem, talium anoulus
calium anoulus E AD est un2. IphuS aurem anguli F A D AMPIMHCMTEM ACHME aICuS
EA D estduarum. Oualium veto quacuor eccrmpem,  cutora circumferencia.
EB. OUaTE ATCHS E B CIETCPLMTA PAIS LDEHIS CICMHHCTEMIL. SHIBTEHOAEHF 19IFF le PIICS.
In 3
aliud.