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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 315, page id 845634801:0321
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ICL SFO H SV M.
P H E O R E M A 1.
Si Fuerieeria criansularectangula, quorum primi angulus acurus, diste-
eat ab angulo acutosecundi, per acutum certii, de lit excestus penespri-
mum, lacera cerrii re cipiunt hanc similicudinem.
lEyporenula, sirlimilis rectangulo sub hrporenulis primi de secundi.
erpendiculum, simile rectansulo lub perpendiculo primi e bale lecun-
di minus rectanoulo sub perpendiculo secundi e bale primi.
Balis, rectangulo sub balibus primi ec secundi, plus rectangulo sub per-
pendiculis corundem.
Sic erianguli primi perpendiculum B. BalISD.
Secundixerpendiculum F. BaliS G.
Perrii peipendiculum eric smile C in B = F in D. BaEISC in D. F Pin B.
Sit rriareuli primi perpendiculum L. basis 2.
Secundi perpendiculum L. basis 3.
Frianguli terrio similis sic perpendiculum 1. basis 7:
T H E O R E M A TI.
Si fuerine eria eriangula rectangula, quorum primi an sulusacutus ad-
lunctus ansulo acuro secundi, sequet acurum certii, latera cerciirecixiune
hanc limilicudine.
tErporenula, he limilis rectangulo sub hyporenulis prini d lecundi.
Pexpendiculum, simile rectansulo subperpendiculo prini ex bale lecun-
a plusrectansulo sub perpendiculo secundi e bale primi.
Balis, rectansulo subbalibus primi de lecundi, minusrectansulo subper-
Pendiculis corundem.
Sicrrianguli primiperpendiculum B. BatiSD.
Secundi perpendiculum F. BalisC.
Terrii perpendiculum erielm ile F in D F B in C. BaLISCin D =F in B.
Sit trianculi primi perpendiculum r. basis 7.
Secundi perpendiculum 1. basis 3.
Frianculs cerrio similis perpendiculum erit 1. basis 2.
AEque hxc duo priora Theoremata Fundamenca sunt omnis doctrina
angularium sectionum.
T H E O R P M a III.
Cujus inventi lariria adFectus. d Dira Melutinis, cibi OveS CenTUM PEO
una Pychagorxaimmolavi.
Si Fuerine duo criangularectansula, quorum an sulus acurusprimi, sic
ub mulciplus ad angulum acutum secundi.
Latera lecundi, recipiumchanc similitudinem.
Flyporenula sic limilis porectati conditionarix hyporenulae primi: est
rem porectas conditionaria, guae seguItur gradum proportionis multi-
ae; quadratum videlicetin ratione dupla; cubus in cripla; quadrato. qua-
eatum in quadrupta; quadrato cubus in quincupta, et eo in intincum
progrestu.
Ad similicudinem autem lacerum circa rectum hyporenusx congruen-
cum, esricitur a bale e perpendiculo primiurbinomiaradice, porectas eque
alta,