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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 288, page id 845634801:0294
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PE EOR E A A F A
AL.) e DB in 1B, aequale est AB in LC (et eM 1Bad IC, ur AB adDB:) erso AC in AB
plus AB in LC pA L B in DBminus AB in LC, 1OCA AG in ALEVC AD in AF pluSDBII
288
FB, aqualiL CFHE AB in A C, hisce isirur ip ( AB axplicaris, orierur lacicudo AC, erirque
AB quadrarum ad AD in AE. plus FB in DB, ut AB ad AC. Ouod erar secundo locb
ostendendum.
prianoulis ALLI, AOB, ACB, nam proxrer criangulorum limilicudinem, crieur AB qua
drarum ad AE in AD pluSEBin DB, ira AB in AHI ad AD in AK pluS DB in KFI: GiquI
dem estur AB ad ACI, itA AF ad AIL, _ EBad KHI, icemque uc AB quadracum 2d AL
in AFI, ita EB in AD minuS DB in AF. ad RHI in AD minuS DBIn AK.
xouale elD BM LDminus DB in IB, (CM CHLCB ad DB, uE EI vel FB minus IB, 20
X
O Y 10
Eadem elt demonstrationis vis, quum criangulotu etvellae sunthyporenula, uc in
Sit trianguli primi perpendiculum 2. basts L.
Secundi perpendiculum L. basis3.
Frianguli tercio similis fit perpendiculum r. basis 7.
junctus acuo secu, Lgue acum terrii, latera certii recipiune hanc
limilicudinem.
dis plus rectansulo lubperpendiculo secundi de base primi.
Balis, rectangulo subvalous primi ec secundi, minus rectansulo sub pet
Reperacur superioris Theoremaris diapramma, in quo est B. C ad AD, ut CB ad 1B,
ec rectanoulum AD in CB, aequale rectanoulo AC in IB.
Atrandui.
Es aurem AB inEB, aequale ipsis AC it
IB, AC in SE e CB in BE id est OB in BI.
plusGBin IE: X es AB ad DB, uc AI ad IF.
de rectangulum AB in IF, equale rectansi
IoDBin AI; sed ABinIE, aequale est A
in IE, plus CB in LE: quibus addatur CB 10
IB, id estDB in IC (est enim GB ad DB, ub
ICad IB), CrunEAC in IE, plus CB in IE
plusCB in IB, aequalia AI in DB, pluS IC it
DB, id est DB in AC. ergo AG in 1B, id el
AD in CB, pluSDBin AC, Xqualia eruM
AB in FB: et omnibus ip(i AB axplicatIS.
aequale rectanguto AB, CCSO AD in IC: Sed rectansulum AD in l
Sutriansuli primiperpendiculum I. basis 7.
Secundi perpendiculum 1. basis 3.
Trianguli terrio similis perpendiculum erit L. basis 2.
A E O R E M A II.
Situerine eria criangula reccaSu, Quorum primi angulus acurus ad
FEyporenula, sclimilis rectangulo sub hypotenusis primi d secundi
Perpendiculum, simile rectansulo sub perpendiculo primi, e bale seculs
Pendiculis Corundem.
erir AB quadracum ad AD in CB, plus DB in AC, uE AB ad EB. Ouod erat demon
Rursus est AB ad AD, ve AIid eA AC minus IC ad AE, ee rectangulum ABin AL
Cuaquale rectangulo CB in VB, (CtLCM AD ad DB, ut C B adt 1C.) ergo rectangusa
bIn AL, aequale ericrectangulo AD in AC, minus rectangulo C Bin DB, ee omnid
Pl AB applicaris, eric AB quadrarum adt D in AC, minus C. B in DB, ut AB ad d
Ouoderar demonstranclum. F odemque modo licer hyporemilae criangulorum inagu
les tuerine, urprius animadverlum est.
FHEO.
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