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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 57, page id 845634801:0073
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et
I1
TC
re
EB E R TE R F + Y 5.
ZE YE YTCV M TI.
Daca media trium proportionalium, e AdIBFCSAEO CXFTEMAFUM IVCtII.
Illud quoque Problema jat anre exposirum est, videlicer. Darorectansulo sub late-
ribus, ex adoresatolarerum, invenire latera.
Sit media 12, adgrecarum extremarum 26, minor extrema est. 8, major 18.
Z E YE FTCY N TTI.
Daco perpendiculo crianguli rectanguli, e differentia balis e hypote.
nula, inrenire balin, ec hyporenula.
Ec hoc quoque Problema jam expolicum est. Iplum enim est. Dara differentia qua.
dracorum et differentia lacerum, invenire lacera. Ouadrarum enim perpendiculi est dit.
Ferentia quadrati hyporenulae a quadrato balis. Sic nempe darum criansuli rectanguli
perpendiculum D, B vero differentia balis e hyporenulae. Oporrer invenire balin et
hyporenulam. Summabalis e hyporenula, esto A. Igicur B in A aequabituE D qua-
dcaro, acque ideo aunocuu requabicur A. Data aurem differenria lacerum ee summa
corumdem; caneur latera.
Daco isicur perpendiculo criansuli rectanguli, e difterencia balis et hyporenula,
dancur balis, a hyporenula.
Sit B5. B 1. Sunc proportionales 2, 5, 25. Leaque triansuli hypotenusa est 13, basis 12,
stance pervendiculo 5. Dua eriam ratione, e id esto
ZEFEZTCYM IV
Daco perpendiculo rectansuli criansuli, e adgregato balis e hypotenu-
Cxe discernuntur balis es hyporenusa.
Sit perpendiculum 5, adoreeatum basis es Bypotenusa 25. Sunt proporcionales 25. 5. T. Itaque
differentia basis es hyporenusae est 2. Ipsa vero basis 12, hypotenusa 23.
Z E FE FFCY M V.
Data hyporenula crianouli rectanouli, de differentia laterum circare
ctum invenire latera circarectum.
IIlud aucem est. Dara difterentia lacerum, ee dato adoresato quadracorum, inve-
nire lacera. Quod Problema quoque jam expolicum est.
Sic nempe dara D hyporenula triangulirectanguli, B vero differencia larerum circa
rectum. Oporretinresire larera circa rectum. Summa lacerum circa rectum esto A. FF-
50 A + B eric duplum lateris majoris circa rectum, A = B duplum laceris minoris.
Ouadrara ab iis lingulis eftormara, ee ad dica Faciune A9. 2, F B9. 2, quae ideo a quan-
TUF D9. 4. Teaque D9. 2, = Bg. XquaBIEOE A quadraTO.
Daca ixicur hypoienula rriansulirectanguli, et difterencia lacerum circa rectum, in-
veniuntur lacera circa rectum.
FC CXETCMAS.
Enimvero,
Perpendiculum trianguli rectanguli proporrionale est, inter differentiam ba-
sis ex hypotenusa es adzrecatum eorumdem.
EnIMVCrO.
Duplum quadratum hypotenuse, minus quadraro disferentiae laterum circa
Sit D 13. B7. AIN. 10 aequatur 289. Et sit TN. N289. Jaque latera circa re-
rectum, aequatur quadrato summa eorumdem.
Aum sune ~ 72 = + 32 8 N 72 = - 3 =, sive 1285.
Z E XEFT CVM VI.
Daca hyporenula criansul rectanguli, ee lumma lacerum cirea rectum.
mrenire latera circa rectut.
Ll