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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 67, page id 845634801:0083
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115
p.
M.
ex
aeis
nus quam7, sed
lum
dracu
t
Perpendicu
E cujus qua
Qua
duo quadrata valene
22 felt 13
dlrata abs 2 8 3
ua
CT
OY AREYS
E F E T FCY H VI
Invenire numero duo quadrata distantia dato interrallo.
Sic dacum incerrallum, B planum. Oporcec invenire numero duo quadraca, dictancia
Per B planum.
Estigicur Bplanum quadrarum à bale crianguli re ctanguli, de guaeruncur quadrara hy-
Porenulae de perpendiculi carionalia, quae distabunc per dacum basis quadcacum.
Acvero balis proporcionalis est incer differenciam perpendiculi de liypocenula de ad-
Bregacum corumdem larerum.
Guare ad sumacue quae cum que rarionalis lonsicudo ad quam adplicetur B planum, or-
rietur quoque lacicudo rarionalis.
Lonsirudoiinque ad quam Facta adplicatio est, E quidem larirudine sirminor, erir dif-
Ecrencia perpendiculi de hypocenula, laricudo vero ipla aderegatum, ee c converso. AE-
que adeo habebunur numero perpendiculum ee hyporenula.
ALI TER. A quadrarum si quadrarum unum e quaesiris, urpore quadearum perpen-
diculi. Ergo A quad. + B plano aequabitur quadraro, videlicet hyporenula. Sic
illud abs A F D. Vndecum sc D differencia incer perpendiculum ee hypoceuulam, A
quad. +. D in A2, F D quad. aequabicur A quad. = B plano. Oua equalicare ordinata:
tan.  avad aequabicur A.
Vnde
P H E OR E M A.
Incrlangulo rectangulo, si quadracum laceris primi circa rectum, mul-
catum quadrato differentix inter lacus secundum e hyporenulam, adpli-
cetur ad duplum illius differencia, lacitudo quae oritur, criciplilaterile.
cundocirca rectum aequalis.
ALLFER. Sit E quadrarum unum equaeliris, urpore quadeatum hyporenula.
ErBO L. quad. = B plano aequabicur alceri quadraco, nimirum quadraco perpen-
diculi.
Sic abSF =D, unde Ec D diferentia incer perpendiculum de hiyporenulam.
EtBOE quad. = D in F. 2, F D quad. aquabitur E quad. = B plano.