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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 62, page id 845634801:0078
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sulum sub extremis vel mediis, aequatur soltud et austealo extremaru es le
etangulo sub mediis vel at
Ouod adnoralle fuir oporrunum.
TE FFCORVM
nis
renire numero duo quadrata, a qualia dato quadrato.
Sir darum numero, F quadratum. Oporret invenire duo qua
drara aequalia daro F quadeaco
Exponatur eriangulum quodcumque rectangulum numero, dt
Sichyporenula Z, balisB, perpendiculum D. Ex Aac eriangulum et
limile habens hypocenulam F, nempe Faciendo, urZ ad F, ita Bdc
aliquam balim; quae ideo erir in. EF rurIuS, uF Z ad F, ica D 2d
perpendiculum; quod ideo crie e. ErgO quadcata abs vme et   aequabuneur daco F
quadraro. Ouod erar taciendum.
Eoque recidir Analplis Diophancxea. Secundum quam op Orteat B quacracum, in duo
quadrara dispelcere. Larus primi quadrari esto A, secundi B - - ma. Primi laceris in qu2.
drarum, est A quadrarum. Secundi, B quad. - sina in D2- p 5 quad. in
quadrata ideo aequalia lune B quadrato.
Aqualicas ioirur ordinetur.
19 a Oux duo
aequabitur A laceri primi singularis quadrati.
Eclacus secundi six nauo. ino.  Sis.  .. Nempe criangulum rectaneulum numer el
finoitur a laceribus duobus S _R, X Achyporenu (a similis S quad. i. R quad. b2(15(1
milis Squadeato - R guadraco. Perpendiculum simile S in R 2. Ieaque ad dispectionem
B quadraci Ac, ucS quadr. 1 R quadr. ad Bhyporenulam Cimiliscrianguli, ita R quadt.
Squadr. 2d balim, lacus unius singularis quadrari, ec ita S in R 2 ad perpendiculum,
lacus alcerius.
Sit B 100, cujus quadrato invenienda sine duo quadrata aqualia. Pffineatur criangulum rectanest
lum numero abs R 4, 5 3. Fic efficti eriangulihyporenu sa 25. basis 7, perpendiculum 24. Iaque fiet. ud
25 ad 7, ita 100 ad 28. Frut 25 ad 24 ita 200ad 96. Duadraum igitur abs 100 aequabitur
quadrato ab 28, plus quadrato abs 96.
Z E F E FTCVM TI.
Invenire numero duo quadrata, equalia duobus aliis daris quadratis.
Sine dara numero B quadearum e D quadrarum. Oporcet invenire alia duo quadra-
cahis aequalia.
Incelligiror B balis erianguli rectanguli, D perpendiculum, acque adeo quadracum
hyporenulx aquale B quadr. F D quadc. ex st illa hyporenula Z, lacus rationale, irra
cionalere. Ec exponatur aliud eriangulum quodcumque rectangulum numero, cujus by
porenusa Z, balis F, perpendiculum C. EF ab iis duobus consticuacur certium exiansu.
lum rectangulum via synareleos, dixreleos. ve, per ea quae expolica luncin noris. Frit pe
primam mechodum hyporenula similisZ. in Z, perpendiculum simile B in C. = D in
F, balis similisB in F, =D in C. Per secundam hyporenula eric similis Z in X, perpen
diculum B in C, = -D in F, balis BinF, + D in C. Ec plana omnia Cimilia laceribus
ellictirrianguli adpliceneur ad Z. Scance igitur Z hyporenula, Sc ba(is Bmv. - Binc. pet.
pendiculum emo. - vinr. per primam methodum. Vel per secundam, Gc ba(is B inv. = Din 6.
perpendiculum Bu c. = oms.. Ieaque haec duo à laceribusrectum angulum includemri
bus quadenca, aequabuntur Z hyporenula quadraco, cuieriam aequari constructum est b
quad. + D quad. Ouod cracfaciendum.
Eoque recidic Analylis Diophancxa, secundum quam oporteat Z. quadracum, pla
num-