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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 63, page id 845634801:0079
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0.
ac
1u0
10
ati.
5s
CM
1dF.
Im
a muadracum
Dua aequalirare ordinata SinRim O2. ad. o S. xquabirur A. Leaque lacus primi con
ruri quadeati, quoderatA = B, Fr  in    :. - 3 quad. im v = a quadimv.. Lacus secundi quadrz-
ei consticuri, quod erar
=D, sic E quud. m B a  roatinior. -novuo. 12 B.. Ouibus bene re-
cextis, duo sunc constitura rrianoula. Primum cujushyporenusa racionalis irrarionalis ve
Z, balisB, perpendiculum D. Secundum eftictum à duobus lareribus S de R, cujus ideo
hyporenusa Hc Cimilis S quad. Y. R quad. basis S quad. - R quad. perpendiculum S in R
2, _ ab iis ettincirurrertium expolica ria dixreleos. Ec limilia lareribus efficta Polida 2d-
plicantur ad Squad. + R quad. Vnde AcZ communis lire primi live cerrii hyporenula.
Acque adeo quadrara a laceribus circa rectum illius primi, aqualia lunt quadaris a lare-
sibus circa rect usus cerrii.
Ouod silarus primi quadrari consticuarur A- B, secundisin a - D, SinRinD 2, + R quad iu B
aquaTuE A. Ec Hic lacus primi conctituri quactrari dinaim D2, - 5 quad. in B. - R quad.a B. Secindi
inR in B=
releos.
D. Ouod est effingere termilanculum ria expolica synae
lacus unum equasiris 18, alterum 1. Vel unum 6, alserum 17.
Rursus, eCSueto duo quadrata, x qualia duobus datis quadraris.
Sine dara duo quadrara, B quadratum, D quadratum. Oporret invenire duo alia qua-
draca iis aequalia. F. Hingacur eriangulum rectangulum numero cujus B sic hypocenula.
Aliud rursus estinsarur simile cujus D sic hyporenula, ee ab iis duobus similibus estinea-
curtertium criangulum, cujus hyporenula quadratum aequale sic quadrato hyporenula
primi _ secundi, methodo quae expolica est in nocis. Erso quadrarum hyporenulae hu-
jusetticti rerrii aequabitur B quad. F D quad. Ouibus eriam quadraris aequabaneur
quadrata lacerum cirea rectum. Ex iseciam modus elicitur ex jam cradica AnalyEDio-
Phancxa.
Sit B 10. D15. Primi triansuli consticuaneur latera circa rectum 8 ex 6. Secundi primo si-
milis, 12 e7 9. Terciilatera circa rectum erunt 18 es 1, vel 6 es 17. a quibus binis quadrata, aequa-
buneur quadratis 10 es 15.
EF E FTCV N IV.
de diducti ab iis certii crianguli balis, compolita ex perpendiculo primi e
balelecundi, CxiECa GUX PEXFINIEE.
Oporrebic aurem balim illam pexefinicam praestare hyporenux primi.
primi de bale secundi. B quact. F D quad. = N quad. aequecur M quad. Ergo didu-
ctirrialseuliperpendiculum erie M. Se aurem Abalisprimi. Pgirur balis similis secun-
Perpendiculum 1dco prnni N - ~in a. Perpendiculum vero secundi
exit A - ML, vel A =M, UE liE M ditterenera incer balim primi ee perpendiculum
lecundi. SIE Tane primo calu A ] - M, erir isitur ue B ad D, icq N.
ad A F M. Manalogilmo resoluro ec omnibus bene ordinatis, RC 3
aqua
c
E R
numre, in duo quadeaca jam dispectum, videlicee B quadrarum _ D quadrarum, rurtus
in duo alia quadrata dispelcere
Lacus primi constirmendi quadrari, esto A ] B. Secundisina =D. Fc ab iiseffingan-
+
ina.
cur quadeara, ee comparentur duobus datis quadraris
Ergo A quadc. F BIn A2, = B quadr. j 5 quadraces
quadc. aequabitur B quadc. + D quadraco
Sit B15, DIO, unde fit Z V325. Exponatur criangulum rectangulum numero, 5, 3, 4. Fit
. L LL L LCVM IL
Invenire duo criangularectangula similia datas habentes hyporenulas,
Sic crianouli primi data B hypocenula, secundi primo similis D. Oporret ab iis
diducere lerdum criangulum. Cases bas xquetur N, compolirx ex perpendiculo
e et