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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 38, page id 845634801:0054
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b L OCTSFICF N. 5
GONSECTARLNU.
St componantur duo criangula rectanoula, unum a duabus radicibus, alcerum ab
adorcgaco carundem de difterentia, similia illa sunc, lateribus circa rectum angulum
permuraris.
L AOFOSTF1O LTTI.
Bale constituri criangulifectanguli, e composita ex hyporenula, et
perpendiculo ejuldens celangulum rectansulum componere.
Sic criangulum rectangulum cujus hiyporenula Z, basisB, perpendiculum D. O.
DOTECAE a B_ Z = D eriangulum rectangulum constituere. Hyporenula isirur ex l0.
lita merhodo hcsimilis BquaatatO, F quadrato abs Z = D. BalIS differentiX COruN
dem quadratorum. P’erpendiculum plano duplo ex B in Z. F D, quo opere BEHC CxAMI
nato deprehenata caoulum illud simile primo
Hlocautem ica demonsErabimus, quoniam à communi mulciplicante non immuratur
PEOPOrTIO, SUMAEUE Z 2 = D 2, e ducacur tam in B, quam in D. Erir itaque B ad D,
SICuEB IDZ 2, -+ B in DZ ad D in Z. 2, + D9. 2. EA aurem D9. aequale
Z. g. =B4. Ouare ( à quarca magnicudine proporrion ali auFerarur D g. Cemel. de Cubsti-
EHAEUTZ9 Bg. erir quoque B ad D, uE Bin Z 2, + B in D 2 2d 29. + D in 7 23
F D9. = B9. Sedtertia proporrionalis estmagnirudo ex ductu iptiusB 2, in Z L D
Orta. AE queZ9, Y D in Z2, Y Dg. eA quadrarum ab5Z i D. Ideo crit uc B adD, ita
Bbisin L FD ad L F Dgaadrarum, B9
Ouare cum haeceriangula circa angulum rectum habeane lacera proporrionalia, c.
runexquiangula. Ouod demonstrandum erat.
Teaque perpendiculum primi ad baln secundiistius
crianguli, eandem haber rationem quam balis primi
ad perpendiculum secundi.
GONS ECTARErMT.
Si à base constiruri crianguli rectanguli, de compo.
Sica ex hyporenula ex perpendiculo, ettingitur alcerum
criangulum rectangulum, secundum illud limile est
primo laceribus permucaris.
C ON SECF A R F V M TI.
In criangulis rectanguliseIt UE COMPOLITA ex hypO.
renula et perpendiculo ad baGn, Sicadoregacnm r2.
dicum a quibus composirum est criangulum ad diffe-
rentiam carundem. Excollarione Consectarii primis
cum Conlectario anrecedenris Propolicionis.
Hoc Consectarium ica quoque porest demonstrari.
Relumatur Schema Propolicionis 45. in qua ex radici
bus Ae B compolicum est criangulum rectangulum.
Ouomat itaque proporrionem non immurat communis mulciplicator, ducarur A - -B
tam in A- F B, quam in A = - B. FririgitE Ag. + B9. -+ A in B2 ad A9. =-B9. SICUE
A - + Bad A = = B. Sed Ag. - t B9. est hyporenusa erianguli abs A -t B COmpOSIci. F. que
A in B2 est ejuldem crianguli perpendiculum, dt A9. = =B9. ba(IS.
Ouamobrem compouca ex hyporenula ee perpendiculo ad balin, cstur adgres2
cum radicum ad carundem differentiam. Ouod erar demonstrandum.
COMSFCTAREVM TII.
In criangulis rectangulis est uc composita ex hyporenula de perpendiculo mulcata
bale ad compolicam eandem adjunctam bali. ita minor radicum ad ajorem. Pet
dixrelin ec synaerelin anrecedentis avalogix
Enimvero per dixrelin analogix ancecedentis Consectarii AC, VE COmPOSITA ex hy-
poremuta ec perpendiculo mulcata bale ad baliu, ica radirminor bis lumpra ad cadi
cum difterenciam.
Bbis in