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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 39, page id 845634801:0055
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AO F A PR IOR E S.
se ad compolicam ex hyporenula e perpendiculo adjunctam basi, ut minorradixad
majorem. Quod est ipsummer consectarium cerrium, cujus Laconice expressa demon-
Eracio exat exempliticanda, quamvisab (que ancecedencis consectarii auxilio brerius de-
monstrari poltE.
L ONSECFARIYM 1V.
le adcopoa Caldem alsueca va la eea Dals a Aspotenuta ad pet-
Dendiculum.
admajorem. Adsumpris enim duabusradicibus B d D, illa minore, hacmajore, cum
sic hyporentila similis B quadraro t. D quadraro, balis D quadraco = B quadrato, AF
differentia B quadrarum bis, perpendiculum vero simile B in D bis. Clerumque planum
2d B bis adplicetur, differenria illa ad perpendiculum erir, ur B ad D.
cedentibus ridelicer Pocenuns ncem crurum, dascsa et
cer Gcontecta, a a GUAMCALCII AIISAIO-
rum, quare dufulus quel lubrendie perpen-
diculum in criangulo primo, aequalis est an-
sulo quem subcendic balis in criangulo secundo. Angulus ieut cu s
ex coirione eA rectIS.
l
dencloto Haclcechypocen rec , adgregato rero batium
in balin, habebebic angulum verricis acurum.
Exper synaerehnejuldem analogix, ur compolita ex hyporenula perpendiculo et ba-
se ad balin, ica radix major bis sumpra ad radicum differentiam.
Fchunc analogilmum inverrendo, crir ur balis ad compolitam ex hyporenula perpen-
diculo et bale, ita differentia radicum ad radicem majorem duplam.
Ouamobrem ex xquo eric, ur compolica ex hyporenala de perpendiculo mulcara ba-
Incrianoulo rectanoulo, ur est compolica ex hyporenula _ perpendiculo multata ba-
Nam ditterentia basis de hyporenulae 2d perpendiculum le habet, ue minor radicum
ROPOSTTIO LIV
Friangulo rectangulo deducere duo criangula rectangula x que alta
exquorum coitione quod componetur eriansulum xque alcum, (uc.
Itine hujus propositionis ur et lequentium legebantur haec verba, eric angulus verricis
lium in balin, habebie angulum rerticis rectum.
rectus, pro quibus aeetum in leges Crammaticas peccatum repolui, habebic aneu-
lum vercleisrectum.
Oporiear tacere quodimperatur.
1DSZ =+ Dueradice una, ee B nc radice alrera, eHinoatuE
aliud crangulum rectangulum. Fryporenula sic similis ipsi L.
balis iplD. Perpendiculum ipli B. Cui sccurdoaSoCo-
Exponacur criangulum rectangulum cujus hyporenula Z, balis B, perpendiculum D.
Sciruacur alluelimile idem habensperpendiculun DLaelens, uc
Bad D, Ita Dactbalin, qux ideocrir o ca L ad hypo.
renalam, quae erit =Z in D. Lacera deniguerum istius tum expolri
ducantur in B. Duo igicur sunc eriansula Tectahota. LIMINuIm
cujus hyporenula Z in B, balis B guadearum. perpendiculum
B in D. Alcerum cujus hyporenula Z iire, VaS D Guacicacun
perpendicutm rurlus B in D. Cocdme M unania auotrian
gula reclat cu. ticeneer hyporetulae Aane
crura alcertus cianguli, adetegacum balium
iplarum udirectum policarum, balIs; altieu-
do iviurmanel cace a proporcionalis in
xer ba SIenEA. F. st enim B IM D pFOPOH
rionale et B quadracum aD quadrarum. In
Eguris aucet planis limilituaelacerum, uc do-
lROPOSTTIOLV.
Triangulo rectangulo deducere duo alia triangula xe que alta, ex
quorum coicione quod componitur eriangulum a que alt, succ
ExpO.