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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 80, page id 845634801:0096
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L F L C O R V 1t
Sit D I, B5. Vnde Z. planum 10 triangulum rectanguluII
erie hujusmodi. Area = 3 24 2 2 auferarur a 10, relinquetI
2
544 quadracum absradice 4 88 sett 3.
EE PE FFCVM ZII.
Invenire numerotria quadrata, uE quod
sic sub binis plano planum, adjunctum e
quod hrab adgresato binorum in datxe lon
sicudis quadratum contrciat quadratum.
Data longicudine Z. Sirprimum quadratum, A quad. - Z in A2 + X quad. 51
jus radix A = Z. Alrerum, A quad. cujus radix A. Terrium, A quad. 4 - Z in A 4
X quadearo 4. Fx ductu igicur primi in secundum, adjecta Cumma primi e se cundicu
eta in Z quadratum, her quadrarum a radice plana A quad. - Z in A. F X quad. F X duit
vero secundi in cerrium, adjecta summa secundi se cerrii ducta in X quadratum, her 9l
dearum a radice plana A quad. 2. - Z in A, F Z quad. 2. Fx ductu denique primi in cet
cium, adjecta summa primi ex cerrii ducta in Z quadrarum, set quadcarum à radice platu
A quad. 2, - Z in A 3, F Z quad. 3. Terrii adaequandi radix eAto D = A2. F18
quad
quad. a xquabitur A.
Sit X 3, D30, fit A 8. Jeaque quadraca quaesita sunt, primum 25, secundum 64, terrium 196
ex satisfaciunt postulatis. Duod enim sic è primo in secundum adjectis 80+ conficit 2401, quadratu
abs 49. Es rursus quod fit e secundo in cerrium adjectis 23 40 facit 2 4834, quadrarum ab5122.
denique quod sic e primo in cercium adjectis 1989 facit 6889, quadratum abs 83. Porro eadem 9
drata eria cum adsciscene singula duplum dacae longieudinis quadrarum: quod fit sub binis plano. pa
num derracto eo quod fir ab adprecaro binorum in data longicudinis quadrarum, erit quadratum.
in exposica hypothesi duplum longicudinis quadrarum est 18, quo addicto unicuique trium quadrai
rum siunc plana eria, primum 43. secundum 82, terrium 21 4 ex satisfaciunt postularis. Ouod el
fie e primo in secundum ablaris 1125. relinquit ipsa 24O1. Et rursus quod fit e secundo in cerill
ablacis 2664. relinguit ip sa 24884. Ac denique quod fit c primo in terrium ablacis 2313, relinist
ipsa 6889.
ZE PE F TCVU XIII.
Dacam Z longirudinem ita secare, ut cum primo legmento addetur B.
secundo D, d ita productx partes ducentur altera in alteram, Aac qua
deatum.
Primum Cegmentum cAto A = B. Alcerum igimue eric X = A. L B. Cum icaque prime
sexmenco addetur B, iplum productum Rec A. Cum vero secundo segmento addecur
iplum Bec X = A + B + D. OHATCD + D +XIn A, = A quad. adae quandu erie quadrato.
radix in a acque adeo ab ea quadearum, Fix 3 quas. in L Wuod.. Fr∞O B - v = Xin X quas. X quabicu
d
quac
Mt L s emo. AICCT II B. + x ia S quo vuse
quad.
Teaque ur lic subrractioni locus op orrebie S quadearum minus esse Xoma. in D = L., (e d maja
od. 1a D
Sit X 4, B 12, D 20. Oporcebit S quadracum minus esse 32, sed majus 20. Sit 25. fit seemeni
primum e, Secundum  .. hoc dum producerur suc   2. Illud 175. Factum sub illis  840 0 qua
dracum a radice 2 = P
Sit X3, B9, D15. Oporrebie S quadratum minus esse 18, sed majus 11 =. Sie 16. fic primt
seemencum 28 allerum  hoc dum producieur sic 2 33. Ilud 2 2 3. Factum sub illis 23 6 25 9
dracum absradice  35
ZE F E FECVM XIV
A quadratum minus C plano adxequare uni quadrato, quo d sicmine
quam D in A, sed majus quam B in A.
icue.
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