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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 144, page id 845634801:0150
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244
DE E M B N D A F EON
Consticutione duem cum tujus cum ancecedentis aequalieatis bene sonica: sune duo
lacera, a quibus quadraro. quadrarorum differentia, applicara adaggregarum cuborum,
Facie B 2: quadracum vero differentix larerum mulcarx ip(aB, ablarum ex ejusdem B
quadraco, relinquer D planum, sive F planum: ec sic Z. plano. planum ex applicatione
cubi a D plano, ad differentiam quadcuxlam quadracorum a D de B. e A est latuS u-
num; hic majus; illic minus.
In lerie rero quacuor continue proportionalium: B 2 es differentia illarum omnium
alcerne sumprarum: Z plano. planum quod sic ab urraris exrremarum in cabum differen-
rix reliquarum erium alcerne sumprarum: _ sc F planum sive D planum differencia (ub
quadrupla incer quadrarum differentix omnium alcerne lumprarum, ee quadrarum dit.
Ferencia extremarum mulcarae rripla differentix mediarum.
Vnde N Bquad. q - D plano q. est distereneia exrremarum minus eripla differentia media-
rum: _ quum prima incelligitur minorincer extremas; illic Ac A differentia erium prima
rum alcerne lumprarum; hicerium postremarum.
Sunto proportionales continue. I. 2. 4. 8.
10O- L SC, aquatur 216. Teitur
1O + 3N, aequabicur 18. 8 fItLN3. EF si 1OO = 5C, aequatur 216. IBitUr 1O = ZN, a
quabitur 18. e5 fitr N 6. Noca est aurem 5. quoniam 1C + 86 4 N, aequatur 5400. ex fit L N6.
differentia subquadrupla inter quadrarum abs dato latere 5 ex quadrarum abs i. unde dienoscitur ipsa
longirudo quae adjecta lonsirudini 5. facit 6. duplum ipsus 3.
T A E O R E N A TFI.
GFBin Acubum 2 = A quad. quad, aquetir Z. plano. plano, de P plani. cu-
bus =Z. plano. plano + in P planum Xquetur Z. plano- plano in B quad. 4:
Innoreleat aurem P planum esse D planum.
SFoo uus. + vrruo 2 A = A quac, X quabitur ,B aom Ao uo.. = D plano 3.
Constientione aurem aequalitaris bene agnita. sunt duo larera, a quibus disterenria qua-
deaco. quadcarorum; applicata differentia cuborum, Facie B 2: differentia vero intee
quadratum agoregari larerum mulcaei B, e ipsum B quadeacum, relinquie D planum: 8c
Ec Z. plano. planum ex opplicatione cubi a D plano, ad agoregatum quadruplum qua-
dratorum a B ec D. ∞ eA A lacus majus, minulve.
In Cerie quacuor continue proportionalium: B 2 est compotira ex illis omnibus:
Z plano planum quod sic ab urravis exeremarum, in cubum composiix ex eribus reli-
quis.
Ec sic E. planum (cu D planum differenria subquadrupla, inter quadratum aBgregari
exrremarum adjunctieriploaggregari mediarum, se quadearum ageregari omniumi.
Vnde VBquad. 4.-XDplano +. Clt 2gGregatum extremarum, plus eriplo agoresari medix-
rum: _x uc A compolica ex tribus primis, Cire ex cribus poltremis.
Sineproporsionales continue P. 2. 4. 8. 15C -1OO, aquatur 27 44. TBITUT ZIN=FC.
aequabitur 98. ex fitZN 7, vel 14. Nota est aucem 21. quoniam 1C 1097 6H, aequatur 617 400.
Et fit 1N 12.6. differencia subquadrupla inter 225 ex 729. Vnde dienoscieur 729, id est longi
tudo 27, quae adjecta longicudini 15. fasit 42, duplum ipsius 2Y.
P R O B E E M A TTI.
i Oualitarem quadrato. quadrati adFectitam sub latere quam quadra-
Lco; per medium cubica radicem habentis planam, ad quadraticam
deprimere.
Proponntur A quad quad. L C plano in A quad. 2 F B solido in A, aequari Z plano-
Plano. Oporter Facere quod imperarum est.
Sane li quadracum estingatur abs A quad. + G plano L F quad. E: eric illud A quad.
quad. F C. plano plano F G plano in A quad. 2. = F. quad. quad.  + F. quad. in A
quad. + C plan. in F quadracum.
Ouoniam igitur exiis quae propolira lune, adhibira meracheli, A quad. quad. +C
plano in A qua c. 2, aequarur Z. plano plano = B Colido in e.
Veri