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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 123, page id 845634801:0129
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8s
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300.
lidus
ligtu
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lid
in
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BOrtI
nac
0. 10
uob
AE OV A ZF O N V M.
127
Sint a pr oporcionalia plana 5. 20. 80. Dicetur 105 OO -- + C C, aequari 50000. (5 fit
N5, vel 10.
Inventio aurem erium planorum proportionalium, quorum medium adscito sire pri.
mo sire postremo, sic quadratum numero, paret exhac lerie.
6
a
ratmuu
Dictance videlicer Zeceli. Sit enim medium planorum P. planum: dt primum A2-
tuatur B quad. =F. plano, postremum C quad. = F plano: quum igicur primo plano
addetur F. planum, Her quadratum, nempe B quadracum: es quum postremo plano ad-
decur F. planum, Rec quadratum, nempe C quadratum: rectat igitur uc ea eria pla-
na proxorrionalia Ene ex consequenter quod a medio fc in se, aequerur ei quod Hc ab
exrremis, qua comparatione secundum arrem inica, u.  5. invenicur aquarI F
PlanO.
Sit BT. C2. plana quaesita erunt = . Medium adscico primo facit r. adscico vero postreme
facie 4. eadem plana ducancur in aliquod quadrarum ut pote 25. fiunt 5. 20. 80. qualia ad exemplum
adsumpra sunt.
De reliquis.
F N E OR E H A XIII.
CFB Colidum in A quad. = A quadrato. cubo, equetur Z. plano. Colido:
est B Colidum constans cubo composiex c duabus primis in leric erium
proportionalium, plus cubo compolitx eduabuspostremis, e insuper loli-
do, quod sic ductu alterius extremarum in quadratum compolitx ex secun.
da d tertia.
EF Z. plano- Solidum quod Ec a B Colidominus cubo a duabusprimis in
quadratum compoliexe ex prima e secunda; vel a cubo compolx ex le-
cunda e tertia, plus solido sub tertia, ee quadrato compolitx exprima de le-
EFHE A composita ex duabus primis, relcompolica ex duabus postremis.
Sine proporiionales L. 2. 4. 2799 - 1 QC, aequabitur 2 268. e5 fiec L H 3, vel 6.
PH E OR EM A XV.
CFBplanum in A cubum = a quadraco. cubo, aequetur Z plano. Solido:
est B planum constans qlaerato compolitx à cribus primis in lerie qua-
tuor continue proportionalutm, plus quadraco compoliea e tribus postre-
mis, minus plano quod tcaceltia in compositam ex tertia, secunda, e pri-.
masvel a secunda in compolitam ex secunda, certia _ QuaFFa.
Fc Z plano. Tolidum quod Ac a Bplano, mminus quadrato compoliEX eX
eribus postremis in cubui Compolita e tribuspostremis; vel ab5B planO,
minus quadrato compoe ex tribus primis in cubum compolite exeribus
primis, _ sic A colpouta ex tribus primis, vel compolica ex tribus po-
Sint proporeionales concintil L. 2. 48. 217C. - 1 Q C, aequabitur 57624. 8 fit 1 N7, vel 14.
C A P V F XIX.
Aqualicatum contradicentium constitutiva
Concradicentium aurem consticutio est hujusmodi.
T E E O R F M A 1.
TA quad. F D in A, aquel Z plano, X rurSuS E quad. =B in P, RquetuI
L. Plano: sunt duo lateta quorum difterentia est B, quod aurem lub eis A,
aequum est Z. plano, d  A minus latus e P. majus.
Sunta
cunda in quadratum compoliex exprima et secunda.
Alemis.