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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 32, page id 845634801:0048
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AD LOGESETCEN SPEC.
Sirpdix binomia A. F B, Sublateralis coefficiens D longitudo. Oporreat planum
Cub A. = B, _ D longirudine, adFectum multa A. + B quadrari, COMPOHerE. DUCATE
D = A = B in A F B, e orientur lingularia plana, A in D, = BIn D, = A quadeaco,
A in B 2, =-B quadraco. Elinc aurem ordinatur
C H E O R E W A
Si Fuerine duo larera, neenon ex sublaceralis coefficiens lonxitudo: planum à larere
primo in coessicientem longirudinem, plus plano a lacere secundo in coeficientem
longicudinem, minus quadraco laceris primi, minus dup lo plano sub laceribus, minus qua-
draco laceris secundi, aequarur plano lub aderegatolarerum, et coéfficience illa, adtcet0
mulea quadeari absade exaco lacerum.
PR OBOS FFETO ZLI.
Olidum sub lacere adfectum mulea cubi, a binomia radice, adscito
conoruenter sublaterali coefticiente plano; eftingere.
Sic radix binomia A. F B, Cublacerale coetticiens D planum. E FFingendum sic solidum
Cub A. F B, et D plano, adFectum multa cubi ex A. j. B. DuCatuE A + B in D planum mul-
cacum A F B cubo. Orientur Colida, A in D planum, = B in D planum, = A cubo,
A quadeato in B3, = A in B quadraruM 3, = B cubo. Hinc concipitmE
T H E O R E M A.
Si Fuerine duo lacera, una cum coëfficienre sublaterali plano: Colidum a lacere pri-
mo in coesticiens planum, plus Colido à lacere secundo in coëfficiens planum, minus
cubo laceris primi, minus Colido a quadraro laceris primi in lacus secundum criplum
minus Colido a lacere primo in laceris secundi quadrarum criplum, minus cubo laceris
secundi, aequatur Colido sub adgregaco lacerum, de coefficienre sublacerali plano, ad.
Eecto mulca cubi abs aderegato eodem.
P R O POSLFFO ZLTI.
COlidum sub quacdrato adfectum mulca cubi, à binomia radice, adsei-
ea congruenter sub quadratica coefticience lonsitudine, efinsere.
Sic eadix binomia A. F. B, Cubquadrariea coessiciens D longicudo. Oporreat Colidum
(ub A I B quadraro, et D longirudine, adfectum mulca cubi abs A F B componere.
In A +. B quadrarum ducaeur D A -B, _ oriencur Colida, A guadracum in D = A in
Bbis in D, + B quadraco in D, = a cubo, = A quadraco in B 3, = A in B quadrarum
T E E O R E NE A.
3, = B cubo. Elinc enunciarue
Si Fuerine duo latera, de Subquadrarica coefficiens longimdo: Colidum a quadrato
laceris primi in coefficientem longirudinem, plus solido à plano duplo sub laceribus
in coetticiencem longirudinem, plus solido à quadrato laceris secundi in coefficientem
longimudinem, minus cubo lacerisprimi, minus Colido à quadraro laceris primi in lacus
secundum criplum, minus solido d̀ lacere primo in laceris secundi quadrarum eriplum,
minus cubo laceris secundi, es aequale solido sub quadearo adgregatilarerum, et coet.
Ecience longicudine, adtecto mulca cubi abs aderegato codem.
P R OPOSFFEO ZLTTL
DLano planum sub lacere adfectum multa quadrato quadraci, à bino-
mia radice, adscito congruenter sublaterali coëfficiente Colido, com-
POnerC.
Sic cadix binomia A- + B, coefficiens sublacerale D Colidum. Oporteat compone.
re plano planum ex D Colido in A -: B, adfectum multa A- + B quadearo quadrati.
Auterarur A. + B cubus ex ipso D Coldo, et ducaue in A + B. Ociencurplario plane.
A in