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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 110, page id 845634801:0126
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110
DE RB COOHEFEONE
Persynecesin enim, est uc prima ad sccundam, iea composira ex omnibus minuspri-
ma ad compolicam ex omnibus minus altera exrrema, quoccunque proportionalium (IE
Ceries. Inunaquaque aurem serie exponirur lua poreltas condirionaria: id est canruplica.
eae rationis, quam excremarum comparacio exigit.
Y H E O R E H A TV.
ET Fuerie series erium proportionalium: est ur prima ad cexriam, ita difte-
Drencia quadratorum d duabus primis ad disterenciam quadratorum à
duabuspostremis.
Ec li quatuor: Cstut prima ad quartam, ita differentia cuborum a cribus
primis alcerne lumpris ad differenciam cuborum a cribus postremis alterne
Tumpeis.
Fclquinque: estur prima ad quincam, ita differentia quadrato-quadca-
corum à quatuor primis alterne lumpeis ad differentiam quadraco-quadra-
rum a quacuor postremis alterne lumpeis.
ECH lex: estur prima ad sextam, ita differentia quadrato- cuboru à
quinque primis alcerne sumpris ad ditterentiam quadrato cuborum à quin-
que poseremis alcerne lumptis.
EF li sepcem: est uc prima ad septimam, ita differentia cubo-cuborum d
sexprimis alterne sumpris ad. disterentiam cubo. cuborum a sex postremis
alterne sumpris.
T St E OR F M A V.
Y Fueric series erium proxortionalium: eRuc prima ad certiam, ita qua-
dracum differencix duarum primarum ad quadratum differentixe dua-
rum postremarum
EEli quatuor: estuc prima ad quartam, ita cubus difterentix erium pri-
marum alterne sumpearum ad cubum differentix erium postremarum al-
CEFHC SUMPEaEUI.
EcSi quinque: est urprima ad quintam, ita quadraco. quadrarum diffe-
rentix quatuor primarum alterne sumprarum ad quadrato. quadratum
disterenciae quatuor postremarum alterne lumptarum.
Lch sex: est uc prima ad sextam, ita quadrato. cubus differentiae quin-
que primarum alterne sumiprarum ad quadrato. cubum differentix quin-
QuC DOSEECMaLUI aIEeEHC LUmPEaEuM.
Et si Seprem: ectur prima ad seprimam, ita cubo- cubus differentix (ex
primarum alterne sumpearum ad cubo. cubum differentix sex poltrema-
cum alterne lumpearum.
T E B O R E M A VI.
Ituerinc quatuor continue proportionales: Colidum compolitum ex
cubo quarix, e triplo cubo secundae, differt à Polido composito ex cu-
boprimx e eriplo cubocertix, per cubum ditterentix extremarum.
Sineguaruor comtinue proporrionales B, D, F, G, eE SIFO major exrrema. DicOC
cubum + D cabOZ -- B cubo = Fcubo 3, equari C = B cubo. Fnimvero C - B cubuS,
constar C cubo = B in G quad. 3 L B quad. in C3 =B cubO, COMPATeTUE auTem C CU
b0. F DC. 3 - Bc. =F C, 3. Superest uE B quad. in C 3 -= Bin O Guad. 3, EgUCTF D CU-
60 3-- F cub03.
Id aurem ica se habet, nam B quad. in C est D cubus, ec B in C. quad. F cubus.
T A E OR EM A VII.
Er fuerine quatuor continue proportionales: Colidum compotitum ex cu
bo quariae _ criplo cubo secundae, adjunctum solido compolito ex cubo
PriMR