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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 88, page id 845634801:0104
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80
DE RE COGHER FONE
ut ex Leceticis limiliter clarum Ac: quo perrinebune trina quoque 
enuncianda Pheoremata.
I E E O. R E M A
A HIO ∞ A YTRHS.
ET A cubus =B in A quad. X quCtIE B in Z quad: SUNE GUatLIOF COnEI
proportionales, quarum prima major, minorre inter extremas ett
agoregatum vero secunda _ quartae est Z, e sc A agoregatum primau
tertix.
Ex Zeterico:
Data prima ex acgrecato secundae ex quartae in serre quatuor continue pr
portionalium, in venire accrecatum prima e tertiae.
Sic data prima B, major minorre inter extremas, ageregatum vero secunda de qua
IX Z, in serie quatuoF concinue proporrionaliuM. OPOTTCE InVENITELBBTESATUIM pEi
X cerrIX.
Sir illud A, FErTIa iBIitUE CxIE A = B, CA AUTeM UE A ad Z, ica Bad ~n Z, quare n= Ct
secunda: quum sruraggregarum primae ec cerrix ad aggregatum secundx  quatiae,
prima ad secundam. Acrectangulum sub prima ee rerria, xquabitur se cunda quadealu
leaque B in A = B quad. aquabitur B oume. inr oune. Omnia mulciplicentur per A quad.
dividantur per B: igitur A cubus =B in A quad. aequabitur B in Z. quad. id auTCM et
Quod ordinatue.
Si 1C. = 8 9. aequerur 12168. sunt quatuor continue proportionales quarum prima inter extreu
est 8. aggrecarum vero secundae ex quarrae 1 =2 288 id est 39. e fit L N 26. aggregarum primal
terrie. Ex serie proporcionalium 1. II. III. IV.
8. 12. 18 27
E H. E O R. F M A TI
E A Y A _ A F. F K H 5
EF A cubus. F B in A quad. Xquetur B in D quad: TUNEQUatIOECONB
nue proportionales, quarum prima minor inter extremas est B, ditie
rentia vero secundae _ quarEX CstD, _ Hc A difterentia primx _ FCTHL.
Ex ZecericO:
Data prima minore inter extremas; ex differentia secundae ex quartae ins
rie quatuor continue proportiona lium; invenire differentiam prima ex rerita
Sic data B prima in serie quaruor conrinue proporrionalium eadem que ininocu
extremas, ditterencia vero secunda _ quariX D. Op orretinvenire diferenciam pih
ee cerria.
Esto illa A, cerria igituE Cxit A. = B, Cs aurem UE A ad D, ita B adt ~ n D, quarC B M, Ct
secunda: quum sicur differentia primxe de cerriae ad differenciam secunda e quaEEaN
prima ad lecundam. Acrectangulum Cut prima de cerria, aequarur secunda quadralu
iraque B in A F B quad. aequabitur ~aud. in bound.. Omnia ducancur in A quad. et dit
dancurper B: igicur A cubus, = B in A qua d. aequabirur B in D quad. id aurem iplum c
quod ordinatur.
Si L C. ; 8 C aequetur 1800. sunt quatuor continue proporrionales, quarum primanet
tremas est 8. disserencia vero secunda ex quarca Y 2~ ~ id est 15. 8 fit L N 10. disfereniia prima
cercia. Ex serie proporcionalium. 1. II. III. IV
27
2HEO