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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 90, page id 845634801:0106
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d0
DE RP COONETEONE
Si F C. = 6. N. aquatur 9, est = seu 2. rectaneulum sub lateribus, à quibus cubi asgregati facitt
9. ex fit LN. axgregatum laterum, ex hypothesi larerum r. ( 2.
Eadem aurem Theoremata Gcomerrice ita concipientur:
A L X TE R,
PR FM V M T A E OR E M A.
ETA cubuS, = BPLAnOFEFIN A XQUCTIF BPLaNO in D: SUINE QUAEUIOF COM
tinue proportionales linex rectxe, sub quarum mediis vel extremis AE
Planum, difterentia vero extremarum est D, ee fic A difterentia in c diarum
Ex Z eretico.
Data differentia extremarum. e rectaneulo sub mediis vel extremis in se
rie quatuor proportionalium, in venire differentiam mediarum.
Si1 C. I 2+ N aequerur 56. sune quatuor continue proportionales sub quarum mediis vel extrent
quod sic planum, aequale est 2= id est 8. differentia vero excremarum est 26 id est 7. (x fit L N. dis
rentia mediarum, ex serie continue proportionalium. I. 2.
A LI FER,
SECY NDYM YA EOREMA.
ET A cubus =B plano ter in A, aequetur B plano in D, sic aurem D
missis quadratum majus B plano: TunE quatuioE continue proxortionale
linex recta, sub quarum mediis vel excremis Ac B planum, aggregatu
vero extremarum eAt D, ee tic A aggregacum mediarum.
Ex Zeretico.
Dato asgrecato extremarum, es rectanculo sub mediis vel extremis, in sest
quatuor continue proportionalium, in venire ae crezatum mediarum.
Si rC =24 N. aequarur 7 2. sune quaruor continue proporeionales. sub quarum excremis vel M
diis quod firplanum, aequale est 2 2. id est 8, aggregarum vero extremarum est 7 = id est 9. ( fil 1 1
agcregarum mediarum ex serie continue proporiionalium. I. 2.
4.
8.
Ouum aurem quadruplus cubus e criente coefticientis plani, prxstac 10
lidi datx mentura quadiato: aliam eo casu Portitur xe qualitas consticuc
nem, ambisux scuci quxe negatur inver se communem: quo pertinet l
quens Theorema.
T A. P OR E M A TTI.
ET A cubus = B plano ter in A, aequetur D solido, ccdac aurem D solia
Oquadratum, quadruplo B plani cubo: B planum ter in F = F cubO, E9ua
birurrursus D Colido: _ enunciatur F de duobus lareribus, a quibus lu
sulis quadrata, adjectarectangulo sub ipsis laceribus, Faciune B planun
Ouod aurem tic ab uno lacerum in quadrarum reliqui, adjunctum la
ctangulo: Ceu aliter quod fr abs aggregato laterum in rectangulum ett
Colidum. A rero enunciatur de agoresato illorum laterum.
ExZecerico.
Daro plano quod constat acore eato quadratorum à duobus lateribus, plus
ctanculo sub iisdem. ex daro insuper solido quod fit abs as grexaro laterum in ta
ctanzulum, invenire laterai vel etiam laterum azzrezatum.
Si 1 C. - 21. N. aequetur 20. quoniam quadruplus cubus ex 7 major est quam 400. iditur 2