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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 112, page id 845634801:0128
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112
DE R ECOGNEFTONE
Sint continue proporrionales 2. 2. 4. 8. Dicetur 15 C = + 0 0, aequari 27 44. e fiet
2 N 7, Vet 14.
T E E OR E N A VTII.
EEB in A quad. quad. = A quadrato. cubo, xquetur Z plano- solido:
est B compolica ex quinque continue proportionalibus, et Z plano. (0-
lidum quod Ec ductu alterius exerema in quadrato-quadratum compoli-
ex equatuor reliquis: et fc A compolita ex quatuor primis, rel quatuor po-
Aremis.
Sine continue proporcionales 2. 2. 4. 8. 16. 3190-- + 9C, aquabieur 810000. 8
fit 1N 15, vel 30.
T E E OR E M A IX.
CFB in A quadrato cubum = A cubo- cubo, aeguetur Z. Solido- (olido:
Pest B compolica ex sex continue proportionalibus, et Z Tolido-Colidum
quod hrductu alterius exerema in quadrato- cubum compoliex a reliquis:
e sic A compolica ex quinque primis, rel c quinque postremis.
Sine conrinue proportionales 1. 2. 4. 8, 26. 32. 63DC = = CC, aequatur 916 132 832.
e sit LN 31, vel 62.
De affectis sub gradibus intermediis quae per interpretationem
deprimuntur.
Y E E O R E M A Z
Ci B planum in A quad. = A quad. quad, X quetur Z. plano. plano: est B
planum compolitum ex duobus quadraris duorum laterum; quorum pri-
miductuin sccundum tic Z plano- planum: d ft A quadratum majus duo-
eum, minulre.
Sint latera 1. 4. Dicetur 17 9 = 1 O C aequari 16. ex fit LN F, vel 4. Quod sinnusnumerus in-
telligatur quadrarum, radixve plana. 17 N - + 9, aequabitur 16. es fit 1 N 1, vel 16.
T. A E OR EM A ZI.
EF B solidum in A cubum = A cubo- cubo, aguetur Z Solido. Colido:
est B Colidum composicum exduobus cubis, quorum primi ductuinle.
cundum AcZ. Colido. Tolidum, ee sic A cubus major duorum, minorre.
Sunto latera 2. 8. DiCetT SI C =-2 C C, aequari 512. e7 sit 1N 1, vel 8. Duod si L N intellisa
cur cubus radiuve solida, 513 N = 1 8, aequabitur 512. es fit L N L, vel 512.
E H E O R E M. A XII.
EFB plano planum in A quad. = A cubo cubo, aquetur Z. Solido. Coli-
do: est B planum compolitum ex quadratis erium planorum provorrio-
nalium, eZ Colido- solidum quod sir ab uno plano in aggresatum quadra-
eorum a duobusreliguis planis: d HE A quadratum majus, minutre.
Sunto eria plana proporrionalia. 1. 2. 4. Dicetur 21 O = TC C; aequari 20. es fit F N 1,
vel 2. Ouod si L N incellisatur quadracum radixve plana, 2L N = + C, aequabitur 20. es fiet
IN 1, vel 4.
T A E OR E M A XTTI.
SFB Planum in A quad. quad. = A cubo- cubo, xquetur L. Colido. 1011
do: est B planum compolirum a tribus planis proportionalibus, de L
Colido Colidum quod sicab uno plano, in quadratum compoliti ex duobus
reliquis: ec fic A quadeatum majus duorum, minutre.
Sint
in
d