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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 125, page id 845634801:0131
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2. 01
OFCO1
lidum
CI
nadi
aesisL
10
ImPI
1e2P
Elceriu
1xli5
OTCC
eliqua
rCI
Am P
N3
(0
solid
M C
Winq
inqu
rellib
BPIa
ldCI
IIC
IL. OV A F F O N VY M.
AlFerne sumpra diferunEP eF DPLU. FiC aucem Z. Solidum, ductu alcerius
extremae in ditterentiam quadratorum a reliquis. e est A prima minor in-
cer extremas, Pterria.
Sunco proporcionales 2. V2. 2. 3N = ZC, aquabitur 2. e7 fit L N L. FF NUr Sus 2 C. - 3 N,
aequabitur 2. 8 fit LN 2.
F H E OR EM A TI.
SFB plano. planum in A - A quadraco cubo. aequetur Z. plano. Colido.
X TurUS E quadrato- cubus =B plano plano in A, Requetur Z planO. Soli-
do: lunequinque continue proportionales lonsicudines, a quibus quadr2-
co. guadraca alterne lumpra differunt per B plano-planum. Pic autem Z. pl2-
no-lolidum ductualterius extrema in differentiam quadraco-quadrrto-
rum areliguis alterne lumpris: ex Ac A prima minor inter exercinas, F.
guinta.
Sine concinue proporcionales L. W 2. WV 4. W 8. 2. TLN = 1 DC, aquatuT 1O. 8 fit LN 1.
EF rursus 1QC = LIN, aquatur 10. e fit LN 2.
P H E OR EM A III.
CTB in A quad. + A cubO, XguetuE Z Colido, S rurtuS B in L quad. - F
cubo, aequetur Z. Solido: sunt eres proportionales, quarum alterne sump.
carum differentia eA B. Fit aucem Z. Tolidum ductu alterutrius extrema in
quadratum differentie reliquarum alterne sumpearum: dx dum incelligitur
Primaminorinter exeremas, est A differentia alterne Cumpra duarum pri-
marum, E disterentia duarum poAtremarum.
II. III.
Sunto proportionales l.
2C, aequatur 4. 8 fiTL N 2.
2. 4. 38 = 1C, aquatur 4. et sic X N 1. FI rursuo 3 Q
T H EOR F NE A TV.
B in A quad. quad. r A quadrato cubo, xquetur Z plano- Colido, e
ructus B in E quad. quad. = P quadraco cubo, aequetur Z plano. Colido:
sunc gunque proxotales, quarum alterne sumpearum difterentia est B.
Fic aucem Z Blano Lolaum ductu alterutrius extreme in guadeato. quad.
difterencie reliquarum alcerne Cumpearum: _ dum intelligitue primâ mi-
NOE InteF extremas, est A difterencia alterne sumpea quatuor primarum, L.
differentia quatuor poltremarum.
II. TIL. IV. V
4. 8. 16. 119O - + + QC, aequaTUr 10000.
 fit IN f. ETrursuS LLQ =+OG, aequatur 10000, Cx fit L N 10.
A E O R E M A V.
EB planum in A cubum =F A quadrato. cubo, XguetuIT L plano. 1OH
ae curlus B planum in L CuBHM F quadr. cubo, aguetur Z plano. Coli-
do: lunclex proportionales continue, quarum extreme ducte in difteren-
tiam quarre _ prime, Faciune Bplanum. Fit aurem Z plano.- Colidum ex
cubo disterentie quarre de prime in B planum plus ejuldem difterentix qua-
deaco. cubo; vel ex cubo differentie quinte de secunde in B planum mulea-
cum illius disterentix inter quintam _ secundam quadrato. cubo: _ quum
Prima incellisitur minor inter exeremas, tic A differentia quartxe de primx,
e P disterencia quinrae ex lecunda.
1.
SAnd
Sunco proporiionales