# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/845634801:0162
# Permalink to this reading: https://leibnizlegible.com/page/845634801:0162?run=74
# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 156, page id 845634801:0162
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=162
# Source image: https://digitale-sammlungen.gwlb.de/content/845634801/jpgs/default/00000162.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 50 lines, status machine
# Lines: 50 recognised, mean confidence 0.89
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line: the recognised lines in reading order, one per line.

156
DE EML E N D A Y F O N E
Zin A cobum 2, EquatuT Z quad. - quadc. 2 = A quad. quad. Cujus equaliraris parre
urravis quadrara, omnibusque rice ordinaris, in cam iplam aequalitarem inciditur qua.
draro cubica cubicam, quae expolita cA.
Iraque A quadrarum tir X quadrarum plusminulre larere binomix residux, seu nesa.
ex v K quad.. quad. 12 - X quad. 3
Sit X I. ALN. 2Q 9 - 2C + 4N, aquatur 2.
Igieur 2 9 = 1 e 8, aequabitur
4 - ~ 12. C5 2 0 fic 2plus minusre latere binomina negaia N 12 -3.
C A P Y F XI.
Singularium aliquot consticurionum, ad aequalicates mulciplicirer adse
ctas perrinencium, collectio.
T E E O R E M A T
CF A quad. = + B in A, xquecur B quadrato: est B dupla longitudo, sect a in
eria proportionalia legmenta; quorum primum idemque majus, eAt B;
secundum A. quo in operc, dicicur B secari me dia ex extrema ratione (emet
CUMPEa.
P H E OR E M A TI.
EF A cubiis -+ B in A quad. - + B quad. in A, xquetur B cubo: est B dupla
lonoicudo, secta in quatuor continue proportionalia legmenta; quorum
primum idem que majus, est B; (ccundum A. quo in opere, dicitur BsccarI
media ex extremaratione duplicata.
T IE OR E M A TII.
CFA quad. - quad.  F B in A cubum -F B quadr. in A quadr. + B cuboin A,
aequetur B quad. - quadrato: est B dupla longitudo, lecta in qu’inque con-
tinue proportionalia segmenta; quorum primum idemqimajus, est B; sccun
dum A. quo in opere, dicitur B secarimedia ee exerema ratione rriplicata.
T H E O R E M A IV.
ETA quad. - cubus F B in A quad. - quad. F B quadr. in A cubum F B CU
boin Aquad. + B quad.. quad. in A, X quetur B quadrato. cubo: eAt B du-
pla longirudo, secta in sex continue proporrionalia Leomenta; quorum
primum idem que majus, est B; secundum A. quo in operc, dicitur B (CCAFI
media _ extremaratione quadruplicata.
TH E OR E M A V.
EF A cubo. cubus =+. B in A quadr. - cubum -+ B quade. in A quadr.
quadr.  + B cubo in A cubum F B quadr. - quadc. in A quadr. + B
quad. cubo in A, aeguetur B cubo- cubo: estB dupla lonsitudo, lecta in le-
prem continueproportionalia leomenta; quorum primum idemque inajus,
esB; Sccundum A. quo in opere, dicitur Blccarimedia e extremaratione
quincuplicata.
E A P V F ZI
Farundem collectio altera.
Y H E O R E M A Y
A quad. = B in A, _GuCtT B IM L:. CIL BPIIMLA MILIOE INEOT CXFFCMAS
inserie crium proportionatum: ageresatum vero reliquarum duaruI
hit Ln d Hl hlecunca.
TLEO-
t
Prim.