# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/845634801:0163
# Permalink to this reading: https://leibnizlegible.com/page/845634801:0163?run=74
# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 157, page id 845634801:0163
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=163
# Source image: https://digitale-sammlungen.gwlb.de/content/845634801/jpgs/default/00000163.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 69 lines, status machine
# Lines: 69 recognised, mean confidence 0.82
# 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.

tis parie
TUF qud
unegt
quabi
est 
Tene
ecta i
duP.
OTULa
secd
seCUI
in A
C0
sec
eI
uad.
FDL
FCH
1aFIII
HFC
A. OV a L LO A V M.
T H E O R P M A FI.
EtA cubus -F B in A quad. = B quad. in A, xquetur B quad. i1 Z: est D
prima in serie quatuor CoMnue proportionaliumi ageresatum reroxeli-
Quarum erium eAt L, _ A Asecua.
EA EOR EM A ITI.
SF Aquact. Guad. + B i A cubum -+ B quad. in A quad. + B cubo in A
aequetur B cubo inZ: est Bprima in seric quinque ContinuE pFOPOKHO-
nalium; asrresatum reroreliquarum quatuor est Z, _ Ac A sccunda.
TH E OR E M A IV.
SF A quad. -enbus = Bin A quad. quad. + B quad. in R cubum + B cu-
b0 i Aquad. -+ B quad. quad. in A, aequetur B quad. quad. in Z: eAB
Prima in seric sex continue proportionalium; aggregatum veroreliquarum
quingue estZ, e tc Alccunda.
E A E O R E M A V.
SFAcubO. cubuS : +. B in A quad. -cubum -+ B quad. in A quad. quad. t B
cubo in Acubum-+ Bquad. quad. in A quad. - + B quad. - cubo in A, X-
quecur B quadrato. cubo in Z: est Bprima in sexic LepteM CONFIHUC PFOPOE-
cionalium; aggregacum vero reliquarum sex est Z, e Ac A secunda.
C A P V F ZTTT.
Farundem collectio terria.
T H E OR E Mt A +.
TBIn A = A quad., Xquetur B in Z: CAB pFIIA MaIOFINEEF EXECMAS in
lererium proporciohalium; differentia vero duarum reliquarum est L,
_EAE A Secunda. Porest aurem ese duplex, nam est eciam disterentia inteK
Primam a secundam.
Sed AA quad. =BI A, ZGuetUEB in Z: estB pFIMAMINOF INFEF exETE
mas; difterentia vero duarum reliquarum est Z, _ Ar A similirer se cunda.
Suncoproportionales 4. 6. 9.
1O 4 N, aequetar 12. fit 1N 6.
9N  1 9, aequarur 18. ft LN 6, atque eriam 3. Sed s
EO R B M A II
EFA cubus = B in A quad. F B quad. in A, aequetur B quad. in Z: est B
prima in serie guatuor continue proportionatium; differentia rero crium
reliquarum alterne sumprarum est Z, _ tc A sccunda.
Sumo proporcionales continue 1. 2. 4. 8. 1C = 89  64 H, aquatur 192. fit L N 4.
Vel 2C - 1D . F YN, aequatur 6. fit L N 2
A E OR E M A ITI.
FB cubus in A = B quad. in A quad. - = B in A cubum = A quad. quad.,
xquetur B cubo in Z: eAt B prima major in serie quinque continué pro-
Portionalium; differentia vero quatuor reliquarum alcerne lumpearum cAt
 _E HE A sccunda major inter medias. Porest aurem eAc duplex.
Sed (A quad. quad. = B in A clbuim F. B quad. in A quad. = B cubo in A,
aequetur B cubo in Z: est Bprima inox inter extremas; difterentia vero
Guatuor reliquarum sumpearum alcerne est Z. _e fc A Se cundaminorinter
Medias:
Suio proportionales continue 1. 2. 4. 8. 16. 4096d - 2560 + 16C - 18. 2
equatur 20480. fir 1N 8. Vet 19D - 1C + 19.- 1N, aquat ur 10. fit 1N 2.
T H E 0