# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/845634801:0105
# Permalink to this reading: https://leibnizlegible.com/page/845634801:0105?run=74
# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 89, page id 845634801:0105
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=105
# Source image: https://digitale-sammlungen.gwlb.de/content/845634801/jpgs/default/00000105.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 70 lines, status machine
# Lines: 70 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.

tem
inue
AB.
1x d
pro.
rima
Z erit
Acato.
d. C
nelt
IYEIII
MBC
Ont
ifte
ia
in se
ria
incc
ria
drato
dir
mesti
1er
Ma
HEO
F OV A L LON V
I a F B O A O Y.
L AE OREM A III.
EB in A quad. = A cubo~ GuCTE B in D quad: SUINE GULACHOE COnFinUC
prepocionales, Guacu prua major inter extremas est B, differentia
vero lecundae _ quarEx est D, _ Ac A difterentia primX _ FerriX.
Ex Lecectco:
Dala prima majore inter extremas, es differentia secundae es quartae in serie
quatuor continue proportionalium, invenire differentiam secundae és tertia.
Sic data B prima in serie quacuor concinue proporcionalium cadem que Ay OFinEeF
extremas, differentia vero secundae e quarca D. Oporcet invenire differenciam prima
eE TeTTIX. FA0 illa A, terria igicur eric B = A: Crit autem UE A ad D. ita B ad v in B, quate
 crielecunda. Ouum sicuc difterentia primae ee cerrix ad differentiam se cundae e
quarrae, ica prima ad secundam. Acrectanoulum (ub prima e cerria, aequarur secunda
quadraco. leaque B quad. = B in A aequabitgE B au. m Dnms. Omnia ducanEuE in A qua-
deacum. e per B dividantur. Peirur B in A quad. A cubo, aequabirur Bin D quad. 1d
aurem ipsum eA quod ordinatue.
Si 27 9 - 1 C, aeguencur 2700. sune quacuor continue proporcionales, quarum prima major in-
ter excremas est 27. differentia vero secundae es quarta, V 23. 5C id est 10. 8 sit L N. differentia pri-
mae tercia. Ex serie proporcionalium. 1. 1I. III. IV.
27. 18. 12. 8.
C A PY Z VI.
alia insuper constirutio cuborum sub lacere affectorum.
Ex Zeceticis.
CdHeque omitrena ett ex Lerericis quoque depromenda lingulat
quaedam consticutio cubi, qui siib laFCrC AHIrmMaEC, acque etiam ejus
qui alticicur nesate: quum videlicet (is enim calus praemonendus CAt) qua-
druplus cubus ceriente coefficientis plani, cedit Colidi datx menlurx qua-
draco. Ouocirca binajam proteruntur Pheoremata.
E E O R E M A I.
EF A cubus F BplanOter in A aequetur D Colido: est B planum quod HE
sub laceribus, a quibus qui hunecubi, ditterune per D Tolidum, _ ACA
differentia laterum.
Ex Zecerico:
Data differentia cuborum, es rectansulo sublateribus, invenire differentiam
laterum.
SirC. = GN. aquatur 7. ESt = seu 2. rectaneulum sub lateribus à quibus cnbi disferunt per 7. 8
fit P N. differentia laterum: ex hyporhess laterum 1. (3 2.
I H E O R E M A FI.
A cubus = B planO TeFin A aquetur D Colido, praestet aurem D Colidi
quadratum quadeuplo B plani cubo: est B planum rectangulum (ub la-
ceribus, a quibus qui tiune cubi componune D Colidum, e hc A aSOr C82
cum laterum.
Dato rectangulo sub lateribus, ex acgrecato cuborum, invenire latera.
Ex ZerericO: