# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/845634801:0030
# Permalink to this reading: https://leibnizlegible.com/page/845634801:0030?run=74
# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 14, page id 845634801:0030
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=30
# Source image: https://digitale-sammlungen.gwlb.de/content/845634801/jpgs/default/00000030.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 57 lines, status machine
# Lines: 57 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.

A A R F E AE A N A L Z F FCF
Ouoniam igitur est
Ac
8 quadc.
quadtacum
Facir
A quadr.
B cubus Bg. quad.
Aquadc. A cubo.
cubus
a quadra.
B. quadi quadenrum
Et ira licebic progredi in infinitum.
A cubo
C ONSECT A R I V M.
Ouitr.
Teaque A sx Cexles maonitudinum in continua proportione, est,
Vebrima, ad Terriam, ica Ouadracum e Prima, ad Ouadrarum e Secunda.
Fx uc Prima, ad Duartam, ita Cubus e Prima, ad Cubume secunda.
Ec Prima ad Duincam, ur Ouadrato. quadracum e Prima, ad Ouadrato. quadeatum
e Sccunda.
Ex ita in insinicum constanti ordinc. FnimVerO Ex POLIT ChCSI SuNE ContinUIC pTO.
portionales.
Prima, A Sccunda, B, Terria, dr.. Ouarta Lao. Tuinez 2 . guade. c.
AC quoniam Prima est A, tertia B meraum DuCatuE urraque in A, ca itaque ductio
ne cum sic à communimultiplicante, non immutabitur Proportio, quare A g 3 quadcac.
exit ut A quadrarum ad B quadratum.
Aque quoniam prima est, A quarTa P ab DuCatUE veraque in A quadratum, c2
isitur ductione, cum sic a communi mulciplicance non immutabitur proportio, quare
A adE gumm exir ur A cubus, ad B cubum.
PaTIEEF, CUM SIEPrima A quineZ ad. DuCatuY utraque in A cubum: ea igicuE
ductione, cum sic a communi mulciplicante, non immurabitur proportio, quare A ad
Bquadr nadc. erix uE A quadearo quadratum, ad B quadraro. quadratum.
Nec dissimilicer in ulcerioribus reliquis, licet arguere d exemplificari lacera ad invi-
ceminratione simpla, porestates carumdem inratione mulcipla. Porectas rationis du-
Pla est Ouadraru. Friplae, Cubus. Ouadruplae, Ouadrato. guadratum. Ouincupla,
Ouadrato cubus, ee ca in infinicum serie ee methodo.
PR OPOS LFFO ITI.
Ncer duo propolita quadrata exhiberemedium proporrionale
PEOpOnanEuE duo quadrara A quadratum, B quadcatum. Oporteatinveniceme
dium inter ea proportionale. Ac rero consticura A prima, B sccunda, extibetur Cx ay-
cecedente rertia proportionalis, ex le habet leries hujulmodi.
Prima A, Secunda B, Fextia Bquadr.
Ducantur omnes in A, cui videlicet, cum adplicatur B quadratum, oritur certia.
Ouoniam isitur A est communis mulciplicator erium expolicarum proxortionaliums
a communi aurem mulciplicanre non immutatur proporrio; erune facta quoque ab A
in proportionales, proporrionalia. Sunt aurem Facta;
A quadratum, B in A, B quadracum. Ouare ineer duo propolica quadrata extibui
musmedium proportionale.
PR OPOS FFFO IV
Icer duos propolitos Cubos exhibere duo media continue proportio.
nalis.
Proponantur duo Cubi A cubus, B cubuS. OpOrteat exhibere duo media Inret La
continue proportionalia. AC vero constitura A Prima, B Sccunda, extribeneur ex
pro.
Oynra proporcionalis.
Geaal. e cub