# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/845634801:0324
# Permalink to this reading: https://leibnizlegible.com/page/845634801:0324?run=74
# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 318, page id 845634801:0324
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=324
# Source image: https://digitale-sammlungen.gwlb.de/content/845634801/jpgs/default/00000324.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 66 lines, status machine
# Lines: 66 recognised, mean confidence 0.87
# 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.

318
snccedat, adtirmata riacuel esaca, nesatx adtrmata: ac proportiona
les illae sine semper alterna, de mulciplices quidem in prima adtectione per
unicatis crementum, in se cunda per numerostriangulOS, In Fertia Per nu
meros quos rocantprramidales, in quarta per numeros triangulo. trian.
gulos, in quinta per numerostriansulo. prramidales, non quidem abuni-
tate ur in porectarum geneli, (e d a binario (UUI dUICeNLCSIHCKCENEUM.
In nocis sit prima concinue proporcionalium r, eademque triangulorum rectangulorum semiby.
potenusa.
Secunda vero concinue proporcionalium LN, quae intelligitor basis crianguli ad angulum persimentis
submulciplum. Erit
(Dupli.
Tripli.
Ouadrupli.
Duincupli.
Sextupli.
Sepcuplio
Octupli.
(Noncupli.
Preo in insinicum concinuando ordine, adscica siplacet numerorum continue trianeulorum à bina
rio suum ducentium incrementum tabella.
AD ADR. LCOM AAL L ROBLE M A
BE
tCC
+C  7 X
lBdC.
AOCC -8 CC + 2090- 169 F2
LCCC - 9OOC + 27OC -- 30C 1 9N
B
A L OL E M a
Si Fuerine criangula rectansula aequalishyporenulx, quorum primi
angulus acurus sit in libmulcipla ratione ad angulos acuros liccedentium
ordine triangulorum, ad acutum videlicet secundi subduplus, Fertii (ubEI
Dlus, quarci lubqua druplus, ee co continuo ordine; construatur aurem le
rieslincarum rectarum continue proportionalium, quarum prima lEx qua
lis semi hyporenulae, secunda perpendiculotriansuli primi, inter succt
dentes continue proportionales et luccedencium triangulorum bales a
perpendicula, haec erit aequalitas.
Prima bis, minus cerria concinue proporcionalium, erie aequalis balicrian
gulisecundi.
Sccunda ter, minus quarta, perpendiculo trianouli cereii.
Primabis, minus cerria quarer, plusquinta, bali erianguli quarti.
Secunda quinquies, minus quarta quinquies, plus sexta, perpendicute
crianguli quinti.
Prima bis, minus certia novies, plus quinca lexies, minus sepeima, bali
criansuli sexti.
Secunda septies, minusquarta quaterdecies, plus sexta sepries, minus
octara, perpendiculo crianguli seprimi.
Prima bis, minus certia ledecies, plus quinea vicies, minus seprima octies,
plusnona, balitriansuli octari.
Sccunda novies, minus quinta cricies, plus sexta vicies septies, minus
Octaranovies, plus decima, perpendiculo crianguli noni.
Ecica in infinitum. inverlo eo, qui in antecedente Theoremate expot
cusest, ordine.
in nocis, Sic prima concinue proporcionalium r. ealemque communis rrianeulorum rectaneuloruit
semits porenusa.
Secunda
d
plum
uiod
Progre
e A
subrena
A cir
a
Elum