# Leibniz Legible — https://leibnizlegible.com
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# Title: [Traite Du Triangle Arithmetique, Avec Quelques Autres Petits Traitez Sur La mesme Matiere] Traité Dv Triangle Arithmetiqve, Avec Qvelqves Avtres Petits Traitez Svr La mesme Matiere (shelfmark Nm-A 605)
# Folio 13, page id 1023099829:0063
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1023099829&page=63
# Source image: https://digitale-sammlungen.gwlb.de/content/1023099829/jpgs/default/00000063.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 52 lines, status machine
# Lines: 52 recognised, mean confidence 0.78
# 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.

ris
ol
de
s
l
 p oso po Eoo qo  E Epo
ese
GONTINVOLrM PROMIL
S F
DE AFATLAIS OVI PRODVeNE
ex mulciplicatione numerorum lerie naturali
Secici.
PTOCCdEREIM.
Tmeri qui producuntur ex mulciplicatione numerorum
ninuorum a hemine, quod sciam, examinari sunE. Ideo
neisimpehonempe, producti continuorum.
une aurem gul ex duorum mulciplicarione FOranEuE;
reiste, 20, qui ex, 4 in s orirur, ee possent dici secundu
Sune qui ex es larione Formaneur, ve ilte 120, qui Cx, 4
in s in 6, Orirur ee dici pollene ternae speciei.
Sic quartae Beciei dici polenE qui ex QuaFROE HUMeTOTUM CONTI-
nuorum mulciplicarione Formantur, de sic in infinirum, ita ve, ex mul-
cicudine mulciplicatorum. Species nominationem exponentis Porrire.
EUT; e Sc nullus esser productus prima speciei, nullus est enim pro-
AIICEUS Cx VHO FAMEHM AUMICTO.
Primum huius eractaruli cheorema, illud est quod obirer in praece-
denre cractaru annoranimus, quod quaerendo, reliqua invenimus, ime
Se generalem porestarum relolurionem; adeo sricta connexione sibi
UEuO CohRreME veritateS.
Prop. 1.
Si sinc duo numeri quilibee; Productus omnium numero-
rum primum praecedentium, est ad productum rocidem
numerorum concinuorum a secundo incipientium; ve
productus omnium numerorum secundum praeceden.
rium, ad productum coridem numerorum continuorum
a primo incipiencium.
Sine duo numeri quiliber 5, 8. Dieo productum numerorum, 1, 2, 33
iis
+
tinuorum
progressione
n
lohutr copaeriom
70t
servavi
0
 ex
estseries progcessionis
nuncs
nivae reducendo
ad unum nomen
E + 113, 4 + 12,+ + 13