# 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 14, page id 1023099829:0064
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1023099829&page=64
# Source image: https://digitale-sammlungen.gwlb.de/content/1023099829/jpgs/default/00000064.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 36 lines, status machine
# Lines: 36 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.

D F L V NI F R O R V ML
4qui pexecedunt, 5. nempl 24; esse ad productum coridem conrinua
rum nucteorum, 6, L0, IL, Hehhpe 7920: reproductum numerorum
1 2,343556, 7 aclaul 6, Hempe 5640; ad productum coridem
concinuor CLO 5, 6, 7,8,9, 10, EI, nempC 1663200.
Exenim productus numerorum, 5, 6. 7, ductus in productum istorum.
2, 2,3. 4, efficieproductum horum, 1, 2, 3, 4, 5, 6, 7. Eridem productus
numerorum, 5, 6, 7 ductus in productum numerorum, 8, 9, 10, XI.
efficie productum horum, 5, 6, 7, 8,9, 10, II, ergo, re productus nu-
merorum, 1,2, 3, 4; Ad produetum numerorum, 1, 2, 3, 4, 5, 6,7; lta
productus nuerOTum, S, 9, 10, IE; ad productum numerorum, 5, 6
7383 93 te3 1t.
e
Propi
Omnisprocucus d Guorlibernumeris continuis, estmulri-
plex producti a coridem numeris continuis quorum pri-
mus eAtrnicas; ee quotiens eltnumerus figurarus.
Sirproductus quiliber, a rribus r. g. numeris continuis, 5, 6, 7, nempe
210, _ productus coridem numerorum ab rnirare incipiencium, L, 2, 3.
nempe, 6; Dico iplum 210 esse mulciplicem iplius, 6. Fc quocientem
esle numerum Aguracum.
Erenim ipsc, 6, ductus in quintum numerum ordinis quarri, nempe,
35, xquacur ip( producto ex, 5, 6, 7, ex demonstraris in cractatu de Or-
dinibus numericts.
Prop.
Omnis productus a quorliber numeris continuis est multi-
plex numeri cuiusdam figurari, nempe eius cuius radix
est minimus ex hisnumeris, exponens vero ordinis est
ruicare major quam multicudohorum numerorum.
Hloc paret ex praecedenre. Fernica verique connenir demonstrario.
Monitum.
alrer alcerius lic quoriens. Ira ve quilibet productus à quorliber numeris
concinuis, divilus per productum coridem numerorum ab rnirare inci-
piencium, re Secunda propolicio docer heripolle, quoriens sic nume-
rus Agurarus in rerria proposirione cnunriaTuS.
Ambo divilores in his duabus proposicionibus osten(i, tales sunE, ve