# 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 10, page id 1023099829:0060
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1023099829&page=60
# Source image: https://digitale-sammlungen.gwlb.de/content/1023099829/jpgs/default/00000060.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 42 lines, status machine
# Lines: 42 recognised, mean confidence 0.91
# 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.

PIVMERTCORNM ORDTNEM
Ecens Poclctus ille vlrimus numeri dari nempe 1392, Factus est ex
numero daco, s8, mulciplicaco per productum numerorum, 1, 2, 3,43
nempe, 24. produccus veropracedens hunc vlcimum nempe, 348, ta-
ctus eAt ex numero dato, 58, mulciplicato per productum numerorum
, 27 3, nemPC, 6.
Ergo productus numerorum, 6, 7, 8, non est major producto nume
rorum I, 2, 3, mulciplicaro per 58. Productus vero numerorum 6, 7, 8,
9, est major producto numerorum, 1, 2, 3, 4, mulciplicato per 58, ex
constructione.
Jam numerus ordinis se rri cuius radix est, a nempe, so multiplicarins
Per numerOS, 1, 2, 3, ae quarurproductonumerorum, 6, 7, 8, cx demon-
sraris in cractarm de ordinibus numericis.
Sed productus numerorum 6, 7, 8, non est major ex ostensis, pro-
ducto numerorum 2, 2, 3, mulciplicaro per dacum 58, igitur productus
numerorum 1, 2, 3, mulciplicarus per, 56, non est major quam idemn
productus numerorum, 2, 2, 3, mulciplicacus per dacum 58. Igitur 56.
non est major quam 58.
Tam sic 126, numerus ordinis sexri cuius radix est 5. Igicur iple 126,
mulciplicatus per productum numerorum 1, 2, 33 4, ae quatur producto
numerorum, 6, 7, 8,9, extractaru de ord. numer. Sed productus ille
mumerorum 6, 7, 8,9, eA major quam numerus dacus sd mulciplicars
per productum numerorum, 1, 2, 3, 4, ex ostensis. Igieur, numerus, 126
mulciplicacus per productum nuerOrUM, 1, 2, 3, 4, est major quam
numerus dacus se mulciplicatus per eundem productum numerorum
2, 2, 3, 4: Tgirur numerus, 126, est major quam numerus dacus, 58.
Ergonumerus 56 sexri ordinis cuius radix elt, 4, non ekt major quam
numerus darus, numerus vero, 126, ciusdem ordinis cuius radix s eAt
prexime major, major es quam dacus numerus.
Ergo ipse numerus, 56, maximus est eius ordinis qui in dato conri-
meacur, _ eius radix 4 inventa est.
d. E. F. L. D.
DE NVMERICOAVM ORDTNVM
RESOLYEIONF.
Problemit 3.
roquolibernumero, et ejus radice, invenire ordi.
LIS CXPOHeNTE
M.
or eteno Plobrema a praecedente, radix enim, ee exponens
Ordinis, RCCIPEOCC COHMETTINEUT, ita vE dato numerO v. 8. 58, ee cius
radice, 4, reperietur exponens lui ordinis6, eadem methodo, ac li daco
numero iplo, 58, _ exponeure ordinis, 4, radix, 6, eRer invenienda