# 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 35, page id 1023099829:0085
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 38 lines, status machine
# Lines: 38 recognised, mean confidence 0.92
# 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.
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# After the first blank line: the recognised lines in reading order, one per line.

S V M MI A.
ve quod vlcimum cA, à numero qui non sit eius pro-
gressionis, et isti 5, 8, IF, T4, quorum prorressio per ter-
narii differentiam procedit, es a numero 5, ipsiproorel
sioni exrranco, exordium sumit. Et quod lane taeli-
cicer inventum est, tam mulci differentes casus, vni-
ca ac generalissima resoluit methodus; adeo lim-
plex, et absque litcerarum auxilio, quibus difficiliores
esent enuntiationes, paucis lineis contineatur. Ve ad A.
nem problematis sequentis parebit.
Definitio.
Si binomium, cuius alcerum nomen sIC A, alcerUM verO nUMCTUS
quilibee re3, nempe A F 3, ad quamliber constiruarur porestatem re
ad quarrum gradum, cujus haec lc exposirio,
A+ Y 12, A F 54, A Y 208, A F 81.
IpSE numeri, 12, 54, 208, per quos ipse A mulciplicarur in singulis
gxadibus, quique parrim ex numeris hguraris, parrim ex numerO 3, qui
binomii est lecundum nomen, formantur, rocabuneur Coefficientes
ipsus A.
Erie ergo in hoc exemplo, 12 coefficiens A cubi, de 54 coefficiens A
quadrari, e 108 coefficiens A radicis.
NumerUS verO St numerus absolutus dicerUE.
Temma.
Sic radix quaeliber, 24; alcera vero sic binomium 14 F 3 cuius pri
nam nomen (ic r4, alcerum vero alius quiliber numerus z, ica ve ha-
rum radicum, r4, X T4 F 3, differencia (Ic 3. Consticuaneur ip (xe in quo-
liberoradu rein quarro, erso quarrus gradus radicis 14. est 14 . Ouar-
cus veco gradus binomii, 14 Y 3, eAt,
24 7 12, 24 F 54, 24 Y 108, r4 Y 81
Cujus quidem binomi primum nomen 14, eosdem coefficientes sertitur
in sinculis eradibus, quos A sortitus est in similibus gradibus in expo-
sitione ciusdem gradus binomii A + 3, quod rarioni consentaneum est,
harum vero porestacum, nempe huius r4 X huius 14 7 12, 243754
24 Y 108, 24 F 81, differencia eA, 12, 14 7 54, 14 F 208, 14 + SI
qua quidem constar Primo, ex radice r4 consticura in singulis gradibus
Propoliro gradui guarco interioribus, nempe in tertio in secundo et in
primo, et in ruoquoque mulciplicarâ per coefEcientes quos A CorrieuT
in similibus gradibus, in exposirione eiuldem gradus binomii A Y 3.