# 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 36, page id 1023099829:0086
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 36 lines, status machine
# Lines: 36 recognised, mean confidence 0.93
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
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# After the first blank line: the recognised lines in reading order, one per line.

36
POTESTATVM NVMERLOARNM
Deinde, ex iplo nuero, 3 qui est differentia radicum consticuro in
propolico quarto oradu, numerus enim absolutus 8t est quartus sra-
dus radicis 3. Elinc igieur elicierur Canon iste.
Duarum similium porestarum differentia, aequatur, difte-
rentix radicum consticuea in eodem oradu in quo lunE
porestares propolicae; Plus minori radice consticuta in
Singulis gradibus propolio sradui inferioribus ac in v.
noquoque mulciplicara per coefficientes quos A lorti-
recur in similibusoradibus, si binomium cuius primum
nomen esset A, alterum vero esser differentia radicum,
constiruererur in eadem porestare propolica.
Sic ergo differenria inter 14 _ 2F, erie 12, 2V, F 54, ZL, F 108, II,
8T.
Differentia enim radicum est 3.
Ec SIC de careris.
ad summam Potestarum cujustibet progressionis inve-
niendam unica ac generalis methodus.
arithimetica
Acis quorcunque numeris, in qualiber progressione
a quouis numero inchoance, invenire quarumuis
porestatum eorum summa.
Quilibet numerus, 5, sit initium procressionis quae per
incrementum cujusuis numeri verbi graria ternarii pro-
cedat, ex in ea progressione dati sint quorlibet numeri
verbi oratia isti, 5, 8; 1F, 24, qui omnes in quacunque
porestate constituantur et in tertio gradu seu cubo. Opor-
tet invenire summam horum cuborum, nempe, 5, 7 8,
11. F 143
Cubi illi Tune 125 F 512 + 1331 f 27 443 guorum
Cumma CR 47 12 qua quaeritur e Tic invenitur.
Exponatur binomium A Y 3 cuius primum nomen sit
A, alterum vero sit numerus 3 qui est differentia pro-
rressionis.
Consticuatur binomium Boc A Y 3 in gradu QuartO