# 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 18, page id 1023099829:0068
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1023099829&page=68
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 43 lines, status machine
# Lines: 43 recognised, mean confidence 0.88
# 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.

VMERLCARVM
POTESTAT
5
 o 
s
 o 
VMERLC ARVM
ENERALIS RESVETEI
ralem Nuarelicarum Porestarum Resolurionem inqui
haec mihi venic in mencem oblernatio; Nihil aliud
TerCadicem v. 8. quadratam dari numeri, quam
ere dus numeros aequales quorum productus aeque
cur numero dato. Sic e quaerere radicem cubicam nitril
aliud etle quam quaeEres numeros aequales quorum productus sit
darus, de lic de
Traque, Porestaris cuinstibet Tesolurio, est indagario roridem nume
torum aqualium, quocesponens porestaris conrineernicares, quorum
productus aequerur daro numero; Porestares enim ip (a nihil aliud sune
quam aequalium numerorum producti.
Sicur enim in praecedenti rractaru, esimus de numeris qui produ-
cuncur ex mulriplicatione numerorum narurali proorestione proceden-
rium, sic ∞ in hioc de porestaribus cractaru, agieur de numeris qui pro-
ducuneur ex mulciplicatione numerorum aequalium.
Visum est ieaque quamproximos esse ambos hos rractatus, ex nihil
elle vicinius, producto ex aequalibus, quam productum ex concinuis
Colius rniraris incremento differentibus.
Ouaproprer poreltarum relolurionem generalem, seu productorune
ex aequalibus relolurionem, non mediocrirer pronectam esse censui
cum eam productorum ex continuis generalis relolurio praecesserit.
Daro enim numero, cuius radix cujuluis gradus quaericur verbi gra-
eia guarti, quaeruncur quatuor numeri aequales quorum productus ae
quecur dato; Si erso invenianeur expeaecedenre eractaru, quaruor con
rinui quorum productus aequerur daro, quis non vider, iuventam esse
radicem quaelicam, cum ea sic rnus ex his quatuor continuis; Minimus
enim exhis quaruor, quater lumprus de cories mulciplicarus manifeste
inor est producto continuorum, maximus vero ex tis quatuor, qua
ter sumptus ac rories mulciplicarus, manifeste major est producto con-
cinuorum; Radix ergo quae sira vnus exillis est.
Verum lacer adhuc ipta in mulcicudine; Reliquum est igirur re eliga.
tur, e dilcernatur quis ex conrinuis Carisfaciat quaestioni.
Hluic perquilicioni nondum Forrelaris incubui, crudam camen me-
dirationem proferam, alias, si digna videatur, diligenrius elaborondam.
EIS.