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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 307, page id 175905688X:0329
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175905688X&page=329
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30, 20
crb
1800, 1
72
COMMENYARESLNLIORaMLIL.
307
nem Colius inventx recta R C accurate exhibetur, propter hujus
cum reliquis alrimmetriam; numero tantum quadancenus ex
iplius ad halce relatione innocescit. Fodem modo inveltigari
queune radices aequationum, plures pauciorèsre dimensiones tra-
bencium.
Caecerum cum radicum inventio res magni sic momenti, atque
eorum, circa quae Algebra verlatur, praecipua: alium modum se-
lixendi dirisores, qui ad aequationem diridendam utiles judicari
pollune, subjunsam, quem communicarit Pacobus à WacRenaei.
Clcrajectinus, Geometra peritissimus, atque in hac Carceliana
Methodo verlatissimuS.
Inveniantur radices requationis x 3 = Z X X - 3O X - ]- 72 ∞0,
cujus ultimus cerminus diridi potest per 1, 2, 3, 4, 6, 8, 9, T2, 18.
24, 36, 72. Unde aequatio propolica diridenda eAt per x 8 L, vel
per x B 2, ec. Verum cum complures hic lint dirilores, de tan-
cum tres hic esse portine, per quos dirilio heri queac: constat, di-
vilionem pluries elle tentandam, antequam forte incideremus in
aliquem, qui qualito Patistacere posset. Ouapropter uc selisantur
illi, quorum prae caeteris est ratio habenda: ausendx lunt radices
vera certa quadam quantitate, hoc est, transmucanda eAt Xe qua-
eio in aliam, cujus rerxe radices sinc dato numero majores. Com-
modissimum autem fuerit ad id assumere + vel 20: quia cum inul-
ciplicatio alicujus numeri insticuitur per L, vel 10, numerusille
sic nonmutatur, sed ipsitancum in finc crphra adjungitur. Unde
Ponendoy ∞ x- L, Cive N ∞y - L, Cxlurg et ae quatio y 3 - 477
=257. + 10000, cujus rera radicesunitate majores (unt reris
prioris de talsae contraunitace minores Fallis. Juia vero in hac e-
quatione, numeri ultimum terminum 100 diridentes, (unE I, 234,
5,10, 20, 25,50,100: ideo diridenda Foret Pery 8 T, rel per Y 82,
vel pery 8 4, ec. quod cum non minorem quam in luperiorire-
quiraclaborem, oporcet similiter exiis quoldam selisere. Atque
adeo cum cognolcatur, ad inreniendas veras radices, dirilores
hujus unicate debere esse majores divisoribus prioris xequationis,
Facile constat, si ex inventis 1, 2, 4, 5, 10, 20, 25, 50, 500 aliqui
idonei lunc ad polteriorem aequationem diridendam, aliquos
etiam inter eoldem unitare diminuros, nempe inter O, L, 3, 43
9,29, 243 49,99, dd priorem aequationem diridendam utiles
tucuros. Dui ur inreniantur, conterendi lune iidem dirilores