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# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 30
# Folio 21r, page id 00068124:0041
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# Lines: 26 recognised, mean confidence 0.94
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est nnst soregrssicit sendem esiot
Methodus generalis investigandi, an aliqua formula rationalis
integra, secundum literam quandam ordinata, sit divisibilis per formulam
rationalem integram ejusdem litere.
Methodus generalis investigandi divisores
Formularum atid rationalium integrarum
ex datis divisoribus numerorum rationalium integrorum
Formula vel cequatio ita transformetur, ut omnes ejus radices fiant
falsae, adeoque omnes termini sint afsecti signo + quod praestare jam quodam
modo docuit Cartesius.) salis sit quaecunque, O = p + qx + rxX + 5X +
txF F VXS + WX + etc. Averitur, an et quae eum dividat, velut
bFCX + dXX F ex3 + etc = D. Erit b unus ex divisoribus ipsius p
et, si W x6 et ex3 sint termini sumni; erit e unus ex divisoribus ipsius
W. quaeruntur b, c, d, C
Prox sumatur numerus h, integer affirmativus rationalio) major qua
vis harum quaesitarum b, c, d, e, quod fiet, sismajor ssit) quavis harum datarum p
dl
a X, Sit, v, i, etc. Utiliter autem ad calculi compendium assumetur ali–
guis quid ex istis 10, 100, 1000, 10001, 100000, vel 11, 101, 1001, 10001, 100001, etc.
Hoc autem numero hsubstituto in formula c, resultabit ex tota formula nu
merus m. Idem numerus hsubstituatur in 3, prodibit n. Qvod si jam
dividi potest c per D, oportet, ut etiam dividi possit in pern, seu ut p+
qh + rhh + 5h3 + th + + vh5 + n hS etc = m, dividi possit per b + ch
+ dhh F eh3 F etc. = n.
Exhibeantur omnes divisores ipsius n p: quaeritur, quis ex ipsis sit n
desideratus) Dividatur quaelibet eorum per h, et notetur residuus primus,