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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 B 11
# Folio 1r, page id 00068261:0001
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soredita
inquisitio in Anatus lsorese primutivos; et rerida-
tivorum divisores
Quia Potentia ipsius a +b secundum e, est
deo si a + C a b + e, et 
i
b2 + C. P-1. 8- 2 C3
1. 2. 3
enes
+etc. usqu ad Ba b seuntad b
odsi a = 1 = b, fict 1 + 8 + e. C2l + e. eal . 82 + ete usque ad +1.
Itaque habemus
hodem argumm 22 = 2 = e + C. C-1 + C. e l.  2 + etc. quodsi jam e sit humerus primitivus oluu
1.2,2
 est necesse est 2. =2 posse dividi per C. Et, si sit primitivus impar,
id est major quam 2, necesse est etiam = =1, posse dividi per e.
afedege sed si e non sit primitivus, aliquis exterminis, 2-2 componentibus
poterit deprimi, ubi scilicet inter denominatores reperitur aliquis divisor ipsius e
EqtaEt tunc non amplius totum dividi potest per e
posus
sed haecnota primitivi difficiliscest prima specie, nec inscrvit ad eum agnoscendum
et mumeus
Hisime enim assurgeret italis fli, numem.
is nisi quibusdam artibus adjuvetur. Considerandum itaque est, hoc dici: Numerum patis
progressionis Geometricae duplae ab unitate incipientis, quem compendio
tam cujqus ex ponens sit
eesus divisionil
ta aliunde autem
datum aliqueri
sumus numeros alicujus progressionis Geometricae per tatem divisos dare rinom
2.
esidpo
residuorum semper recurrentem, it constantem ex numeris minoribus
divisore. Itaque sufficit haberi seriem residncrum, ut reperiatur an loco deside
proposito cato inter eos sit 1. nec opus est immanes illos numeros progressionis Geo-
metricae reapse adhibere et dividere, cum Numeri sufficiant divisorem non excedentes
porro  constat, si residuum divisionis multiplices per aliquem
niorem
multiplicatorem, et productum divistas per cundem divisorem idem prodire
residuum, ac si ipsum dividendum priaris divisionis per eundem multi-
plicatorem multiplicasses, et productum per priorem divisorem divisisses.
A sit divisor d dividendus f,  quotiens divisionis q residuus Y
patet esse f = g4 FY jg +r sit multiplicator m, fiet inf = mgg + mr
orro sim Mr divisisses per g se
fit Px IY = seu si fit X n si sit  Cx (M het) = R (i f.). vel omisso
ipso g
compendi causa atque sibintellecto communi divibre B (M EF) = R (n f)
Itaque itaque si velimus invenire Residuos Numerorum progressionis Geometricae
per ab eodem divisore, non est necesse ut ipsos numeros dividamus, sed
residuos multiplemus per progressionis constantem multiplicalorem, et productum
per constantem divisorem dividamus, sed operae pretium erit in progressione
1892
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Exponentes