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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 B 11
# Folio 22v, page id 00068261:0044
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Utile credo erit adhibere Canonem
generalem divisionis à me deter.
minatum; qui prius mutandus
in inversum inde applicanda
additio lgadica, sed servata lege
homogencorum, etsi enim
sit bb = b in dyadicis, hoc
tamen initio dissimulandum
Et quia sanon divisconis a me
datus est secundum divisionem
vulgarem, ubi possunt residui,
fiat et canon inversus qui
solum locum habet pro divisione
Sine residuo succedente, appliceturque
etiam ad dyadica. Et comparando
binos canones invicem prodibunt fortasse
Compendia. Utilis consideratio de
conservanda in dyadicis lege homogenectum
Egregium, quod apulliata canont generali ad
casum praesentem, ubi omnes divisoris nole
dividendo sunt aquales interse et unitate
hoanescunt pb legen femogeneor
si posset illic lex numerorum haberi spes
esset successus etsi non fieres additio
euadica
deberet enim succedere tan-
dem destructio
Videndum an extractio jadicum feri
possit inverso modo saltem ni dyadics
eoent fortesse etium solvi priblemala
Rolum
gundiulur et similia sine
additione hyporea, quia
ed C b+
e
in apactis succedere tandem
rehet extractio, ne sit opusfiumpraeter
1
assumtas seu quae cila
ictas, quae sunt ovel 1, sumere alias quae
da
non smultales ad vilandam illam additionem
Pre
E
tEdee
+VB EdB
Ea 
ed
3=0
1-2 + 2
C AItaB al
B- ab
0
e+1B
1- 21B
it 1CB+ BdCB fit d =1
e
Non dum adhibita est consideratio
quod b est 0 et c est _B et
Bt B n Rest 8 et daet
-P.
is
B +b 2lβ- 8
+BSc
canon extractionis quidra
torum cuborum aut Biquadrulom
quaeritur generaliter sum etrom
pro non duadicis, ut Canon divisio
nis.
at comparationes et destrncti
nes institui possuit
20+21XL Z2XX + 23 X+ 2 X
26FEyX+XXt3+2.24X + 2.25. X + 22026X +222 X+ 220 29X
20+ ax +n Xx + B X+2X
2. 23
2. 21. 
5u
2nn
2. 23.24
2. 22b
14. 24
P +HXHLXL BX L 14X + BX +16X + 17X + 184
ex canone divistonis potest fieri
Canon Extractionis quadraticae,
si ponantur aequales divisor,
+1. 2t_AR + 24.2 X + 2, 21. 23X
quotiens, et edanescant residuus
2020 -10
21 - 1 22 = 2 0
23 = 13 - 2. 21. 22
24 - 14 2. 21 25- 1. 22. 21
25- 15 vel 10 =20. 20
2.20. 2 = 11 2. 20. 22 = 12 - 21. 21 8. 2021 = 4. 20. 12- 4, 20. 20. 21. 21 11= 2. 20. 21
J. H1. 12= 22022 +1. 2121
Ergo 8. 28. 24 = 4. 26. 12 - 11. 11 2 20. 23 = 13 221. 22 Haut
2.4. ZC multiplicetur per 20 et per 8. 20. id est per 8. 202 firt. patio
2. 20. 24 = 14 = 2.21. 23 - 1. 22. 22 multiplicetur ob 22 22 per 64, 20 ob 21. 23 per. 2. 21. 23 per  16.20
16. 20223 = 8.20313-16. 20.11, et fial 16, 20. 23 = 8. 28.13- 4. 20311.12 + 113
ermo sussicit multiglicatio per 64. 206. Et prodit 128. 20724 =64. 205.14 64 2 220. 8. 20582. 21. 23.-(4, 206. 24 22
milati fiat 21 = 00. 11 22 = 00. 12 - 2  8. 28 11 - 4. 2. 1. 2+15 -1 6. 202 - 113. 8. 20. 11. 12
et fict. 128. 20. 24 = 64, 20.14 =16. 2011 +8
1.00. .  08. 00. 1. 11
082 (i. 12 20 + d6. 1 24 = 00. 14 - 2 91. 2  222c
2
re aer
24. - 0 6r. 14. 25 64. c5. 14 20 - 34. co . 1. 13 B, 60. 15. 1 20 00t. 1+ =  16. 00. 12. 20 + 8. 08 1. 120   - 602 11
supplendae legis homogeneom causa alhibeatur
e
20
ut divisiones vel extractiones, sint iractae duplici modo obtinemus, uno cum residua evanescunt; alter um et ita tot sunt
 128. 20
praestat meo sanone divisione uti, eumue hac transterre
d de bini canones naus divisionrs prorsan, alter
dem prdire debent quotientes. Generalitem austitur
destnctorie aquationes, quol notae in drasor ad summan. Altero 
potea ista ductum sunetium comparatio 1. Sadendu Hic plares prodtunt aequationes quam necesse est, quad videtur itilead nova
uni plures utrobim enim
divisionis petrorsum comparentur inter
theoremata