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# Title: Leibniz-Handschriften zur Mathematik LH 35, 4, 16
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dota dividendi ratio reducitur ad sublationem incognitarum simpli-
cium, tanquam casus geer specialis ad Generalem. Exhibeamus rem in exemplo, ut
sit Divisor 10X + IIX + 12
Dividendus 20X + 21X + 22X + 23X + 24
Erit Operatio contracta 30 X + 31 X + 32X + 33 X + 34
Quotiens purus 30X +31X + 32,: 10
Fractio adhaerens
cujus numerator
est Residuus
Nominat
X +34
est Divisor:. .. 10X + 11X + 12
Lexoperationis
10.20= 10. 30
10. 21 = 10. 31 + 11. 30
10. 22 = 10. 32+ 11. 31 + 12.30
ete
IL
etc
Unde tollendo ordine incognitas 30, 31 etc
habetur cujusque ex his incognitis valor, et ex
his quetiens pariter ac Residuus.
valorem quotientis ac Residui, itemque
Super est ut demonstremus (aequationes in Lege operationis contentas. Itaque
tota exempli operatio ex explicita  exhibeatur, ordinatione tali quae
commodissima visa est:
ORDINATO DIVISIONS
CHARACTERIS TICA
+37
20 ac
ouidenis 20+21, +22. . t 23.
c 1ud) = 1t.2B,
((= 10. 11. 21 10. 12. 2
 1. 1o F 112 20,
Hic 30 = 20. 31 = r21, - 11. 208
10. 10. 11. 22 = 10. 10. 12. 22
+ 10. 11. 12. 20 + 10. 12. 12. 20.
+ 10. II. II. 21 4 10. 11. 12. 217.
= 11. 1L. 1. 20 = 11. 11. 12. 20.
10. 12. 20
= 10. 11. 21
+11. . 20
32 = 22, = 2, 20_ - 10. 11. 21 + 11. 11. 20
 B Rm XD e3AX
33= 23 + X
+
lic DY VS
∞10. 12. 21+11. 12. 20 = 10. 10, 11.22+ 10, 11. 12. 20+10. 11. 11.21 - 11. 11. 11. 20
102
10
= 10. 10. 12, 22F10. 12,12, 20+10. 11. 12. 21 -11. 11. 12.20
stellulae replendae forent, sini (quae loca vacua designant) si divisor esset
10
34 = 24+ X + X +
altior, et in eo esset etiam 13; si scilitet esset 10X3 + UIX + 12X +13.
jam valores ipsarum 30, 31, 32, 33, 84 consideremus. 30 = 20. 31 = 21 = 11. 26
seu 3t = 21 - 1, 3B seu 19,21 = 10. 31 11. 30. e
31= 21 - 11. 20 seu 31 = 21 - 15. 30 seu , 21 = 10. 31 + 11. 30
32 = 22 - 12.30 - 11. 31 seu 10. 22 = 10. 32 + 11. 31 + 12. 30
33 = _n 234X - 12. 31 - 11. 32 seu 10. 23 = 10. 33 + 11. 32 + 12. 31. E vanescait hic 13. 30
via 13 ab est
Et ita porro habemus ergo aequationes in Lege operationis continentas.
Apparet etiam ex nuda inspectione valores R Quotientis et Residui
uoniam ergo Aequationes in Lege operationum contentae simplici
esse quales assignavimus.
admodum regularitate procedum, h et earum incognitae sunt simplicis gradus.
hinc regula aequationum reducitur ad regulam ad regulam jam a me
inventam tollendi simplices incognitas, ejusque harmoniis suas proprias seu
visionum
speciales addit. Sed placet ad jicere modum inveniendi valores temminorum
operationis, 30, 31, Ck, maxime proprium et Axalysi converientem, qui cous
comparatione succetsus cum quaesito. Nempe 30XF 3X +DZ multiplicabimus per
empe Quotientis partem pulam 30X2 + 31X + 32 multi plicabimus per divisorem
producto ad damus residuum 33X+ 34, et proveniet formula coincidem
 atum divitendo 20X +21X+ 22X + 23Y +24. Unde habebuntur aequationes comparatitis
Uni fiunt aequationes copanempe easdem quas ante 10. 20 = 10. 30 10. 2 = 10. 31 + 11. 30
1020(+ 10 21  t 10. 32X +IO2YH034 2t 10. 22 = 10152 +11.31 + 1. 30  10. 2) = ,0 33 + 12 32 L 12.31 et 1024 = 1 a)4 + X + 12. 32.
ubi ex natura residui  in ultima aequatione contingit hiatus per stellulam expressus
neupe abest 11. 33. cujus rei ratio est, quod ultimi germini operationus, qui residi
istituunt, non nisi inne hoc loco 33 et 34 non nisi per 10 multiplicaatur
non vero pes 11 et 12. se cus fuisset, si continuata fuisset divisco. in calculi exeem
esset 11. 33. ascriberdo ei notam seu includendo, ut regularitas melius servetur
otienre
divisione. Item inquisitio
34 = 40X + _, .B3, +
e
quationit
sine Residuo eont
+10. 1. 22
20X taX +2X +23XF24
10x +
+ 1
Qvonens totus
equ. IOX +uXFC
30X +31X 132, 10X ux+12, F3X13
con ronauxter
30X2+ 31X + 32 (.10
10X2 + 11X +1
10. 30X7 10. 31 X3 +10. 32X H1O. 33X1
+ 11. 30. +11. 31. + 11.32X X
+13. 30. +12. 31 (ri 10 Xt + 11X + 12
40X + 4 1(: 32
B3X + 3
33. 40X43
 
10. 35X + 11. 337(+ 12. 33
ox ruxr
13X + 34
ost as.
his etam aaebitur sories insine
com
jui
dasper
uti WX FIX + R,
pensura, siquitur subtalia
lnis in tad laita
dibunt omnes e4
 r. 313a iams at sec lolos trctatioum uiterarum
aequ.
EoX + 31X+32 + 2+
tione fingere licebit pst etia