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# Title: Leibniz-Handschriften zur Mathematik LH 35, 4, 5
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Sol. 5
Ut jam investigemus numeros coefficiertes formis praescripi constabat dudum, sed adductum tamen est, ut Methodi successus
rcesut appareret, quam vero alia innumera, et in facile nine ita obtineantur
ine  sequantur, patet. Illudus palmarium est, hinc consequint fieri hinc consequi
prodit ter, quia tres ejus transpositiones, seu conflationes, nempeut Cademratione vel verum provenientem integrum, quoties datur;
aut quotientem finitum cum residuo si placet; vel seriamifinitam, si
malimus, consequamur eruamus
Si quis tamen postremo velit, valores quaesitorum, ,31, 32  3, etc
non exprimi per valores quaesitorum praecedentium jam inventos
verbi grati (nempe 31 par 30; et 32 per 3D 31; et 33 per
et 32 per 28,  3I; et 33 per 30 F, 31  31, etc) sed per initio
datos solos, quod nempelo, 11, 12, 13 etc, et 20, 21, 22, 23, etc.
quod est multo implica (cujus indagatio est multo implicatior, res tamen
ipsa maxime absoluta). rem nihilo minus per combinandi artem ita
quam
consecati sumus sit ergo id quoque per combinandiartem
consequemur, hoc modo: Sit aequaformula div
Farmul Dividendus +10 + uX +1 X + 13X + 14 X etc
divisor -20 + 2X + 2 X + 23X +24, X etc
quotiens ot 31X +3L X + 33 X 134 X etc produendis vel usq ad potestatem, quae
lue a e
proveniens
Residum
e ad
 e +inX
erf 30 = 1020 31 = 19 21 + 1. 20,. 20
-32 = 13. 8.C + 1p. 20. 21. el + 12. 207: 20
=33 = 10. 20. 23 + 11. 20.22 412. 20.21 + 13. 20,: 20
avia. 20. 21. 22 11 20. 21
24 = + 10. 293 24 + 11. 28. 23 + 12. 28 22 + 13. 18. 21 + 14. 207:20
410
2. 10 26 81.13 M. 20. 2182  
10. 20. 24
1.
2
3. 10.2021. . 22  24
 erit -30 = 10: 20 - 31 = 10, 21 + 11. 20,: 20
-32 = 1 10. 20.22 + 11. 20. 21 + 12. 207: 203
-33=
34 =
dif
tum diviso
producendus usque ad potestatem proxime inferiorem summa potestate divsoris
prad
e
10 21
10. 2023 + 11. 20. 22 + 12. 20.21 = 13. 201: 20
(2) 10. 20. 21. 22 11. 20212
10. 20.24 4 11. 2823 + 12. 20. 22 + 13 28. 21 + 14. 2017. 205
10. 213
(3) 10. 20. 21.23 (2111. 29.21. 22 12. 20.25
10. 26, 27
11. 213
fu Et ita porro; ea servata lege, combinationis, ut
(3) 10. 20. 21. 22
(constituendo invicem ducendorum
potentio gradus nc ut 20r ea servata lege combinationis, ut
 quae sint gradus
quarum gradus formalis seu numerus biterarum ate vincat oeficientium ab intiodatorum pro membro
cem duoror
efficien
radum virtualem coefficientis cujus valorem constituunt: gradas
quaesiti
vero men et quorum gradus virtualis (summa notarum ultimarum (quadtum 3+ 1, habet summam
inca
Buin
indicatus) gradui virtuali,  dicti coeficientis quaesiti aequetur
sed ita ut non nisi unaquantitas ex invicem ducendis in
membra sit coeficiens dividendi, reliquae vero sint coefficientes divisorisea
13
lo
quaesiti, (exempli gratia (ipsius 32, valorem, constare d duabus mombris virriti
tium dignum e
Motat sed quoniau menero Et dignu mmitude
partibus una nova, quae  confinet primum coefficientem Dividendi, (nempe 10. 20. 22 +10. 4. 27
altera soriata ea paele quositie progune puro eeneisteie dstauituas ie diui, degu
=sine residuo per sernem
sic membrum quodlibet in valone
ipsius 33, constat ex literis or
notarum ullimarum 3
u
velute  ex digide ado
ex dividente
ar
im ult
ib
1. 2