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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 325r, page id 00068196:0645
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1 septemtur 9s.
dy = 10 + 1y + 12 y+ 139+ 14 yt ete :20 +21y+ 22y + 9 y + 24y ek
(2)
30 + 319 4 32 1 +33y + 34 st Betc. 20 fit d, L 30 + yd31 + yd3r + 9 d33 + g 3 F 131 229 1ii
fit (10. in 1. 31 + 2. 329 + 3,33y 4 4. 341+5. 35y + 6. 36y3 + 7 27 y etc
1. 31 232 3.33 4.34 5. 35 6. 36
1.31 2.32 3. 33. 4.34. 5.35
1.31 2. 32 3.33 4. 34
etc et etc
20 n d3o du. dir d33. d3+ d35 d36
deo, dyt  d32
d33 d34 d35
d3.0 d31  d32 d33 d34
d30, d31 d32 433
et et et
Haec oq. 4. debet esseidenci
cum aeq. 2. Et cum aeg. 2
ponatur esse formula ratio
naliter in divisibilis
sequitur multiplicitam
per arbitrariam coincidere
eum ipsa 5q. 4.
Multiplicata ergo aq. 2. per formalam generatem 40 + 41y+ +2y +3  es
dabit:
eo 4 1o
30. 40 + 30 41 y + V. 42) + 30. 1G G. + 2. 44y 4 30. 4519 +30461
+31.40 31.41 31ge 31. 43 31. 44 31.45
32.40 32. 91 31. 42 92. 49 3244
33.40 33. 41 33. 4e 33. B
Et coincident aeq. J. et
per nihil omniuo, deinde quototum
et et etc
Et examinemus primo casum quo multiplicatur aeq. 2. solum per 40. deinde
quo per 40+41y, deinde cusem ubi per 41 +427 + 431, et ta porro
quetalibet horum casuum, ducamus per casum quo differentiae primae
ipsarum 30, 31, 42 etc. sunt constantes, seu quo secundae differentiae comnescunt
Inde pergamus sunt aequales nihilo, inde pergamas ad casum quo secunde
tertiae sunt aequales nihito, inde ad casum quo quartae. Ita casus ubi scundae
evartescunt, potest intelligi comprehensus in ex quo tertiae evanescuntu, et ita
si per nihil omnino multiplicetur 8g. 2, debebunt comparari
aequatio 2 et 4. Et sint primum, omnes termini 30, 31, 32, 33 et
R
aauatua at
porro. P.
Higus fit 30 =  10. 1. 31 + 20. 50j Ergo 307 = 10. 1. 3H F 101. 1.39 ( 20. 3091 201301
deceu
un
Ad observandam in calculo legem homogeneorum res ad numeros revocetur, et quidem
10, 2, 40 sunt dimensionis o d d3, vel d3t, et suibatur 301, s 3II; et sunliter
et dd3o vel dd31 scribatur 302, 312. et ddd3o vel ddd31 sctibatur 303, 313, etc.
11, 21 etc. dimensionis - 1 12, 22 dimensionis - 1. et,
3, Rro, et  suit dimersionis e, erit 3
101, 201, 301, etc. dimensionis - 1. et 111, 211 es dimensionis -2, et 121, 221, 327, etc. dimensionis - 3
10, 20, 30 sint dimensionis 0,
et 102, 202,302, et C. dimensionis - 1 et 112, 212, 312 e d mensonis 3 et 122, 222, 322, etc dimensionis -4, et
Hinc sequitur ut comparari possint aegg. 2 et 4. salva ege homogeneorum, debere mmultiplicari
aqu. 3b. saltem per 41 vel 42y etc. Et Ret 20. 41 + 3141y + 32. 4115 etc=0 comparanda
cum aeq. 4. ita fiet 30. 21= 10. 1. 31 + 20. 301, ubi servatur lex homogenectum, nam ubique summa
Et diffeatiano fit Caecterum sponatur revera aeq2 non fuisse
multiplicata nrisi per contantem;  sumemus 4l. pro qconstante quasi valeret 1: a, seu a. et
characterum, (non cputatis primis) est 1
301. 4) = 16. 1. 311 + 101. 1. 314 20. 302 + 201. 30)
uinque 10 sit data, si 101 non est acoportet esse 31 constantem, ex contra
ihil variabid. Et ex aey. 3. differentiando1 Alco 
E1.41  L10. 2. 32 +11. 1. 31 + 20. 311 + 21. 301.
301. H. 4
101. 311. 4
a
(10 i 32 toll a ngur +. 20, 311. (041 4 21, 301. 1ol1
te
H. 11.1
=101. 311. I1. 1
Eot hor ut 
vadto tamen si VI Lo si 10 constans fit 311 = 201. d
 10. 1
in 31 constans sil 31, = 301. 41 - 201. 301, : 101. 1
Asi ergo 31 fitostans, et 32 - 8. fiet 30C fvanescet 301, et fiet 41. 41 701. 41 = 41. 11. 1 - 201. 11. 1 f 21 41,
seu fic a1- 201. H M a Y
I1.
L