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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 79v, page id 00068198:0158
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Divisiones non semper procupari possunt explicando
Datur 1oyy + 11 ay +12 aa ofiat y = 30 v r41a mita ut explicatione facta fiat C= .. v+. a
O= 25y +21 a
iomm + a mn+ 12nn,: un
21M + 21 n,  n
40v + 4 a n
+ 11. 30. G0 vp + 1. BB. 8B qp a + 11. 31. 41 aa 7 :,, + 20408+20. 31 a, 4ov + 41a
+ 10. 30, 30VV + 2. 10. 30. 31V + 10. 31. 31 aa
+ 1. 11. 21. 40aV
21. 40V + 21. 41a
compendio fiet 60vV +61 av +62 aa dividendum per D + SIa, posito 60 = 10. 30. 30 + H1. 30 40 +12.40.40
+ 12. 40. 40vv. + 2. 12. 40. 41 av + 12. 41. H av
et posito 5t 20. 50b. + 20 H4., 2t 44. 51 = 20. 31 f 21. 41 = L
62 = 2. 10. 3031 + 11. 30. 41. + I.31,40+2.12.4
62 = 10. 3p. 31 + 11. 31. 41 + 12. 41. 41
20. 90 + 2(. 40 60 51. 51 = 61. 51 + 62 =0. Htaac ergo aequationem
expliscanda fiet seu 6opp = 61 pq + 62 qq = Htanc ergo aequitionem explicando, fit
Copsit (ll. 30. 40
(2. 46.40..... .
+(10.30.90)2. 20. 31. 31. 41 = 19. 30. 30. 21. 21. 41. 4)
11. 30.40.. . . . . . .
(124040) ....
i
bru fr. 10, 25. 20. 39. 30, 313 L.II. 202830. 30. P1. 4)
un C. 10. 20. 21.40. G)(= 11. 20.21,30.40)....
( J. R. 2020. 24. 46) - ( 710. 20 21,20. 7) a. 1.
9. 10. 21. 21. 344.-
 l. I1. 20. _,40 d 2
s
13 F10. 26 30
20, =. 3b. 41
Cxt, 1. 21. 2). 90.40
= L 12. 25. 2H ZP. 40
( 12. V. 21,  4
es
l 40.40)
=D. 21. 9v. 3v E+ 1G
( 11212. 300)..
(-. 2. 12 l. 301407.
2 C 21.21.4010
31,31 +. p 25. 3ot Y Z1_+ 12 c20. 30. 41. 
E. B. 202304)
Ht
1
ul
(li 7 261 2130
10 + 21.2.40, 40= 1, (1. 1. 21. 46)-
(2. 17, 20 =2v3o4St..
....
(13
2121. 9949, 1.
det
L 18. =1. 2 1 .s  131. 31.40, 40 - 2. 10. 2.2]. 30. 3140. 9) + 10)21 21 315.34+ 4,
= 11 29. 21
T12, 20.20
-
+ 2. 11. 20. 21 .. . . - = 1(20.21.=
2, 12, 2020... .. +725 2. 201.
quae aeqn tio puducitur ex S qu (31. 40 - 30, 41) in 10 212) - 11. 20. 21 + 12) 20. 20, sed
heutrum nihilo aequare permissum est
Et travideri haec poterant, nam idem est ac si vel i5
30431a,: 40b + 41a, fit + 30Y + 31aa
y + b, y+C
au Cord vi.
otest ips
ytb 40bP + 41ba
lu
1
+C
40 v ut 41a
fieri
c
s
datis y + b et g + et facierdo y-
30aD + 31 aa
10 cD f+ac
40v+41a
deberet est 3ia + 41 b
30 B +40b
30 a + 40c
31 a + 415
6
e
seu 50- 3Iaa, + 30. 4nC 40. 31 ab f (. 4ibc = 3B. 21 - buc
= 30. 2) ad F, 30. 4 ab + po b + (+8. 41bc)
40. 31 ac
40. 31
ll.X
. Sit _ = - 26 vn L 3 116 + Z2a c 40 ro +2 40. EcaY)
et y + b _ qu(400 + 414.-- 39V∞ = DV + 31800 aV + 32. 00 a
mun
30 et + 4 7
ab p
2. 404) b
30a + 40
4l. 41 b
B∞ t in F aM habut radiles vn + lB + : l =: H1 =am seu V + hilAl-am,
sit v 31. 00- + 2. 40. 41) = Y C 3i. 31 00 00 f 4. 00. 31 . 40. 4( F 4 10. 40. 91. 4 ( 4. 33 00. 3.0cp 4. 30, 00 41. 4 ) ab )
v +
4. 32.00. 40007 4. 40.00. 41. 41()
Haec radix habet duos valores pront signum radiala est afforimativuum vel necalion. H duo valores sint l, n; arist afformativi posteriorueus
3oa +40b
Eodem modo habebimus aliam duplicem ex y+ , tantum pro b subistituendo C. Iti duo valores sint B, 
Penique habebimus aliam duplicem ex yte tantum pro b substituendo C. Hi duo valores sint r,5.
quod si efficere possimus, ut Im pus sit dinsibile per Y s, velutis. l  Y, et q 5, habebitur desideratum
ertque 00. 3la +2. 43 b + 1f 880. 31. 31aa + 4. 00. 31. 40. 91 ab + 4. 40. 40. 41. 41 bb)
400100. 30 hEla 4. 00. 30. 41. 41 al = 4. 00, 40. 4l. 41.
30 a + 40b
+. 08. 00. 3140 ab
et 0b. 31 a + 2. +a _C - ( (ut prius mutato b inc.. ..)
30 a + 4
Hinc jam (ot
in quo ontum vide quid ilste
a +40
idem debet esse adhue semel si conjungu C et e t pius b et e
10. 31a + 2. 40. 41 e + Y (00. 00. 3D. 31 aq + 4u. 3tto q ae  foHC
400.00 30. 32.. 4. 00 30. H. 41 a (2 qeo 10
30a + 40e
aquiv. 32. toac e
ut Perius tuntum At C. 1 imatando in -. + C.-
habere divisorem colmo aq debent habere divisorm. comm
exq lx +am
e
oa . aet eA quadcali itd ut 1000 +Ct  DEs. t dibilo. pe. 206 4 E. DC
V+. 14
p9 = 20. 20. 30. 31
20. 21. 31. 4C
20, 21. 30. 4
(21. 21. 4041
e
 5
e
 24 aquadrat Epd