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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2c
# Folio 168v, page id 00068199:0336
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130Q +9 (31 : 2130), qu = 302Z + 31aZ 7 (311: 4.30)
40  = 30 ln +20. 30lm + 20 I = 0. Habetur ergo 40 per 20 et 30.
(3om 2. 20121B+ C  (20 M = 2. 30n) 31 = 2. 40. 41 seu compendio )10. 21 4 80. 31 = 4041
superest 2. 20. 22l+ 21. 41 l + 20. 32m + 21. 31m, + 22. 3om + 2. 20. 32n 4 31. 31 n = 240. 42l+ 41. 91
ubi ponendo 22 =20. 32: 30 et  1, 4 et et 42 = 90. 32: 30 et 22 = 31: 4. 30 fiet
22= 20 (31: 4. 30) et 92 =940 (31: 4. 30) e et explicatione facto
at
2. 20. 31+ 21V. 4. 30 4. 20. 30. 31 m) +21. 31M. 4. 30 + 3 10. 30. 3i m F27030. 31 12o. 3n
= 240. 31+ 4. 30. a
2, 2030.3 In p 
seu 1, 4.  2i ll + ~  21. 31 l m + 21. 3 In
1. 16.30
2
ea Lel
seu (4. 40 79) art 21. 2IIL + (9 40 lm 30S, 31 1(2 4dtn- 50)) 31. 31 -a
4. 40 70,  4. 30 In (+ 4. 20. 3olm + 4. 201) - 30 mm (C 4. 20 Bobn  4. 2011) = 30 (aln - mm)
A. 4= 2 9 = 2 2In +. 20 3olm + 2. 26H- 2. 3omm - 2. 20. 20 pn. - 2. 20 2olm - 4. 20. 30 In
240 Um- B.1a Vol- (23o lunt (3 20 3olma( + 2 2o Umf 20. 30 mm (2 30l m 2. 20 Un.4 203olln
Ergo 4. 40 Um - 2. 70. 10 l =220. 30l (min - 2ln) 
superest adruc
2.401 801 = (2. 30 lnn + 2. 20. 30lmnt 2 20 lly- 20 b  (9) 2030l mn - (30 lun
seu 2. 40 ln - 80 l = .  (_ Un -mm.) - 2. 30 (20 nan + 30nn)
et 2. 40 ln - 80 = - 20 lp C (2.  2. 3on (20m + 30h)
ita tandem
seu
.
2.20.3 ollp
20. 3 lp +3, Vo. Upp + (2ln- (p) (20 lp + 2. 30n (comt 3on))
30 (4ln-mm)
-200 enn
2ol p + Y (20 UpP + cillnp (= 20Upp) + gatr a. 20. 30 lnum + 2Bho lu - vmo lenm
30 (gln- nim)
2. 2dUn um - 2. 28 ln 2ln + 4 uo. 2 lmnn (+ 4. 3 ol  2. 20. 20 mn + 2. 20. 3 donn Eln - 2. 30 nnmpri)3on, uln
Quod sub vinculo est explicemus erit
ubi tamen non apparet compendium
quid ergo si faceremus 2. 20 ln - 2 20 3o2m - 2 30 hn p
fret seu 20 l - Lv. 39m = 30n=0 manerdt siti
et fint 2
-20nm + 2. 20ln + 2n Y(20. 20 lm + 90. 30 ln)
30 (An - mm)
20. 30 ln = 28 Im  d + Cum + 4 lu)
= Jomin +2. 20ln + n2 H 2noln
i
=20 m
30. (4Ch - nm)
Lam +2.n + 1. In S n+ S
alis
30 (40- 70) 2Ill + 4(430- 129) 40 - 30. 70. 8e r. 31l
Hoc aequatio est e voletenda explicatis 40,70, 0.
I
1
roll Frel 3om + 3omm
aequ. L 3omm + 30l
seu 20=   30m( unehs
eralu) vel 3nn + on. 2om = 20 In
+
Zonnthon romt 2omm aqu.
42ommezoen seu
alo= 30-m t rium+ aln
Eohon
2n
1X 20l = 20om + 30n
(2 (20+30 30. 807) 3Il
4, 40 - 70 = 3d (aln- mm) n 4 4ellm  1 20. quUn , 2.3670. 80l 130’ pono l19 3o m
-+.  gotrum (4). 30. olm  i. 0 Ums 10. 3omm (2. 50tmn-2. 20. 3oum oo l
4. 30. 40Um - 1. 20. 40Um = 2. 3070. 80B = (4. 30M 30 ln) + (D. 30m. 20. 39lp (14. 3om. 20U
= 1. 2om 30 ln = 1. 20m 20. 30lm - 1. 20m. 20l= 2.30. ∞ 130. 20 mm (- 2. 30. l. 2. 30m 1 230 l. 220  3. sc
= 20l, - p. 20 In = 9. 3CIn + 2. 30mm = 1. 30 mn, seu 20l, 30 imm- mn-8ln) n 20 
1. 2030, 3 = 2. 20 2 38 In +2. 109 20. 3olg +2. 10n. 20 l-7 deoni . 3o (9 20 3.  2os  0
tandem 2. 20. 40 Hn +2. 3040 ln - 30. 80
= 2~ 2. 203Un +030. 20 (2IR= i. mm) +2. 2030l (nh =MN) 3. 303 nn
sit ero sit aIn-mm = +pl
et 2m un- d = 2pl  mn = gl 2ln
i
et fint 30d 30 pl. 214 + (20l309 20l2o 2 - 20l 2oromm) E1. 31 + 2. 20 Un r 3ol in + 2030 7. l X 20 4
n