Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 73v

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The machine reads it as

1. Sidua sint aequationes, continentas Z, Aqe, do simplici ratione, possunt inde fieri aliae binae, quarum uni desit d, alteri dpsit dez
2. Itaque jam tum sic scribamus 100 + 10Z + 120 d 2( = 0 200, + 210ZH
3. 2o rorto f ita in priore millimus 10r dyx. disserentiam dugues note mtir 2, peste tagriloi enq noiti)
4. posteriore
5. rior
6. 220 dZ prior dabit
7. compendio 10 + dno voleituus 130 et 201 + d eor voce mu) 203. Et quatuor istas pric2es equationes e multiplicatas respectiva per l, m, n, p, addamus n unum. fiet:
8. 100l, + 1101Z + 101 lv + 120l. 1Z
9. 200ma +210 m Z + 201 mV
10. +2o2m do
11. deo B vid
12. 1202l
13. 3(7) Tentemus an haec aequatio possit rrodi tractabilis seu ec Dentificabilis tractabili
14. diaonaranonz =+ le1KV+ on dZ = 10In du + 12on ddlk + 202 dlv)
15. troopa Hlno pZ toloipV + 20 p Aq + 203p do
16. 0o ha +310fZ + 301. fB +320f dZ + 302 f du
17. )(1)
18. 50+9d0 +00h = 8 = 0 faciendo O = 9 = 310Z + 301V + 320dZ + 302 du. unde dispereatiando
19. Hyo 9Z. + d 30190 +3109 17 + 301 g dv + 3rogultzu 1302 g dldv =0
20. fiet d(= d310Z + d301. V + 310dZ. + 301 dv + 320 ddz + 202 dax
21. d320 d d302 dv
22. Et hos valores D et do substituendo in aeg. 8. fiet.-
23. Et aequationes 7 et 1 ientificanda punt inter se, contrahetur autem alcilus facilndo hoco
24. 302=0 fint etiam p=0. fice ob quanesci ergo terminus ildo. Et perinde est as acti
25. non tantum aequ. 1, 2, 3, multiplicatas respectior per l, m, n, in unam aeg.7. composuissemus
26. Omisso ergo termino dao, relque ut identificemus aequ. 7Z et 1, aequabimus coefficientes reliquorum termiporum. Ob Terminum habentem ddque, fint n = 14 = 3209: 120
27. +d3209dZ d3orgdv
28. Ob terminos et V, erit 110. cuol +210. n + dy0. 320g 210s, +.d310q et 101 L+201 + Ao1. 3109 = 31 f id 301g quaerum binarum aequatiogum epse invenitutm et m
29. Ob terminum Y F Ao, cum evanescat p, et fob 202 = o) etiam pruodibit sine litins 101.3r ag orgor , 2o 30cg Ubi feliciter omnis abistdissernisfis.
30. Ob terminos dze et av, habentur singulatim valoras psarum literarum L et m; et ob aZ firt , nol. . (30: 120) 320.. + 320 f +3109 +d3209 Et 202M = -(01: 10) 3209 +3019. Quos valches
31. ipsarum literarum , et m, substitie us in aeg9. pe 15 et 6 prius per 202 multiplicatis , ex eu apis fiet in 2o B. 3og. + 10. vo. 320)- H0 202 3lg + o 202 d qag ti. 1 bo va za g
32. + 12 2B2. 32s , 120 202 d30g + 202 12C 3209 hlaq ib fir l 101 202 2C9209 + 101. 262. 520f ,rot 202. 3109+ 101 02 d3209- 120. 20t Siog to. e1 3019 = honot 101 f 19 1. 202 d301 g
33. 20c
34. 10. 202. 120l
35. 202 320f s
36. + 210, 120. 202M
37. = 10. 202. 130 3209 + o2 B∞ f F 40 02 yege
38. + 110. 202320F
39. + 110. 202.
40. +110. 202 89
41. Ex aeju. 1 6. 101. 202, 120l
42. = 101202 Bo 3209
43. +101. 202. 320f
44. +101. 202.
45. 3109
46. F101. 207. 13269
47. Etexaqe 2d vidi nanss.
48. Et ex ay 2a ordinundo fit:
49. +1d. 210. 161 3169
50. + 120. 210523019
51. l. 202m
52. - 120. 201. 1 3209
53. + 120. 201. 3019
54. -120. 120.502. 310
55. C-atro or tes 2og
56. Et exay. 19 firt: porrrb. 40 3olg
57. Et rpaey. 20 fiet +
58. 3320a
59. + 202 d 110. 3209 120. 202. 310 f + 120. 202 d 310g
60. 1202d110. 3209 120. 202. 310f + 120. 202 d3109
61. +202 dio1. 3209 = 120. 202. 301f + 120. 202 d301 g
62. +202. dio1. 320 g
63. (20) 120. 202. 301 f + 120. 202 4301g
64. siata et 5H. 310
65. ono. es
66. a + 110. 120. 202. 320f, + 110. 120. 202 d320
67. = 110. 130.202.3209
68. = 120. 210. 101. 3+09 (=5. 30
69. +120. 2041103209)
70. 1620 (20oC (=L212 dx - 10I. 120. 202. 320f, + 101. 120. 202 d
71. dibe + 120.120. 201. 3019 = 10on2v. 102 d301 9
72. =120. 120. 202. 304f
73. =101130. 202. 3209
74. = 120. 101. 201. 320924320
75. invenio autem nullo fructu 350 et 301 reduci ad se invicem +120. 202d01. 3269
76. seu fieri 301 = 5t. 310, vel contra, sam ita a quando loefficientes ipsorum d31o in diversis aequa-
77. tionobus tit 51 200 seu 51: 00 = 1, sed aequando coefficientes ipsorum 310, coanescunt f, et 1
78. nec possunt inservire ad aequationem. Ergo reducamus 310 ad 320, seu frat 310= 8t, 320
79. + seo d. SP 320 a + 110. 120. 202. d3209 +120. 120. 20. 3019
80. +110. 120, 208.51 3209 = 120, 120, 2025 dg20 G
81. = 120. 120. 202. 51. 320f
82. = 120. 120. 20t a 56. 3209
83. + b1. 120. 202. d320 9
84. + 120120. 201. 3019 = 12o. n0. 2e2 4309 0
85. = 120. 120. 202. 304f
86. it bis dabus aequ aequemus harum duarum aequationum termues d320, et 320, Ob dero fiet 51 == 00. 10 -00. 101, :120
87. Aequenus has bines aequations 3 10]. 120. 202. 5 3209
88. Terrinos 320 mop aequationibi aequaba. interim ex refiduotum aquatione, fit d301 (5) 2019 - 202f - 2109. Et posito f:g hubetur 301
89. Jam f. g inveniemus aequando terminos 320, hoc modi X+ 00. 110. Ro. 202f
90. 00. 10. 10. 2020
91. -00. 120. 210. 101C
92. +00. 120. 202. d110C
93. A+0S. 101. 120. 202f d unde fiet 00.1205+202 d101 +120 C2f. . 5,
94. or auo
95. . -00. 101. 130. 2029
96. .-00. 120. 101. 20f
97. - +00, 120. 202 d10t
98. . +101. 120. 202. 51 G
99. habetitur
100. fe
101. + 210. 101
102. 120. 202 520. 51 = 120. 20r 4
103. d sedita evunescet f et g ob evanesceatem nom
104. 1I. comparundam cum aeg.7. fietus ob taz, n mrog: 120 et 2) Jorg: 202
105. tut 1olL ob dq fiet nol of + 3log. L d3rog - (130: 4120) 3209-(150: 212)302g ob de fiet 202 m ) vorfF 301g +d 3029 (101. 120) 32og - fro 3. 202) 3org
106. Ejm non licet omittere 302, sed redenndum est nobis ad aequ
107. Hag secundum Z, fiit: 110. 202. 320 f. + 110. 202. 409. + 110. 202 d320y - 110. 202 (130: 170) 3209- 110. 202 (210. 2023029. + 210. f9 D. 30r5 , 210. 120. 3019 (+. 20 120 d362g. 210, 120 (101: 129) 3rog- 20. 1 20 (203. 202)3029
108. Ae superest a supersunt aequationes ex coefficientibus ipsorum Z et v, quae multiplicentur per 120. 202
109. Et ex ap scudmu, fiet. 101. 202. 320 f + 101. 202. 3109 + 111. 202 1329y - 101 202. (130: 12o 13209. - 101. 202 (210202) 32g, + 201120 3ors pro112o. 30191 201. 1o deorg- 201. 1 40 (1o1. 20) og - 2o1. pro (203. 102)9029
110. + 120- 202 (a110: 120) 3609 + 120. 202 (d210: 202) 302f 3 19 120. 202. 310f + 120. 202 4310
111. + 120. 202fl101 : 120) 3209 + 120. 202 (d 20] - 207)302y (7,
112. -110. 202. 3205- 110. 202 d 320g + 110.248. 3029 20. 210 dv25
113. 120. 202. 301f + 120. 20243019
114. Ex aeg. 16 ordinando firt 110. 202. 3109 =120. 202 d 3109 120. 210. 3019
115. l
116. E. ex aequa simndo fiel: C
117. 31
118. =101.202. 3109
119. Hiora
120. 12o. 210. 3028
121. +120. 2102 3C2
122. = lec. 210 - 610C)
123. 400.8 a
124. + 120. 28. d 510
125. +110. 202 (130 ) posroa
126. + 120. 210 (106) 3209
127. -120 d2103029
128. 216 dirS. 3209
129. +120202. 301 f + no202 dholg. - 101. 202. 32ofu = 140. 202. 13209 + Br 210. 3org, - 120. 2o) 1302
130. 120. 201-. 3019A
131. Fiut 2 vs, 310 = 3to 20 1507 302 et 0g. 301 = 1y 20 t60. 302
132. sit ex aeg. 18 firt - 110. 282. 5109. 320
133. + 129 202 510 F
134. .. --
135. -120. 201 3027
136. fint
137. Exaeg. 15.
138. a 2, 20 202 hof A1on or 43103
139. +0 eq oi
140. 2)
141. lO1, 201. 3209
142. 2 202d10. 32
143. tas jam bini
144. XI. 10. 20Y 22g 13oca
145. + 10
146. 120d20. 30
147. aequationes aeque mus inter se pens
148. sadem ut terminia 302, et termini 302 utrobe
149. 1302. f. t 60p= ob. (201 - 210) + 202. 5017 : 202
150. 30 ut 21. Et ita qu
151. oi
152. Dloroni G+a
153. atipduc
154. 120.4105
155. I6. 2 hol. 501 ) 400. ror d a
156. v1. 202. 5019 +00t 202 la +, 20g def 2019) (0201. v0. 20 + 202 501)
157. Bt )urtoctsom ngetouohomon
158. 20. 202 d cot
159. =D orre 2 2um
160. 1209 Morsooo vi eo
161. 501
162. Edere
163. de
164. Die 29ceetre
165. o vorlood
166. d30 + 10 022
167. nu tareii ponumm
168. sai itit
169. io aspioiin
170. tod
171. =1812022 3209 173104
172. eliuosimu
173. (= 101. 120202- 3109
174. eo
175. o no ga
176. e por
177. +110. 120, 20451
178. =1 20. 120, 202.5,F
179. = 120. 120, 202. d510
180. = 110. 202. 501g. 302 - v0. 10. 202 9d320 -1
181. (30)
182. + 120. 201611.
183. 302
184. 4 120. 292 5e .. . . 410. cdt 3169. 1. 4+ 128. 202. 302
185. = 120. 210. 809
186. +00 I a
187. + 129202 d5019.-. -
188. - 00. 11. 2029320 -00. vio. 2019. d302
189. in ussoatvroed
190. A exagitospit
191. +00.
192. de
193. ja
194. =1012d2. 5109. 32 - 101. 2c. 50
195. +(2b. 2006109 111 4 l∞. 202 46 . . ..
196. devau

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 73v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0146?run=74