Leibniz-Handschriften zur Mathematik LH 35, 3 A 28, fol. 5r

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The machine reads it as

1. sit Aequatio
2. fiet o
3. 0X + 1 aequ. eihil.
4. et 10 X + u aequ. erih.. Artic. 1
5. 1. 10 = 0. 11 aequ. nih. seu 1. 10 aequ. 0. 11
6. (1
7. C
8. Aitic. 2.
9. sit aequatio 0X +1 X + 2 aequ. nih. et 10X + 11 aequ. niho fimulliplicando 2 per Xfi et
10. (3
11. et addendo 11t3 fic
12. 8
13. 10X + 1 qu. N et a 1d X +, 10X + 2. 10 aego N. Ergo .
14. Ergo 1. 10. 10 equ 0
15. +o 0. 11. 11
16. - O. 11 X
17. (5
18. Ergo ex 4 et 2 fiet
19. 2, 10. 10 aequ. 1. 10. 11.
20. 0. 11.
21. Aliter idem: mulliplicetur aequ. 1 per 11. et aequ 2 per 2. fi
22. adtantur subtrahantur a se invicem producta, et residuum dividatur per X,
23. fiet: +n X + v 10. 1X + 1. V aeq. Nik. Ergo ex 2 et 6 fiet:
24. - 2. 10
25. 1. 1D11 aequ. 2. 10, 10
26. O. II. H1
27. (2
28. sit aequatio: 0 X + 1X +2 aeq. N. et 10 X+ n X + 12 aequ. N
29. a mult. R qu. 1. per 10, et aequ 2. per: 0 et anferendo invicem, fit:
30. +1. 10 X + 2. 10 aequ. N. unde per praecedentem articulum: ex 1. et 3 fit:
31. = 0. 11 X = 0. 12
32. + 1. 1. ∞. 10. 10 aequ. 2. V. 0. V 11
33. =0, 1. 1. 10. 12
34. = 0. 1. 2, 10. 11
35. 40. B. 1. 11. 12
36. =(2)2. 0.1, 10. 11
37. 2. P. P. 10. 10
38. Sed cum in aequ. 4. 10. 11. 12. non tractentur ut 0. 1. 2. signium est calculi
39. imperfecti, uti etiam deprimi potest. Itaque aequationes 1 et 2 multi.
40. plicemus per illam per 12 hanc per 2 sintu et oductum peu per
41. pucem et productum unum ab altero aliferendo, sufferenitium dividendo per X fiet
42. +0. 12 X + 1. 12 aequ. 0. et combinando aequationes 3 et 5 habebrinus
43. = 2. 10 X = 2. 11
44. per articulum primum. +1. 1. 10. 12 +0. D. 19. 19 16)
45. -1. 1, 10. 12
46. seu quadr de 10. 12 aqu +1. 2. 10. 1
47. 22. 10
48. + 0. 1. 11.
49. 1
50. = 0, 2. 11. 11
51. ∞1. 2. 10. 11 5= 0. 2. 10. aqu. N.
52. =0. 1. 11. 12 2= 0. 2. 10. 12
53. 40. 2. 11. 11 4 2,2. 10. 10
54. ubi nota si in aequ. 6. ponatur 12aeq. nihilo
55. redibit aequatio 5 prioris articuli divisis omnibus per
56. sit aequatio DX L q N OX +, X + 2X + 3 aequ. _ 10X + 1 aq. a
57. multiplicentur per crucem in ultimos fiet + B. 11XF + L.HI X + 2. 11 aequ. N. Rursus eodem
58. i
59. modo multiplicentur 2 et 3 per crucem in ultimos, fiet: 8.11. 11. X + 1. 11. 11 aequ. N
60. ~. 2. 10. 11
61. et rursus multiplicando 2 et 4percrurem in ultimos fiet:
62. + 1. 10. 11. 11
63. = 2. 10. 11. 11
64. +3, 10.10. 10
65. = 0. 11. 11. 11
66. ubi si
67. ag. 0.
68. 4 3. 10. 10
69. Atic. 1.
70. OX + 1X + 2X 13 aequ. N. D0XZ IX + 12 aeq. N Arlic. 5
71. multiplicentur per crucem, in ultimos fiet. ex
72. 0. 12 X + 1HX + 2. 12 aequ. N, et res redacta ad artic. 3.
73. - 3. 10. = 3. 11
74. Ergo adimitationem aequationis 6 articuli 3 fir aequationem scriberemus
75. a 12 tunc displicet, quod video incognitas it 1. literas eo ven
76. literas quales 10. et I1 et 12 assurgere ad quartum gradum, cum tamen
77. non debeant assurgere ultra tertium. Itaque aequatio 1 et 2 rursus multiplicentur
78. per crulem in summos, fiet: +Il0 X 4 2. 10X +3. 10 aequ. N.
79. = D. H1 X (∞. 12 X
80. conjungendo aequ. 2 et 3 per crucem, sultura summarum, fit:
81. O. E + 1. 1012 X 4 2. 10. 12
82. -3. 10. 10. = 3. 10. 11 15g. N.
83. conjungendo aequ. 2 et 4. percrucem ultimavum fit:
84. 41. 10. 12X 42.10. 12 aequ. N
85. 20. 11. 1
86. = ∞. 1. 12. = d. 12. 12
87. O. 1 12
88. 23, 10. 10. ~3, 10. 11
89. Unde deniqe multiplicando per crucem, habetur quaeduae quationes coincidunt
90. Unde exaequi2 45 ad exempulum articuli siet:
91. conjungendo aequ. 2 et 4 per crucem summorum fiet 42. 10 10X + 3. 10. 10 aey N.
92. et ix aequ. 5 et 6. per crucem multiplicatis fit:
93. + 0. 0. 11. 11. 12. 12
94. 1. 10. 11. 12. 12
95. destinendo L= 6 1. 10. 11. 12. 12
96. 10. H1. (+7. 12 4 1. 1. 18. 18, 1. 12
97. =P. 3, 10.10. 11. 12
98. via possunt L = 0. 3. 10. 11. H1. 12
99. 2= 1, 3. 10. 10, 18. 12
100. 43. 3. ∞10. 10. 10
101. 0.0. 10, 12, 12. 12
102. 4 0. 2.10. 10. 12. 12
103. 40. 19. 10, 10. 11. 12
104. 0. do. 11. 1. 18. 1
105. =0. 2. 10. 11. 1. 12(
106. quet
107. 10
108. lu
109. =9. 19. 12. = 1. 10, 12
110. + D. 2. 10. 10. 11. 12 ∞0, 3. 10. 10. 11. 12
111. = 1. 3 10. 10 11. 11) 42, 3. 10. 10, 10. 11
112. = 2, 2. 10, 10. 10. 12
113. = O, 11. 12
114. +9. Vd
115. itaque vertenda liters numeros
116. 40. 3. 10. e1. 11. 11 (2)0. 2. 10.19. 12. 12
117. ∞0. 1. 10. 11. 12. 12
118. ∞0. 2. 10. 10. 12. 12
119. = 1. 10. 1
120. n
121. : f(1) 0. 0. 11. 11. 12. 12
122. = (2) 0. 1. 10. 11. 12. 12
123. +; 2mr 12
124. = 0. 2. 1C. 11. 11. 12
125. 4 1 12
126. 4 1, 1, 10, 10. 12. 12
127. ab ea quae est in actis Einditorum, quae tamen deberet coincidere, ponendo a et 10 esse unitatem
128. +2. 3 10. 10, 10. 11
129. tesse nihilum 2 esse p. et B3 esse q. et 12 esse y + a et 11 esse Z quia hic predit yyz7 quae illie diessevidetur
130. utroviq
131. descresidaa
132. 1
133. dividi per s = 1. 3. 18. 10, 18. 12
134. Artic. 3
135. ubi nota omnes terminu
136. quadratum non con-
137. tinentes affectas
138. signo
139. signa-videntur
140. oriri a terminis
141. i quo
142. rum signa mu-
143. tata radice
144. mutari possunt
145. Nam si ambarum
146. aequationum signa
147. mutata radice
148. vera in fal
149. sam mutare
150. tur, endem
151. tamen prodiret
152. aequatio uttima
153. sublata incognita
154. ipsius et autem
155. valor fieret contrani
156. is non
157. sequem
158. tin apparet.
159. haec. inductio
160. Isulende
161. prmen oligutur
162. ex multiphici modo
163. quo eadem qua
164. Eycrplicens
165. latis titas produci
166. potos
167. 0.0. 11. 2. 2
168. pro 0 adhibitis 10, pro 1, _ H1. et
169. v2, 12. dit 2 p
170. bis 0. 811. 11, 12:12
171. B puto ex his series in
172. infinitum scrrbi posse
173. videtur haec equatio differre

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 A 28, fol. 5r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068241:0009?run=74