Leibniz-Handschriften zur Mathematik LH 35, 3 A 4, fol. 42v

Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German. Mean line confidence on this page: 0.83.

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The same scan as fol. 41r (00068217:0083), where its text is given.

The machine reads it as

1. a b aequ. ab ab - abc. seu abX - abc
2. aebc aegu abc a. aequ abc X - 4 abcd
3. abed aegu
4. 5 abes qu scuabrexus abede
5. a aque abcecq
6. ab ab qqu ab a aequ. abX = 2ab
7. ab1.
8. Vigu ab aequ y aequ ab.
9. y aequ ab + abCX -4co
10. c
11. a in a aequ a + ab
12. X aequ a X aequ a + 2ab
13. 6 xde
14. yZ. aequ a
15. 2ab
16. a rab
17. X’aequ. a +3 ab +6 abc, seu a 4+ 3 ab X - 32
18. aeb. rau aba aequ abX - 3 abc
19. S Ergo ab aequ abX 3abc X 12 abcd) - 4aeb
20. 6abed) -6abc - (6 a l1d) 10gbi de
21. 9 a bed
22. 26abC cd
23. - 1Babcd = buabede
24. 6
25. (= 12 abcd)
26. aeb aequ. aeb 4 aequ aebo x - abc ) aebe rqu abe a rquabex- rabi rabed
27. a Ansic brevius omnia investigare licebit ab aqu ab c a est autem a aequ. X- db 3ab. X +3 Habe
28. Ergo a b aequ ab XC - 3ab ab X + 3abc ab
29. ZabC rqu. XabC 2ab aequtabC X-Ga. bcd -20 abede - a bc( a bed). 3a b - babek a bex
30. et ’abc, ab et ad +de abc + 3 a bcd +sabcde
31. rujus baVc aqu. V ab 6 abc, aequ. ab. X 3 - ( a bcd -( ab ede - 3ab - (3 a bcC 3 ab cd) - a b - abc
32. 6ACd.
33. 6 cde
34. ab
35. a
36. 9aebed
37. avx abd
38. 29b
39. u
40. cb aequ. jam supra invenimus esse: ab. aequ. ab X - 3abe X + 3ab C. Ergo a bX seu (ex labula) a b + a b bC aequ. ab X - 3 abc X + habe X
41. e a
42. et eodem mobo: abc aequ. ab cX = 4 abcd. Ergo ab CX seu sextabula) a bc + a bc + a bcd aequ abc X - 4 abcdX
43. habedx - salede
44. et eodem a b X aequ. seu ex tab. ab 1 b +3 a bc 2 a V + 9 a be (9 4 ab 6 abcd, erit aqu ab X - 3 abCX
45. Nusus aliter
46. 3abX
47. ab aequ ab a aqu. ab X - 3 ae b abed - Z8. aebc aequ abc 2 aequ abe X - rabid
48. 2ab seuaequ abX - 3a b ab ac
49. 3ac3ac
50. rede 3C
51. abe
52. Z aequ. abc
53. pro seundo gradu A, ab: 4 ab ug. ab. 4 aqu ab X - 2a1). absrqu ab 9. agu ab X - 3 a b. X). ab s b
54. 18
55. abc abrab ZX - aZa A X aqu. a + 4 a b + 6a b + 12 abc + 24 abcd
56. ab aqu aeb u iqu a bX aeb
57. aeb aequ ab
58. de
59. b
60. X- rab
61. a a
62. ab
63. intribus 6
64. in quatior
65. in qualuor 12
66. in quaeque 20
67. in duobus ab
68. in tribus 6
69. OabEdX- 30 abede
70. Jitaque tres sunt super sunt literae ab. a bc abc
71. aequ a + aeb aequ X 3alex + habex. ergo a b aequ. XZ at - 3abX +habCX. equ. Ergo a b aequabX - 5ZX + 4c - 2ab abaju abx - 17+ rabn 8
72. - 2
73. (, 16. = 12
74. =5, 4 t + 8c0
75. (192591 -20 (- 510, 5) +40
76. 25
77. aba aqu abX - 3abX - 29
78. 3abX
79. abe
80. + habe
81. EabX. gabiX 2al. -gabeX +4u
82. ablaequ. (ab c a)se eiqu. abcx - 2a bc- a bcd. 2e abcde-
83. abbd aequ. abed quabedra aequ. abedx - sabede
84. 20
85. tab
86. 2a bc aequ abc 2ab aequ abeX - 6 a bcd - 20 abede - abc - a bed
87. 3e
88. 90
89. ut subtrahatur ab 21. relinquat 6.
90. ita solis numeris, ponendo a + b vel a + b + c. vel a +b+ C + d vel a + b+c +d + C, et possit eequ aequete ru
91. posito C tn 2 aequ. a. aequ. b. aequ. c. Mn. progediendo ordine omnes numeros afficientes sine
92. ullo alio calculo inveniemus pr sufficiebret progredi usque ad a +b+C+d. sed aus ad 5 nonissime
93. processi comprobandi causa. In sequentibus enim in infinitum numeri lex o
94. qi Conclusio hujus paginae.
95. video n p omnes formas a primo usque ad
96. quintum gradum indusive exprimi posse per
97. potentias ipsius X affectas formis aequaliter
98. in uno quoque motao exemplo compositis
99. ut a. d. a. ab. a. abc. a. aeb. abcd
100. a accedente forma abC, seu abcab. quae sola
101. per illas aequaliter compositas explicari non
102. ad abed scum psta porius in tulam resolvatur ve
103. ae ascendendo ad ab, at. Tales igitur
104. omnes solli non possunt,ut in
105. a bc aego abc Gabe ab4X = 18 a bcd - 60 abede - 3ab - (6 a b. (- 6 a 1.d - (bed - ab =, a bc
106. Bacd
107. aevede
108. 60
109. aebequ. ab a aqu ab X - 3a VX ∞. -6abc et hinc certa demontratione
110. TB - 27 -121 6 -487. quodnon proredit riho quia nec ZX valorem hum ingreditur
111. +6 ab
112. 250. - 60 - 190 - 30.
113. 25 -5
114. 250 = 120 = 20, - 30 - 20
115. 2s
116. abab
117. 6 = BZX ratio quia ut tribus non potest cddi nisi Z. id est in truibus unilotem facientibus, 3. debetantem esse 15. ergo 15 dabit 5. mnerur. 15, ut
118. X2 1ab X, 3Z abc
119. in dusius ab in duobus est a ab a aequ abX - ab
120. a
121. ab aqu a b a equ a b x- glc.
122. 2lb
123. ae
124. 52
125. 1
126. ope trium saequationum quaerendae.
127. Rurs aiter a a. aequ. a + ab. aequ X - 2abX. Ergo H a b aequ. + X - a - rabX.. jam X - a3. aequ. 3 ab X = 3Z. Ergo a b aequ ab X - 3Z et supra.
128. B a x (abe)
129. quae aequatio quia conerdit cum illa qua inveni a7b. ideo
130. hino disco tandem erustra quaeri modum tollendi forman abc
131. ideoque tuto relinqui potest.
132. sepemuom aded, abc
133. seu qu ex imro
134. et in sext ab, a00
135. Vide et paginam
136. versam
137. 3abX colligo quod a a valore ipsius 6a colli libera ri non potest.
138. 6abc
139. nam si posset deberet ad exprimi per solum Zo nec
140. exprimi per solas illas formas: eodem modo compositais nam
141. Sid posset tunc deberet abC posse per ZX neque enim
142. alia forua superest, neque enim X vel E redire potet quia
143. redire efiam deberent ab et aV. circa quae tamen per
144. novae literae accessum nihil mutari potest.
145. ab + ac + ab+ aC4+ b E + bc
146. ab a + 3ab +6abc.. - 2abx
147. ac
148. ab
149. ev.
150. a
151. stC
152. 18 b8
153. beab a + ab C + 4 abd, abc LabC
154. ab abc
155. ea
156. ac pa + acb3 +3 aC + 3aC6, (3 a cB 46 abc
157. auc3
158. bc 13 bc a + 3bC +3bca Hbca 16abc
159. bC
160. bea
161. bX
162. 4ab
163. ab3
164. 2ad, quabex. 7a bid. 2 abc- qabede
165. abc ego ab aequ ab X - a b2
166. abcc ab. aequ
167. ab aequiat Ego
168. abaequabx - 22
169. fit ab X abc- babC
170. -6aVc
171. 27
172. 34b
173. 3ac
174. ad
175. abe
176. abc
177. -346
178. -64bc
179. 8c50 =bdabede
180. o Vere
181. =abe
182. baBC
183. 0ab
184. =18ab10
185. -9abcd
186. acb acb
187. aego ab X- abc = 3ab - 6a b c.5abc
188. 2, li 21
189. dissimiliteonsmnes tolli posse praeter abcd, ab, et ratio
190. est quia non possunt ad potentiam ippius accommodari
191. nisi iteram reascendendo ad abcd, a seu redeundo
192. potest. In sexto gradi similiter videntur aliter
193. ab aequ
194. bca

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 A 4, fol. 42v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068217:0086?run=74