Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 90v

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: 0.79.

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The same scan is also registered as fol. 91r; its text is given once, here.

The machine reads it as

1. dat
2. sit Formula quaedam
3. orta
4. alteri, explicando X p
5. aequales in numetatore et
6. sit X: a = E 10 27 + 11 aZ
7. Radices ipsius formulae dat
8. secundum quamlibet X, ipsa Z
9. e quaerendo Z opeae
10. Causa pro 20. 2027f
11. et fiet tn +10a
12. =30
13. naa =3 1ax. - 120
14. = = qu 10a = 30X
15. 100
16. Compendio sit 11. H1 - 4. 18. 12 = 113
17. et fiet Z - ) - 11 a + 31 a X +
18. se Radpes aequales, poteri
19. -11a +31 a l + a 12 aa + 13
20. 2, 10a = ab 30l
21. =ua + 31 al = a Y(I2 aA + 132
22. 21 10a - 3ol
23. sit ta C = 1 (12 a a + 132 al
24. il
25. - 11a + 31 l = 10sR
26. - 11a + 3lB = 1F 13
27. =ua +31 n = f13.
28. fiet Bilutra O: 13
29. 1311 = YaC;
30. Ex aeq. 6 fiet 1311
31. 1380
32. per compendiu
33. a 2.
34. seu fiet 1220
35. 1340V
36. 10Hagoa 17.
37. den Eeudem hutd nigra aa
38. vidpamus an -13)
39. namfieret 15AO
40. si 11 et 21 = 0, fier 7= 2a L(-10. 12aa 413. 30aX), :, 2.10 a- 3. 3ox. ubi diudi potest nominator per nuneratorem
41. et fiet Z- ai mai qu. lon -3ek)
42. 1129
43. = d
44. -10a +3oM
45. pa
46. et rursus +.
47. =+12a sed ita evanescentet via,
48. 210a +3ol
49. omisso 21, unde et 31 et 32 evanescent
50. -10d + 30n
51. et fiet Z7 1 a ta s aa + 4. 12 30 aX), : 2, 10a - 30X. Ergo ut habeamus duas rudices aequales, fiet
52. sint 10 a -3ob = 150 a
53. 10 a - 30m = 160 a
54. 104= 3on, = 1704
55. AH. II aa = 4. 12. 30 a M)
56. N, aa = 4. 12. 30 a l (4) 1 aa t aY (= 4 l. 12
57. 2, 104 - 50l
58. ia
59. 2, 10a = 30m
60. 1. 1012.
61. i
62. 0a + 30d = 250a
63. 10a + 3om = 2t0a
64. 104 + 30g = 270a
65. et fiet 1a F e Slum = 4. 12. 20) B) na + a ssum - 412. 260) et La = spril - 4u2 250) (5 1a Fa + (ug - 2. 270)
66. 2. 150
67. (2, 10a - 30n
68. 2, 10 a - 30l
69. Exaq. + fint l1. 160 + 16 aB ~ 1. 150 1170 L a 2 N et ex ag. 5 filq 11 170 - 170 faC = 11. 60 + 150
70. 160
71. vel pro ag.6 scribemus ta ta 2 - 16L o 160 Ya C) - 150 1a 2 = 1 1 (19 - 160) se 160aO - 15 a 2 3am- ) e
72. 2. 150
73. sit l.em = e l+m = f (ln = h. (n = 9 et fiet 150 a4 - 160 la 5 =1. 30e. Et pari jure ex 49.4∞
74. fiet 150 a Y + 170la C 2. 3bh. Ex aeq. 8 fiet 150a4 +16074) - 2. 150. 160a504 - 30 ée. seu
75. 150 a 2 +16040 -(35 ee = 2. 150. 160 a 102 et quadando utrobique 150 aa 42+16 aa 30 + 2.150. 168a02
76. 150a 2 + 30 t = 4. 150. 160 aa (32 vel 16+1 150 aa 2 2 16 aa )- 2. 155,160 aa2
77. Ca2 - 30. 30 ec) Et pari jare ex a.9 fiet 150 aa 24 + 17 abB 150. 17dac = 30. 3ohh (2. 150 a - 30. 30 hk)
78. ibi ut melius obtineatur e calculi contractio inclusa patestthesibus in 99. 10 et 11 aequemus quadrati o a sit
79. = 2. 30, el 1160 a0
80. et ex eplicemus a27 a0, a fiet . 62 Et ex parcathesi aequationis 10,fiet fiet
81. = 30 30 ee C3. 160 a
82. + 2. 150: 11. 11aa - g. 8150. 12,3(030. 30. C =100. 100 seu 12aa = 18a (11. 302 -2. 11. 1504- 2. 11 160 a
83. 2 158, 260 + 160, 250
84. +2. 150. 112 a - 8. 150, 12. 270 au - 30. 15= 205 at seu -412aa = 200 + 15. 38hh - 2. 1I. (150 + 176)69
85. +2. 160.... . . - 8. 160. 12. 259 ract, odi
86. Sed ex aq. 10 ope aegB fict 150a24 -160 a0 30. 1100 seu 10 1N = 4. 150. 12. ∞ - 165. 11 + 4. 165. 12. 250 = f 1B. 30. 1oaC
87. X, 138. 270 = 1702.250
88. Et ex parenthesi aequationis 1 fiet
89. e v = 150- 160 - (10 a5 = 2. 10. 304l + 301= 10 a) + X 10. 3e am - 38 mm = 30. 9 d. VF, - 2. 10.30a
90. 30. 14e
91. Et pa
92. +2. 17
93. 8. 170, 12. 250
94. honto seu 30e, 305 - 2. 10a = 30C ap. 41 e, et fiet 10- 168
95. gure
96. rit 30g 2. 10. 29
97. et ex ag. Hop5 aequ. 13 fiet 150a8 - 170 aC = (+) 30. 11, 200ah Et faciendo 30g- 2.10a = 24Y fiet actiqus ad imitationem aequati
98. purs 17 fiet = 4. 12a a (4) 1. 30. 200. a h - 30. 2e41 1.H F, 3 175. 250- 158. 270. Resolvende sunt ergo aequationes 12, 13,10,19
99. 1 168. 250 = 1 10a + 101030 aal - 240 504 n - 2. 10. 30 alm + 10. 3 eamm + 38m. Eodem modo 180. 250 tan-
100. 2. 10. 36 alm = 10. 30 all + 38
101. tum pro M pbicuod R
102. 190. 260 + 1002. 250 = 130 310 150. 270 7 170. 27 - 320
103. 150 260 4 1602. 250 = l9V et 150 20 + 110. 250 = 90. Et ex aqq. 12, 13, 15, 17, fietit values ipsius Aurna
104. 102 a + 10,10. 30 aa M = 210. 20a
105. mesta 3C +168 = Eib f 4. 1030 af +30Utmm) Sed compendio sit 150+1602 = D et 150 + 170 =
106. L23
107. olo Sad quiac in hisc Honrinuolviture et Et pari compendio s
108. 150. 260, =
109. Easo ex aegq. 12, 13, 13, 11 fiet - 4. Laa = Lob a +11 30 ee a 460 aar: 2
110. -4. 12aa = (4) 1p. 30.200ah - 30. 241. 11k, : 520 Aefe
111. -4. 12aa =3200 a + 11. 30te - 2. 80. 1 a - 2. 8203 se
112. unde ducendae sunt tres aequationes, intervenientibus lise quanditatibus _ 1c, 200, 31, et passim latentibus 10, 30.
113. 11
114. 15) + 11. 30. 1002C - 30. 141. X C,: si0
115. +. 1005203 ae() 200. 5103 ah,, 14 1. 520 241. 518
116. Sed ex aeq. 12 et 13 est 11. 113=108. 3203: et 30. 320 e 1. 2d0 310 aa. Et ex ag aequatione
117. =4. 12aa =
118. Ex 15 et 17 fit
119. quaddandi fiet
120. 3. 180, 320
121. 11. 112100.520aC, f (() 2. 100. 200. 518. 50a eh, L H 41- 520 a = 2. 141. 241. 510.51 a eR
122. 1760. 310 a
123. =30. 03hh
124. ratio inter 100 200. Sed opus est ad huc gna aquatione
125. 224 S aahh
126. Ex 12 et 15 liceret r iN. 11. per 1002 et ex 13 et 17, R pera 200. Aempe ex 12 et se ea
127. 4+200. 5108hb
128. quos duos valores saquando habetur
129. compendio 3oceur 180a
130. 2.30141. 318. 11C
131. sit (aa et th 2. Buq 1ra Ex 12 e15 fit 51D. 10a 51P.616I = L 303103. 1o0aC
132. seu t a2 3 .5 ta C. 10030 qu (61 100. 100 d. 30 (318: 510) 114. 109 + 30 qu (313: 510) 11 d ee
133. (+) 220(32D: 520) ah F (38qu (3103 520) 2th- (20 d - 2. 30 241 (3 W: 5203)
134. et U, et firt tandem. L 30(3 + 30. 340 (5202: 5103) a ee = 529C (30 qu (3103: 510) a
135. 30 qu (318: 310) 11 lee 610.14
136. pror modo 200aa
137. in aeq. 18, eva.
138. 19. 3163 (38: 510) a hh ( S1h, 5(30 qu pro . 510) ath - et,
139. ione suo et it
140. quos valores suc gitue
141. 14152e +241 510 ah
142. 50e = 510252, 141. 520 de -241. 5W a h
143. Hac aequatro moltiplicetur utretique per sioine ut tollgntu ra
144. 30. 310f2874a CC + 520 CY (30. 318 a= 610 a = 2.39(4 5103
145. 30. 2b. 51 aahtil H) 516hr (3 . 320a h = brex 5ec aa f 30. 241. 320. 520
146. 31= e 40 +1
147. 32= 41. 41
148. 31 = 2. 40. 21
149. 32 = 21. 21
150. Ma2
151. 2 1
152. te
153. per +13AMI.
154. a (T3A (1a L. 131
155. simili (13AM- 2.1
156. aq fiat
157. caeteris tracturi potest
158. tur extra HL
159. 2. 13 n5. +naa + L. 13
160. ura
161. x aeq1+ fict
162. ex his quatuor aequation
163. tractabuntur
164. erit aequ. 12
165. 1.
166. vae praestandae
167. 13XM
168. 13A02 + 13105
169. et ex 13AM seu
170. Ergo 13A (I= 10.31
171. pe 200. 2dt
172. oo 50.
173. 50+68
174. Umme al = I + runsit ak. 1
175. 298. 201c
176. lit et
177. a ex aeq. 14, 15, 16, 17
178. A+3e hk 2.G
179. 2ooroe . t inga-
180. 14, 1
181. . 102
182. 3.7
183. +) 81.200. 201
184. a 2 6 ud et
185. el.
186. eto
187. a
188. Sia q
189. = 13
190. E et fiet ex 8 et 10
191. Uonna

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 90v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068198:0180?run=74