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Leibniz-Handschriften zur Mathematik LH 35, 6, 25, fol. 4r

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: 0.73.

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The machine reads it as

  1. sua= Z1b- sdZ posito)
  2. Sitiu
  3. (2V2 codu co- 2t iea eot sit
  4. cs
  5. 6
  6. 21a+ 20C
  7. e
  8. (iiq a dZZ
  9. 214 + 2622
  10. (4)
  11. Ergo 2 - 2a saZ s siXtio
  12. Soz 2((+207
  13. Nai Sit ZZ = ax fiet: H2zd - adx et ea seu 2dz- o adx: Z Ergo 2adz. q ( adX: 4Z = ) dx: X
  14. lodq - 24B + 11Z. 142
  15. eda
  16. Ergo V(odx siponx. Quam vucamus quadia
  17. tau
  18. 1)
  19. _ 1 f1CX: 21+28+ = vv: aa ( t +10 x = 21 ∞V + 20V seu fiet
  20. X= EevD -iiaa, : 10a - 2VV et dX 10c - 2opp. 2. 2 vdv - 2, v - 1aa - rn
  21. (13) + 262. 10.2ia4 vav (= 2202 du
  22. eu dx =
  23. et dxiX
  24. =2. 11.208
  25. e
  26. (2 10a ( - 2eav
  27. + 2 24 PP ap dg: 1 lidaam bvo
  28. =11. 20, 2aa vav 21VB -1 a: (3500a - 20∞7... Ergo per 8 et9 fit
  29. (14) 4202
  30. du () +co 2 avav.
  31. X, 1olona 2dvv. Eervlcaa D
  32. 265) 10. 21 2VA. 2FvV - 11aa. P3I vaa - 20 V et 22
  33. = - 11.20
  34. 1ona -0u. 2dvv - 1iaa
  35. simil alare Reperi cognata ratione Ya- vel simlia summari. sit pro curva
  36. Ilochiona acalcu paracentulo, in curva alibi posita reperi. at: t = dm: aX
  37. potito am esse elementu arcus circuli _t radium exs centio circuli ad curvam; et
  38. intero allum curvae abscissam seu intervallum a condirectrice per centrum ducta
  39. sit A sinus veru rom coplementi arcui M respondens fiet du = ad2: taa-
  40. jam X = tA: a. Ergo dt: t = dn; 1tX seu at: vat = dm San
  41. jam habetur per M ex quadraturae circuli recipioco. Ergo set
  42. summam summarum habetur re latio inter t et quo et ipsa rusus
  43. ex circuli quadratura pendet
  44. Cum Hurgenius mihi quadraturam hius curva proponeret cujus aequatio sit
  45. X + B = RXy. Posui, y = Xv: n sit x = n3B: H + B sit 1 + V = aco fit et
  46. fet (ydx = nb n. 240 + 2n: 3aco ads es sumta ab ut adjectione summationis
  47. nempe yax = n vVdo - 2n v dv,: (3(V+n si restituamus X et y
  48. fit sylr = nb = p. 199 + 2nXX: 39 se, X inerpit a 0. est b =0
  49. 2025)
  50. mn
  51. mm
  52. =,1= 202. 21
  53. Sen v1 est, 20 10
  54. 20
  55. 20 21 20
  56. V - 18a, - 2.10 - 1 11, 10 + 19.
  57. IL.Ao
  58. 20
  59. oexetto ui 2o matro a
  60. V+ Va, H- 10 11 +10 _2. 11, a
  61. 12
  62. 20
  63. e
  64. 20 21 20 21
  65. p
  66. v a, 2a, E 20. 22
  67. t
  68. Le
  69. 20) 21
  70. 2u a
  71. ra, 13 + Lu. 1 - 1ero p Bori d) seu v- na -11 al 2 +10 0 1 +tromnu
  72. n um -mm
  73. 2.20. 2 a
  74. 10a + 20Y, 10a +2OV, 21V + na, t1V- 11a, VF ea, V. rea, v+ a, V- H a
  75. vrea LD 1 1 0 ua
  76. seu ve a, + 10. 18
  77. M
  78. m nin nmn
  79. en
  80. X 25+20aX
  81. quam summationem ut reducamus ad Quadraturas ationates, frat:
  82. (11
  83. 102- 208, 21V-W a resa
  84. (18)
  85. A
  86. ser
  87. seu
  88. 21
  89. Ergs A
  90. 213
  91. 2 212 202021 2a 20. 2)
  92. 20, 20.21
  93. 2 213
  94. 21 2 2021 21 20. 20. 21
  95. Seu r - a, 20, - 11 + (10. 10. 1
  96. +2, 101 - 18. 1= 18,1 B. + 101 V
  97. Seu 210. 115 + 2. 1011 =4. 18. 153
  98. Ca(1 -V, p= v2, 103- 10 112, 1 - 1. 10l sen 183. 153 - 1 85. 114) seu
  99. viea, 18- 1B. H v. iea, -1 + 101
  100. 203 20. 4
  101. 20 202
  102. + 1 10. 1P 10. 15
  103. vtra, 111. 10 v- La, - 13 + 1. 10
  104. 213 21. 20
  105. 21
  106. 2B 2128
  107. (et 2.20. 2, 18 -W a (.9) 20.10 20: 10 21:1 21: 11 (2(2, 10 21 - 11. 20
  108. 2
  109. 10a 20, 21V- 11a
  110. oies
  111. vert 15 - V, 102 D, B 1 10 41i -v, 10∞ 1. 11.8 +10-V, 11LV) 162 10. 1 + 18 - V, 1 AV, 18- 10. 1
  112. 16. 10a30 Seu, 2, 10. n - 183. 1 L 10. 1 B +1 8 V
  113. Ergo =
  114. 2(18) 10d- 20v, 21V- il a
  115. 10. a 2V, 21V- 18
  116. n
  117. vrea v. lea vFa v- a 10a 20 v) 2v- 1ia
  118. 22
  119. 20.10 20.10 W.n 21. 1. jam Bvv
  120. Ergo ap (uBdo, vrs v ea vita viua
  121. v+ b
  122. +b
  123. ubi b est a vel- 10 a vel t a vel - 7 a
  124. vib
  125. Ero alp rv. 20 ro 2- ion 2 +: vr. 2) b) (.1) o 20 1 aV r2or a ru nav. . naB) + G
  126. per isit 1Z.
  127. + 20 10 aa (av
  128. poro savsto = vrbs.
  129. 1020 vea = i ta
  130. 1
  131. na seu p 10 fdo - 10 (dx 1 pdie nsdo
  132. de
  133. a 20) vrea 20 v ea 2) vita a va
  134. v. EnBi va io 4 verum hic haeremus nam quaeritur siet
  135. non vero spdo. Sed dZ per v rarsus est rrationalis, cujus reductio ad rationales quaeritur
  136. vtb
  137. Redeundo ergo ad initium, paginae quae quer sit O= (dx. xe siet .. explicanda est e sic ut sit ax = 23
  138. X, 4 +28 ax
  139. etaex= 2ZZ et C = p22a2 27. a, N 4o . un
  140. nsasta
  141. 22 +202Z
  142. e si
  143. (112 41022
  144. Aqq X tro
  145. ergo ex equat. sit B- sax si+1o ax. quarum ergo finsur s compentii caursa serioque
  146. i i tro ax
  147. 2+20
  148. e129, seu e- 2
  149. ago aefiat
  150. vocemus D
  151. X= Ddu
  152. o aln ttu venus
  153. ae shero
  154. X Dax et
  155. no deripi dxomnes tenmini habentur dento srimo quarenda ergo lex serier
  156. n eo ZZ
  157. qu
  158. M -Hn
  159. +e
  160. n
  161. +MM
  162. mur
  163. a
  164. si
  165. seu restituendo
  166. ad- D, v. H a
  167. 10 seu 2. 202s
  168. 10a 105 a B. La
  169. sit desidevabatu

Cite

Leibniz-Handschriften zur Mathematik LH 35, 6, 25, fol. 4r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068070:0007?run=73