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Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 77v

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: 0.78.

Original at the GWLB · Page image · Annotations (IIIF) · Download text

The same scan is also registered as fol. 78r; its text is given once, here.

The machine reads it as

  1. n
  2. diveuendus
  3. Resii subtrahendi, qui una
  4. cum dividendo consti-
  5. tuunt Residua
  6. evotiens
  7. Ax 1X divisores
  8. 44 uX
  9. qu = C
  10. 2eri - D
  11. 2
  12. seu f - 26c edr. 2
  13. e
  14. 1
  15. dabit
  16. Ergo si Aad. quadr. de:
  17. (i 122
  18. 2x 1X
  19. 8
  20. 2
  21. a
  22. eX)
  23. -2Besca
  24. MAX
  25. Ei.
  26. invyx
  27. Hoc absolutum
  28. 30 X2, 31xt , 3 A 1 qu
  29. AA N ARX ACX+
  30. 41. 31 3) Rt2. 31 3 2.31. 33 F2. 31 3 42. 3. 25
  31. ∞
  32. +1. 327. t2. 31. _ +2 313. 12. 32. 25X
  33. 15333 21724
  34. 42. 33. 35X
  35. +1. 24. 34.. 12. 37 XX
  36. 175.7K
  37. 1, gus ade b) 10X = u X + 1. X - 13X + 14 X r s X abk mto gt ssirrot
  38. 10 = 130. 30 1 3
  39. 11= 2. 30. 31
  40. 12 = 2. 30. 32. = 1. 31. 31
  41. 13 = 2. 30. 33 +2. 31. 32
  42. 14 = 2. 30. 34+ 2. 31. 33 41. 32. 32
  43. 15 = 2. 30. 31 + 2. 31. 34 + 2. 32. 33 + 1. 33. 33
  44. etc
  45. coincidit prioribus pro A, B, C, d, etc
  46. ponendo 30, 31, 32, 33 et
  47. addidi autem 10 vel A, ut primus temunus
  48. et ultimus eodem modo tractentur
  49. 31 = 11 L: 2. 30,
  50. 32 ~ 12 - 1. 31. 3] (: 2. 30)
  51. 33= 13-2. 313C, .
  52. 34 = 19 - 2. 31. 33 - 1. 32. 52
  53. 35 = 15 - 2. 3134 - 2. 31. 33 : 2. 30)
  54. Hin exigero residtum ne + c
  55. 1
  56. et
  57. 2+ 14. Quod si residui
  58. scet et 5
  59. hoc accuritus ex aminanda
  60. F
  61. X +AK +uX 1BX +14K + 5Xm l + 1X BX +BX +GA +20X
  62. X= Bx +Cx +DX +EX rF XS etc
  63. X + JuX
  64. Nota 12 non latet in BB sed 11
  65. 1 non latet in BCsed 11. 12
  66. 19, non latet Ed, CC sed 11, 12, 13
  67. la
  68. Hinc continetur in hoc calculo modus
  69. etiam altoltend inveniendi potentiam
  70. ex radice generalis, quia est
  71. 1 = 2B et 12 = 2C + BB
  72. et B3 = 2d + BB .t 14 = EF 2BD +CC
  73. unde video potuisse haec erdem obtinesitem
  74. extractione, si modo instituissemus n
  75. cationem. Et quia extractio fuisset incommoda
  76. et laboriosa in altioribus potentiis, pro ea utem
  77. mulliplicatione excitatione. Eademque exrtatio
  78. serviet pro affectis aequationibus; seu pro extrecton
  79. radicis affecta
  80. Residuus constat ex terminis quotiontis pondentitu
  81. multiplicatis per 2. Et (quod notandum, set extra eu ter salis
  82. terminorum7 verb.gratia; erit Ex etiC quotieutis,
  83. sumamus terminos quatuor priores pro
  84. tres sequantes per
  85. Il
  86. l
  87. autim nem , e
  88. icalo soll
  89. EBE B
  90. 216
  91. pasietx si ase astes
  92. Haist
  93. aec radix commode applicari
  94. otest ad Duad
  95. exp
  96. Numeri extractionem, nam
  97. devisio per 2. tantum removet
  98. in gradum sequentem
  99. potest etiam ex pro X,
  100. substitui X X, X, et
  101. quasi esset Y 1X + uX ex
  102. omniaque privibunt eodem modo
  103. quod aptum d dicis,
  104. ut
  105. t cum exacte
  106. sucedit
  107. pructio nihil refert auat
  108. unde incipias, ab initio an a
  109. fine, et in 3adicis mneo more
  110. tractatis per periodos columnares
  111. utile est incipi a fine
  112. i tine incipere licet etian cum
  113. resiri sant sid eoanidant
  114. vel XX
  115. LHt.U
  116. vol de sbrcoX + nosx
  117. +4
  118. mxxtramuxraanu
  119. PIXX + 2 apgx Faaqque
  120. +15) 416d
  121. et 17)
  122. De-
  123. 14 2. 11. 1. 12, 12. 12
  124. 1610) 4. 10 1020
  125. + 1 1
  126. Pa2
  127. 17
  128. C18
  129. 2+19)
  130. si volumquse non omitti eu et A, quasi
  131. osset 10 X = y X2n.t etc
  132. et AX + BX et
  133. et ft si - 2BCF 13-0
  134. Hiil 13AR. 810 = 2 1011. 12 + 11 = 0
  135. Hae series sunt ex numero maxime
  136. intractabilium, ubi scilicet
  137. 4 .. etsi A. cenrafit 14 AA 641 3 - 16. 10.1 0. 12. 12 + 8101.1112 = 1 0 terminus sequens indiget omnibus
  138. A = 10g c = 14
  139. AX+ BX FC AANAEAOxAIACXY
  140. Px ga
  141. E+I5.
  142. 410d
  143. AA
  144. 10X a r3 4ei 113 X +4Y
  145. sit his ab taac aequanda qto, posito m+na. sint m Xx + chamux+ haana
  146. posito y-
  147. +4
  148. vel uesa
  149. Haec est alia ratro procedendi, ubi primi et ultima termini tactaatur eodem
  150. modo, videndum quomodo duci queat ex priore.
  151. ar ∞to
  152. C pXY + C a P4X +C quqq CpE t p aq X feb pp aa qu ex + 4 pa X A
  153. bem pX
  154. praecedentibus.
  155. .2 s10.14 + 11. 13 = 12 fiol 8. 10.14 e -4. n. 10. 14 + 11. 13 =0
  156. 4(10. 14
  157. Haeunqque
  158. b2 ppannx
  159. dest 10X + 1 ∞3
  160. a nnxibrapquanx
  161. apt rox xax a
  162. Et resioni crunt
  163. prout longius
  164. proceditur, quin
  165. semper numerus
  166. terminorum
  167. residui, est
  168. unitate interio
  169. numero termi
  170. norum radicis
  171. ne
  172. fielte prodt
  173. es
  174. B- 20
  175. cc=
  176. si aequatio habet duavamtmet
  177. duas rndices aequanes, videndum
  178. an aequatio factu multiplicave
  179. arthmeticae prog. habeat adhuc
  180. duas radiées aequales. de
  181. i , B, d ntert relip) vel etc.

Cite

Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 77v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068201:0154?run=74