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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 350r

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.

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

One image of two folio pages side by side, registered by the library under both labels (also fol. 351v); this page is its right half.

The machine reads it as

  1. per 4 et 63
  2. per 13. )aegul (B) n3. 123n + 100. 112f = 313, 323n + 300. 31h 112. 123m + 100. 113f = 312. 327M + 300. 313a
  3. seu a) 100 () +313. 323n + 300031 h, : 12 +312. 323M + 300. 313h, : 113 100f qua alores
  4. 12. 123
  5. aequando fiet. 300h 12 312. 323 m 4 113, 113, 1231,:, 112. 313-113.312 et pari jure permulando 3.. et 1..
  6. in his duobus valore
  7. oppotis ynisfiet
  8. =112. 112. 123,1 = 113. 323.313
  9. 100 f+,2. 1n3. 312M + 313. 313. 313N, :, 113, 312 = 112. 313
  10. - 312. 312.323..- 113. 123.313..
  11. s
  12. similiter per aequ. 7 et g itemque 4 et 6 fiet:
  13. nhis duobus valoribus
  14. n et l differunt ut 23 et (3)
  15. oppositis siguis
  16. Aex 13 et 14, permutando l et n, item R. 12 et .23
  17. 123. v2. 323 m + 313 1B. m l,:, 1333L1 13. 313
  18. 1
  19. - 323. 323. 312.- - 113. 112.313..
  20. = 123. 123. 112 . = 113. 312, 313.
  21. =p2. 113. 123. 3r2. 323)M + 113. 313313213. 323n 4 112. 113. 127. 312. 323 M
  22. n
  23. Aequando valorus 13 et 15, fiet
  24. =112. 123, 123.312. (213
  25. 123. 313. 313. 343). 323
  26. 327
  27. - 113. 113 123 (31
  28. .
  29. 113. 31. 31 2313313)L
  30. = 112. 317. 313. 313319..
  31. = 112. 112. 123.313,323
  32. =113. 312. 312. 323.323).= 112. 113. 113.312813..
  33. + 112. 312. β313) 323323.. + 112. 112. 113,313BB..
  34. Agmerdind pe Mecta N L et n differunt ut. 12 et .23, item m es una parte ab m ex altera parte
  35. +123, 312. 312313, 325 1. - 113. 123. 123. B13)317
  36. 113. 312 312. 313. 325)
  37. intera quando valores 14 et 16 prodibit aequatio (19), quae ab aequ. 17 differet sola perimration
  38. It teth
  39. nemal
  40. in lest 42 et 213 et quidem loci
  41. 12 eto 23
  42. 12
  43. ea ontes
  44. initialium notarum 3 et l et n) differunt ut 012 et 12Z ouB
  45. et M ab
  46. in hac aequatione 17 itemque mabipera parte
  47. x
  48. it
  49. b
  50. 13
  51. erat
  52. ab altiqoinquam latere, vel quod idem est, in eodem sed oppositis signis; si mulque ibidem
  53. qudestruendis, factaque divis
  54. prodilne er aequatione 3
  55. a
  56. ut s
  57. Similiter aequando valores 4 et ab, prodibit aequatio fig), quae ab aeqiy differet sola
  58. permuatione initialium notarum 1.. et g. et eadtem lges quae in aeq.1, locum hrabebunt
  59. 3
  60. in ltjor
  61. E t tota combinationis lex ratio sic explicari potet: in lest. 12( et + e quarto
  62. in lest 12 et ∞13 Has notas posteriores in quovis Amosunit
  63. I
  64. n
  65. quinto
  66. 012 et 023 voco correspondentes quatuor quantitates
  67. B et 023 in litera a qua
  68. divessarum literarum memora
  69. oppes uidem signi sunt quae duo
  70. habent producentis communes
  71. sed mota ultiali et 3
  72. ocunno
  73. pantuus, quaet
  74. una in prmbro
  75. in iis utraque notarum
  76. semel, altera tet
  77. nascircur. Quodris membrum continet duos producentes aequales
  78. Ad eadem literam cuivis
  79. n opponitur
  80. aliud diversum.
  81. nota initiali
  82. sta
  83. posteriore corrispondn
  84. iael
  85. ae possibile seu est prena
  86. es hac lege possibiles seu est plena
  87. Nempe similiter aequando valores ipsius h duos nempe ex aeq. 19 et 16 prodibit aequatia 19)
  88. quae ab eod aequatione 17 in eo solo difert, quod permutantur 1 et 3. Sed quia
  89. opos cont
  90. iprodbit ex procedenti lege combinationis differt in speciem tantum; nam quia ex corollario
  91. etiam coincidunt item quod aequatio
  92. legis combia ationis paule anl ante posito omnes combinationes nobalinitiali et 3, et posterio
  93. Fribus 12, 13, 23, secundum literas l, m, n prodeunt in aequatione 17, nec aliquam novam combi-
  94. inandi materiam legem praebet aequ. 19. necesse est eam coincidere, cum aequ.
  95. jam praebeat
  96. Unde aequatio valorum h, ex aequ. 14 et 16, nihil praebet, quod non exhibeant puestitis et omissis
  97. 13, 14, 15, 16,t
  98. sumere initio 2i, 2423, 24
  99. aquabiae valorum f ex aegu. 13 et 15. Quod feliciter evenit
  100. 322 + 159 = 3 + 16a jumque 25, 26, 27 28, 29
  101. 22m+ 239= 1 + 267
  102. sana s esset p = () ron tun rn + 14f
  103. 1242 (ad 41t 245=
  104. + 35g = 13 t. +3Es
  105. 3n taS = 33n = 16fr. sit f =+ 9 + 16h, : 14 ut a 345 = 131 + 3bh. fit f- l
  106. (7) = H l. + 34
  107. 31M. 7,9. ita et procedemus ex valoribus 1, 2; 4, 5; 2, 8
  108. (34
  109. prodibunt
  110. 3 et 2, et pro E ponitur 4. et fiet f = (20) ut 13 et . 2009 = (21) at 14 et 1005. (22) utls et 2009 23) e
  111. Porro ut prolissimus ex a valoribus 113; 4, 67
  112. qum Etsi autem superfluum sit ultra progredi, post quam enim aequabimus ub quae ex 1.. et
  113. et .. M +.. n =()... M +.. ut 14 pro 3. ponendo 2..
  114. quae ex 3.. itemque quae rex 1.. et quae ex 2.. etiam aequabuntur quae ex 2. et quae ex 3..
  115. 38s29 quae ab ipsis 20 (21, 22, 297
  116. praestati tamen et aec postrema ascribere, nempe a49. 23, 26,
  117. 2009 = (26) ut 14 et 30oh = (27) ut 15, et 2009 = (26) 16 et .m +. B = (29). M +. l, ut 17 tantum
  118. (29
  119. hot solo different quod pro manente 2. pro t
  120. 1. ponendo 2 (24 tuI2M. 113 21 l + (13. 113. 227. 22G A((in ag. (4 31. 3n.313. 2yM L +31. 312. 313 21 L +319)31, 213 213 n
  121. 1alago (Fu2. 1Z. 12 V3M= -2. 22. 213. 43
  122. 12. 212, 723, 133
  123. 24 eit = Ar. 123. 123. 12
  124. 4, 27. 212. 212. 123
  125. Haec sex aquationam
  126. =112. 113. 113. 212.
  127. 4113. 21222. 213
  128. membra ponamus
  129. t rao . B) + s. s a f ut big it
  130. = 113. 212. 223. 2235 29eri - 312. 12. 213. 28. =312. 213213,215. - 313. 213, 23, 2270
  131. -1B. 213. 213. 21)
  132. 4113. 123, 123. 213
  133. aea
  134. 2. g Bi
  135. = 312. 323 43. 212. 3t. 313. 313. 212. 343, 213. 213. 23.
  136. +3123. 212. 212223. 4313. 212. 212. 213. 4313.523,313.213.
  137. limus bis, quam
  138. aib; et
  139. vis ex his terminis quansitalibus 22, 3 +bf9 20
  140. 212, 223 ponendo f9 fint +
  141. f. itus or (99+bb) t. (6 +2 b9g1 b 4bb9a
  142. + 46. 438 1. h b69 vrgo bel a 5 b. 9 vil c 15 = 3b 360

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 350r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0695?run=74