Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

Leibniz-Handschriften zur Mathematik LH 35, 12, 1, fol. 310r

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.

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. 309v); this page is its right half.

The machine reads it as

  1. seu 4tZ an(+ee 4
  2. KK+CLLrr = ac
  3. rY+CC+KK = nn
  4. differentia inter
  5. rr et ce vocetur du
  6. 99 + kk vocetur ii
  7. si inter AG, et HG media
  8. proponalis in AH suma
  9. tur G5, et jungatur
  10. Cs, viceturque d fut
  11. ~ N = cC + oK
  12. ad Circulum
  13. Si velinus aequationem localem secundum duas convergentes
  14. AY et XY vel secundum V et Z tunc tantum insaequatione proxine
  15. praecedente pro X substituemas CetDV - ZZ,:2C, a unde pro
  16. XF substitustur V +Z + C- 2V1ZZ + reevr- 20122: 4 ee. quod
  17. acta faciendo, ex v 2atDv, ete. fiet
  18. ge V-egeeerr-Saegfee + 4 bl V - 8bb v0 ZZ
  19. deeatvD
  20. + 4bb (V
  21. eged
  22. ogervvr-gacdt ov + 4bbZ
  23. +0bb eerio
  24. +8ge 22DP +8a C9fZZ + 4bb+ - 8 bb ee 22
  25. +8aC2Z vV + bbee sp +gatger
  26. -8b65
  27. geeat
  28. + Aeeaat
  29. 8bbees2 Bateceu
  30. +4bbC
  31. easge.
  32. 4bb-9ge = 4cc(494 89g- 8gH 4 4ee = 4CC - agg- ggk- AKK taKK t + eC
  33. 1d. FCit
  34. =. 4cC = 4e0 + 4KK + 4 Ce = 4CC + AKK. = app. Unde prodit apMV
  35. unde provenit 4pV 4 pp V respondens ipsi 4bbZ+, stu per decussationem
  36. ob vvZZ fit ge - bb = g9 + gk -99 +CC = CC+gK, et fit (8 CC + 8gK) vV2
  37. ducitur AY in HC, et HY in AC
  38. 0b72 ft af g. bee = (991C - rr) (99+gX) - ( (cc 199) (99 + KX + 2gK) und sit
  39. unde sit -8 (rrgG+ CCKKH (99 + CC FrY) GK) ZZ sen -G(Bg ulet r.d. ar B Sig
  40. Ob vr sit eeat f geee t geas - bee = (rt t.gH.) r+ (5- 99) + (99 F9L) (gHXK
  41. 9+ (Ccg9)- rrgg H 9 30
  42. (9g+ KK + 2gK) (YY + CC C99 + g9+ gk - gg -cC) +. (99 +94)
  43. dd n
  44. g9 +CC LYY) =
  45. q9gGCC +KkTCKHCGtNignFXggCLC un tadin d
  46. ob vZ fit debet resolvi 4e, aaff - 2af eg + bbee ande fiet auff -1as eg + bb =
  47. qu (9gtec-rr) ret ruggue Errgg + (CC + 1) (99 + KK+ 29K) - 2 (9grec r1) l
  48. rr+ 9g =
  49. akk = CX OX
  50. 4((29kce
  51. -8 (rKK F Ccg9 + ggKK = gK (HK + CC + YY) vV seu - B(DD KK Hx tuggt ung H) v1
  52. gorrt qu cdt 9
  53. drbe (+ ) 4 99ccle
  54. V
  55. 2NICCC Errgg + ucqus teckiKt. rccyH +ggg gghX (+ 299gB gea geurus rg uous
  56. EA= 4eC (ggHK + CCCggHKK) + arrgK + qu (+ cc _ + nr)) et fiet tandem
  57. aequatio +qu e vr Z L 2 ggl t ep - 2rrg 97
  58. + (bb2
  59. AppB +2 0 a brZZ - 2 cc99 vV
  60. IVKK
  61. RngK.
  62. cc KKL
  63. mink)
  64. =DCCKK) 99
  65. =eetrr
  66. X99C2a.
  67. +2 G rceii
  68. dgrk
  69. mimgte
  70. gtr gK
  71. 5N = CC + 9tC
  72. DV= rrga qu. AR.. cebii
  73. paspini Yr + cc+g4
  74. e=9 + K- AH EXX = rrikt nd nn = rr + cc + kK
  75. i ggrtck
  76. ubi pp = cC+ KK = qu. G(B)
  77. in qua aegratione, v, q tractantur ut Z, K; at Y, C, ee s edem mode se habent
  78. ii = Gg+KK
  79. bb = CC +gg = qu. GR
  80. Utrinque. Et ad ec si permutarentur V, 9, cum Z X respectiae maneret aequatio eadem.
  81. Habemus ergo lo decicut aequationem localem ad Circulum
  82. secundum binas convergentes ordinatus convergentes, pa quitu qualum quarum
  83. cum non nisi quadrata dentur; erit Circulus locus ad aequationem secundi grad indeterminata
  84. secundi gradus binarum indeterminatarum quae iclationem excrimentem, quae
  85. cum eadem con quarum una cum constante posit v altera cum constante
  86. issit Z. Itaque 2 ad problema per convens binas convergente construendum
  87. Conjungi possunt vel hini circuli, vel binae rectae ut in pagina prima, vel du
  88. Sed cum problema
  89. bin circuli ut hic; vel rocta cum circulo, ut ibi et hic
  90. est solidum, et per rectas et Circulos construi nequit, identificatio aequationis
  91. localis cum data no ut coefficientes inveniaatur, nos ad problema solidum
  92. ve non succedet nos vel ad impossibile , vel ad constructionem problematis solidi
  93. praeliminaris, ducet; adeoque constructio fiet vel impossibilis, vel inutilis.
  94. potest ad huc augerio varictas coefficientium in constructione locali si vit Z, ve
  95. si pxponatur X angeatur vel minuatur per datam, ducta parallela ipsi AH; vel si Z au V aut augeatur vel minua
  96. irculum tervenilt. Sed nunc ad sectianes condias pergatum
  97. sim AG et HS sumtur
  98. partes si G cadat intra X et D
  99. anas potest esse excessus per
  100. agius respectu a aerius
  101. sit quadraitum suma
  102. rr+ cC-99, et gu 9G + CC. tr = a F) YYHCC- KH = ab H
  103. s Eridatur CR
  104. ralius angulo ad CG
  105. RG volctur C
  106. abet eoder
  107. tit pr- Ce+ (R
  108. recto, et puncta
  109. erit U=er+C
  110. irtertg=mm
  111. ageaas

Cite

Leibniz-Handschriften zur Mathematik LH 35, 12, 1, fol. 310r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068194:0619?run=74