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Leibniz-Handschriften zur Mathematik LH 35, 12, 1, fol. 329v

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.

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. 328r); this page is its left half.

The machine reads it as

  1. Datis duobus terminis progressionis Hamoniae
  2. inventie tertium santo, illi termini Ae+ A
  3. a +h +b. Fy Invenire tertiuu harmonice
  4. proportionalem Dati sunto Z. primus. Z. a.
  5. secundus. Q- a + b. tertius; quaeritur b.
  6. vel quarit atb, ralio differentiam
  7. est a
  8. Ratio termini primi
  9. 2 ad testium est
  10. a 2.
  11. vel B= 2- a +b
  12. atb,
  13. Dit
  14. Multolicatudter lmin agintionus
  15. per fieta b2 = 4- a +b,
  16. a 1+
  17. ergo es
  18. a
  19. et b a
  20. a +1 = 2a - 34
  21. ba
  22. (4
  23. att) e
  24. 2+ a+1. = Z 2
  25. a
  26. ga-
  27. ba-
  28. 1+ 1
  29. ati = 2 ba ehqe 5 +1
  30. ba
  31. a+1
  32. 2 se 11.
  33. ba: ba.
  34. p
  35. sibbaa L
  36. b= 2, 7a XB, seu
  37. 2 +
  38. t
  39. A=
  40. er
  41. 12 a-b
  42. b2- ZF atb.=
  43. sei 2 Z = Z -a- 10
  44. e
  45. seu Z + a = q a seu 7 +1
  46. tia
  47. dseu
  48. =
  49. +1
  50. Bt1 a 6 L f1
  51. d- IseD
  52. = 1B. 1
  53. Dato probler sic ergo rectius cocipretur
  54. problema: dato termino primo seu
  55. maximo proportionis harmonicae,
  56. dataque differentia maxima
  57. (qua terminus primus differt a secundo)
  58. et per consequens dato termino primo
  59. ad et secundo; in venire differentiam
  60. secundam, termini secundi a tertio, seu
  61. edium fertium. vel quod dem est
  62. Ad continuare progressionem Harmonitam in
  63. ainfinitum A
  64. del
  65. 2a = ()
  66. fatbo et
  67. dC
  68. 1
  69. 32p a +b
  70. ua
  71. 3
  72. eanon t etf
  73. e
  74. e
  75. a + e tf
  76. +nC
  77. e-5
  78. 1. L
  79. 2ca- 1C es +a
  80. 37fg.
  81. odejus resolutio i
  82. 2aF caeteras datas
  83. fab se quaeritut
  84. 10
  85. 324 = dca = C 1d c- Qca. Dividantu
  86. 32
  87. ber
  88. na per C
  89. ut
  90. Jam Zualet
  91. Binao laradu
  92. ax + Xt2bL(4 (1Z6 ab
  93. agtharitea v.
  94. 2- ac
  95. Ta
  96. dic
  97. c
  98. e
  99. b. ergo
  100. +a
  101. 2. _E. Z. a = 5 in Z- (a - b - c
  102. l.s 5+ e c C xd.
  103. In prosie (o Harmonica, 2G ergo X - 1 ergo C=
  104. Est ergo haec problematis solutio datis duobus
  105. fier
  106. 7a-1 c H = 2a 5 v. -aa g2at ab
  107. (4)
  108. 4 - aa eu 2+ 4. L- gei 12+ a
  109. 26 a) 1, FI51A S(1) 3u(2
  110. seu
  111. d d. C = ASZ Ea puo Z substoliat
  112. 24a 2a9a
  113. 2.1 = 27.1
  114. maed (26 = 6+ 14+
  115. (a
  116. e
  117. terminis, invenires differentiam secundinuri item a
  118. 2. GEuo Zd = C hoe
  119. a tertio seu tertiu. minimum. quad ita fiet:
  120. A Terminus sependus, dividatu per 2.a = C Ergo ZC- a C = C. Et Z a - L seu
  121. dibterenti Primgu dividatur per differens C =C: Item B a- b = s E Ergo
  122. tiam plud actus addaber unrtate suma
  123. a
  124. aucto dividat terminum primum difet
  125. 2f- af - bf = C.. Et 2- a b +
  126. rentia prima minutum Quotiens est differentia
  127. Vatertia. Sic eego rectius concipiet problema.
  128. L. 4. b f,d c 5
  129. L.dib 3quf
  130. la habemus has
  131. tequatione

Cite

Leibniz-Handschriften zur Mathematik LH 35, 12, 1, fol. 329v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068194:0660?run=74