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Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 293v

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: 0.77.

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The machine reads it as

  1. Numeus Terminorum inqualibet forma specimon est artis Combinatori
  2. sed usum praeterea debet
  3. formae refficiende
  4. 1. (1.
  5. 30) et.
  6. Im (l BI) c.
  7. em (Bm. 131)
  8. Iun (lnir. (m 3 3)
  9. l’nn emin. 1m
  10. Bmin (mn. nn)
  11. C
  12. Imno (ek).... . 0
  13. Imino .......
  14. lano. ......
  15. reece ea ec
  16. Bmno (P mino no). 0
  17. Uneno
  18. maeximum ad
  19. 15
  20. se
  21. 1
  22. 20 35
  23. multiplicationes formatum in se invicem compendio faciendas.
  24. 2E
  25. 56
  26. 60 165 16E
  27. 120 20.
  28. 15 35 70
  29. 84
  30. 10 A. Numliis literarum teu Naturales
  31. 54
  32. 108
  33. 120
  34. 252 360
  35. B. Numeri Combinationum seu rangulares
  36. 2B. .. . . . . .. dupli B. Nam 1n) dabit
  37. vuns
  38. nen mu
  39. Numeri Conhuationum seu Pyramidales
  40. 3C.---- -tripli C. nam lnn dat l’orn. ln. lnn
  41. 2BC.... . . -- Nam varietates, 13nin. fiunt ex varie.
  42. 126 210C
  43. 60 10... ..-
  44. .90 210.
  45. 180
  46. C
  47. latibus lmn. hoc modo. Quolibet hujus
  48. formaeterminus, ut l’nn dat duos seim
  49. nos prioris formae, ut l’n del lmn,
  50. aa 1m
  51. Ad.... - lmno. Io. lmnc. lmno ex imno
  52. 3,4D.-- - (1igo (lnno (1nno ex l’mino.) ubi pates terminum PNno bis prodire
  53. -34d
  54. producendae formae ut
  55. (M) no. Ino. mno ex Imno eodem modo et reliquos omnep.
  56. Ergo ad habendum numetum terminorum formae lmino ex fea nino
  57. debet variatione unius termini in forma lehuno, debent variationes pro
  58. venientes dimidiari.
  59. Bm n0. lmno. Pmno ex l’nno.: Nec metuendum hic, ut si caeteros
  60. formae variandae (1hano) terminos, ut Impo varies rede at aliquis terminus nn Imo. Imno ectmno. ratio est quia nunquam iterum
  61. redibit 13. Quod sasecus erat in prodiuenda forma l’mno. ubi 1 duobus modis prodire potessat, uno ex forma varianda, altero ex variatione.
  62. Imnop...
  63. l Mnop..
  64. lmnop.
  65. 0
  66. 3
  67. 2
  68. 24
  69. 120 360... . . . . . ..
  70. .. . 2, 3,1. D.... . .. . . - l4 M 3p20. 14m3nO ex l m n0
  71. Vm2no. 13otno
  72. BB no
  73. 26 5b 126 22 E........ Numeri Consnationum seu Trangulo. Pytam idales
  74. 30. . . . . ... . . . ..sE.....-
  75. Imnop. Im nop. lmn op. Imn6 p. Imnop ex imnop
  76. 60... 560......... 45E......... (Om nop. (Omnop. (1) mnop. Omnopre l’nnop
  77. nnop Iop. (m nop. L(n) noB. (m nOP
  78. Unde patet. Nunerum formae emnop esse 45E. Nam si nulli repeterentur etermini variatione producti foret numerus 45E. idem aptera terminus
  79. non nisi sene l vedit, quod jamtum praescire possumus, quia 4, 5, seu 26 non potest dividi per 3, sed per 2. Nam so non posse manifestum est
  80. Nam quater aut quinquies prodire non posse, manifestum est.
  81. 20
  82. 120.. . . . . . . . .. 4,5E.. . . . . .. lm nop. Bnnop. Bm.no p. Pmnop ex l’mnop
  83. 180
  84. -
  85. 3,4, 5E
  86. CNam numerus terminorum hujus formae, fit ex 4, 5, E numero terminorum praecedentis formae, multiplicando eum per 3. Cujus rei ratio est, quod
  87. omisso (3, quia per variationem non producitur, perinde est ac si ex mnop. per voriationem produceremus m ox. sive si ex lmno prodneremus
  88. d
  89. vaciando cujus numerus erat 4D, produceremus em no cujus numerus est 3= D. quod fit numerum formae variandae multiplicando per 3
  90. 60 360... . . . . . . .
  91. 120 720..
  92. ... 3, 4, 5E.
  93. 21 4,5 C.....
  94. 28 84 210 F....... Nameri Conbnationum seu Sestarido pystamidales
  95. 6 42. 168.504 1360 bF
  96. 15 185. 240... .
  97. 30.210....
  98. 280
  99. e
  100. 120 840
  101. 60420
  102. -
  103. SB. F . . . . . .. brevius, quod sex rermu combinationes 15
  104. 5,6,F
  105. 15,b F
  106. d
  107. 456F
  108. BhCF
  109. e
  110. (mnopus 1Imnoxqu Imnopq. minopu ex minopas bierius,
  111. a
  112. lmaopus hnc p mnopus unop ex Vm opq
  113. eninopus lmnopus min opus minops ex l opus
  114. 245,6Fsa. . . .. fit ex lmnopg. quia q recumnopq. sex sunt
  115. combinationes omnem duae
  116. qualibet ad cubm possunt altolli
  117. 30
  118. d
  119. 12nD13
  120. Mnop.
  121. linop
  122. Imnopq
  123. lmnopq
  124. lmnopq......
  125. Pmnopu
  126. lmn opg.
  127. le
  128. .
  129. a
  130. lnnopus ......
  131. lmopus
  132. nnopqus
  133. e
  134. .0
  135. 0
  136. 0
  137. op (o ).
  138. 0
  139. accu
  140. 2mno
  141. lmino
  142. Imno
  143. emnor
  144. o. 10. 117))no
  145. )no m o
  146. 1 130
  147. m Ini
  148. 1mju l) enile) hnon b)
  149. go(2

Cite

Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 293v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068201:0586?run=74