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Leibniz-Handschriften zur Mathematik LH 35, 13, 3, fol. 127r

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.

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. 128v); this page is its right half.

The machine reads it as

  1. Ires Numeros invenire quorum diffecenbia sit quadratus
  2. Tres Numeros invenire ita ut duorum quorumlibet differentiae Cail F Z + X M
  3. summaeque sint quadrati.
  4. Numeeus pumus. Vat.
  5. serid
  6. Numerus dy
  7. Num F.
  8. Num. 2
  9. Num 3.
  10. at
  11. al-
  12. al - X Z
  13. 4) Dift. Numg r. et. 2. X2
  14. ) diffra Numeri 2 et 3. 72
  15. (6) Diffra ctumeri 1. et 3.- X (2) ⊓ C) . Z (Z
  16. (7) Ergo
  17. s X2 = C bC - c
  18. +) 2C
  19. (0) summa Numeri et 2, 2al = X, 2
  20. (9) Ergo.
  21. (10) Numerus 2.
  22. (11) Num: 2.
  23. (12) Num. 3.
  24. a e d + X.
  25. d 1X
  26. 1 =x
  27. a X
  28. F2
  29. Ergo Z
  30. d X 2292
  31. (14) Summa Num. 1. et 3. (4) - Z r(d) ( 2dg + g
  32. (15) Ergo
  33. al -XV
  34. N tal - X, 2- X a + 1.
  35. 1 -at e aleX Z+ K
  36. al - X Z ∞ al- d
  37. in his 4 aequationibus continentur
  38. omnia Responsa possibilia ad quaestionem
  39. quoniam nondum ulla facta est deter:
  40. minatio, atque inde eruere deteret, qui integros
  41. minimos possibiles quaereret
  42. -2641
  43. puc en h, fet 1
  44. 2 seu vidinum. 15, 2 9
  45. poeps,to
  46. (14) summa Num 2C, (1). X Z ( )dg 1 g2
  47. 15) Ergo
  48. (+) 29
  49. a
  50. 41
  51. seu f 4 gr vet num. 16.
  52. seu 5+(4
  53. 1610+
  54. 41+ aequari quadrato
  55. + 1- hef
  56. 4(4 I
  57. a1) N E
  58. =14 157
  59. Z fiet 5af 25 h )vcl 1618
  60. 16lo 4(4
  61. siom 16h + 5 Na
  62. fiet n aequali S
  63. 4 N vel 572
  64. IT.
  65. ponatu
  66. 5+Y , +
  67. d F. Z- g. sive per 3. a V, et poundo C1 ED. fiet dpj 4 14 = 9 et p2
  68. (6) summa Num. 2. et 3. d.- x2 yk
  69. ++
  70. (1)2 fal. 3,,
  71. Ergo (4) ponefti.
  72. vel (d (4) 2dg + 9- X S1 (d )idg +9 3) sg + f
  73. vel -h 1
  74. sver
  75. et 5
  76. - h et. vd. pumit.
  77. () A
  78. )
  79. ( NF ) afC+D9 sg + f2. d 1 g CCFD5., dant quadratum.
  80. Ponamus L sq fire divisis omnibus per f fiet:
  81. L 1
  82. a a c) dt tud 1g d Wis
  83. h fa g. e C+ 29(g (119+ f. Pdans l r 4
  84. Ergo f habetur pure cempe
  85. f,29
  86. +2647985, t 4
  87. onans h se
  88. Ponamus 1+(+ s 13f+ f 70.
  89. eet
  90. (+) 140
  91. D +S
  92. () et
  93. f + vs + H g r sed hac divie.
  94. f. +Cd H0.
  95. Sed ista duisio aequationum per alias Aequationes non est, nisi raro et per accidens apta
  96. instituto praesenti cum enim duos praebeat ipsius f vigs valores hinc eos conferendo
  97. (nom enim hc de potest ipsa f. eaditur. hud minime ut jam vided, tantum enim
  98. duo habentur iptius F valores, seu rudices aequationis, id est utroque modo satisfit, apta
  99. + vs + W ig 9 f 4 v co epo Ergo vC -Co e _ g2 Ergors
  100. ergo inisi fallor inftituto nostro haec divisio censenda est:
  101. Acof- cos
  102. F - co + c
  103. su + cof
  104. pone q E co, fiet: vas- co - W cor
  105. et cop dest2 Ergo fp ut
  106. Wx + (3
  107. Eve
  108. WX + 13
  109. Nac mihrodo divitendi utcadum, quando non licet Quobus valoritus in locum ipsarum f. et g. substitutis videbis
  110. is e. vo
  111. sue pre ut g. scontneas vel contra, quia
  112. n continet i
  113. iu numeris rationalibus, v. L, W. X. pro arbitrio sumtis
  114. satisfi eri aequation. Hime jum quaelibet aequatio quadratica
  115. affecta, nullo negotio in numeris explicari potest, facilius
  116. quam si eam volut spemus apta re ad extrahendam radicem.
  117. Si Radicem inde voluissemus extrahere sic fuisset procedendum;
  118. Quando ergo N quadratum est, ut in nostro su aut facile reidi potest caeberique
  119. V S + vs + W gr 10
  120. V hiet gr
  121. +2F4 P
  122. apta sunt, in nostro casu, etiam extractio commode institui potest
  123. ne sri a ctg i 9 C 9et s sp. 2. cen moo E si n. iga
  124. 2C2
  125. 3400. X (

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 3, fol. 127r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068200:0255?run=74