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Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 140r

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: 0.82.

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The machine reads it as

  1. voctam, quaeritur fdx sCaxtam, Extan) quadratura rationali. Fiat XXtam = OC)D artan = D98
  2. C erit ((X Xtam, XX+an) = OD8
  3. o=2ct + 2t + 2 18
  4. X = 11 Vh2 + u2 1t5 + 13 (46 +0 8 = 41tq + 42 N2 + 4318
  5. 90 = 21. 2lat +, 2t. 22a lt4 + 2. 21. 231 46 + 2. 21. 23 (46 10D-
  6. 1.2
  7. 23. 23a8
  8. 00D = 2121. 30 at6 L 2. 21. 23 30a (S + 2. 21. 2231 a 2 16 4 2. 21 22. 312t 126
  9. 2. 22
  10. 23. 23
  11. 2. 22. 23. 31346. +2. 22. 23. 312a4 n
  12. 2. 21. 22. 312 ah2 + 2. 21. 22. 300ab.. + 2.4. 23 300a6 1..
  13. 2. 21. 23. 313at8
  14. 2. 22 23. 313a276
  15. am) 113. 11346
  16. 123. 12326
  17. 100. 100 84
  18. am
  19. +2, 4. 23. 31 at
  20. +2. 22. 23. 300a8...
  21. + 21. 21. 312at.. +4. 4. 313at ... + 21.4. 323at..
  22. 22. 2
  23. 2723
  24. 2.2
  25. 3.23 S
  26. aequum coincidentiandum cum
  27. 22. ve
  28. 23. 23 X
  29. + 2. 112. 100. 8 Th 2. 13. 100G 1h6 + 2. 123. 1009128
  30. = 2. U3. 123.816. - + 2. 112. 1232..
  31. + 2. 112. 113 t
  32. 3a
  33. mMederi tamen fortasse malo liceret faciendo, quidem 312 = 313= 323, (quod etiam jam huilicapius catculi aequatio coincidit prion
  34. jam tumlicet et 212932 et 712 = 113 = 173, et 21. 22 = at 23 = 22. 23
  35. et 291222 12tn27 g.2+ 2ne
  36. ab = ac = bc fit 1B 113- N= 122 et
  37. 21 21.22 = 21. 23 = 22. 23 t 31L = 313 -323 ita. in atraque aequatione primaria una irra-
  38. 112
  39. 13
  40. 13
  41. a1. 42 = 91. 43 - 42. 43
  42. 112
  43. 113
  44. 123
  45. iIX +12y + 1Z + 10 =0
  46. =20. 13 (2b. 13 X _ 22. 139,-23,132
  47. +10. 291f23. 32 2
  48. = 20. 135 22.33)
  49. -(123. 30) fl2. 23
  50. 2 20. 335- 22. 13)
  51. + 11. 237p+23. 3
  52. =21. 13542237
  53. =az. 3115 F 1217
  54. l. 21.335
  55. per X, 9, Z, in elligemus Z, H, 6
  56. et +.
  57. 113
  58. 123
  59. tionalium coincidentiatio efficeretur
  60. 2F. 23
  61. 21x + 22y + 23Z+20 =0
  62. 3lid
  63. = 22. 13
  64. 112
  65. qq
  66. 1. 42 Em
  67. H3 41. 43
  68. +2330 + 23,31X 7 + 232932y
  69. du - 10. 225153
  70. +13. 20.43
  71. - 12. 23f13) 30
  72. 3
  73. quoda
  74. 3AX + 32y +53 + 30 =0
  75. 20. 33 -2183 -27.33 y
  76. +10. 25 (e oqu
  77. =13, 20() 32
  78. + 13. 2252330
  79. + 12, 20 23 7
  80. + 11. 23 (27. 32
  81. = 11. 22. (23,. 33
  82. (2. 21.43332
  83. F19. 21. 22.3
  84. = 12. 27. 23 3
  85. 13. 20. 22,33)
  86. 00D = xxtam = X +lam, X am, et _D4Z = X + - ar, x - 1. qu
  87. X 13, 22. 23, 3
  88. F. 12. 21. 63737
  89. 13. 21. 22. 33)
  90. ergo D aequale vel proportionale alterutri, v. g. D = BX + βf an ergo i 112, 113, 123 sunt ipsis 312, 319,323
  91. proportionales, et seu B. 12 = 72, B2 3: β123 = 323., ut β. 100 + β1 - am = 3008
  92. Prsus 00 = X - l + a sed par jue foret D = B)X F 9) suam, unde ficret
  93. V112 = 312, et ita porro ergo ) = β. ego foret (-am = - s an vel sinu tale quod sed hoc non licet
  94. itaque talis resolutio non procedit.
  95. an ergo
  96. X F V.am is rursi resolvere in binas, et X
  97. Ar ergo licebit. X+ daam, et caetera rersu resolvere in bina, quorum quodlibet sit quale O vel E, siet
  98. X. F Y-am = f9. X = 1-am = hl, X + 1. an = mn
  99. X - l- an = p 9
  100. siet et similiter D resolvemus in 5t, et fiet OC st = fghl, quorum quodlibet constabit
  101. possum satere fghl. si jum extribus irrationalibus simplicibus.
  102. foret
  103. et D seu 5
  104. quol eremus 3D = fg, seu X + Nnam extrahibilis, fieret etiam X- nam extratibulis ergo
  105. Rursus ste8 = mupus. ubi portebit face
  106. non licebit facere st = ma, vel p9, quia feet Xalam - x+ Lan vel tale alius vid. Ergo
  107. eu quadratus, et foret D X- 1-am.
  108. faliam
  109. sus ergo ma p aut tale quid seu
  110. et X 1 an habebunt divisorem communem sed nq vel onsi - eg. ita
  111. seu) in ed
  112. d
  113. s
  114. x lam
  115. videamus ergo an haec duo simul quad praestari possint, ut X+ Jam sit quadratus
  116. X + f-an,
  117. an, et X- s an habeant divisorem communem. intio ad hibermu sotu duas
  118. et ut tidnall
  119. u
  120. empe ves
  121. s b9 +cZ bv + cZ in AV. + m Z
  122. ectpabit CmZZ + bm + cl) vZ sit et sit Liap + blovtemZZ + (bm +Cl) v
  123. sit de pro ductum ex
  124. = quadrali ab v +7, quod est 0 + 2Z + 2VZ, et fiat bimt cl = 2β
  125. blvo + cmZZ + Yam = v B0D + B2Zs quod licet ponendo v et Z esse irrationales
  126. simplices
  127. X+ Ynam = sit + X = b sB + 16 in f + 91S, = s +c96 1(bgt . NGs
  128. hoc aequandum quadato a hv + KZ
  129. nam
  130. V.am
  131. Si saleremq 21 = 22 = 23
  132. et 312 = 313 = 323
  133. et (12 = 113 = 123
  134. coxxtam
  135. omnes irrationales binis
  136. binis aequationibus effici possent, una
  137. foret 2521. 312 = 112. 112-
  138. altera foret
  139. 2. 21. 21. 3005 + 21. 21. 312 (t + 4 +6)
  140. aequ. 2. 12. 1008
  141. Et similiter ob xxtan = DEG
  142. fierent bina aequatione
  143. 41. 41. 312. = 112. 42. (Erg . X- 4
  144. sed possunt esset. AeC 4 = - 21
  145. et 2. 41. ar sed ita semoa a posteria
  146. sed ita fieret 41. 41 foret = 21. 2
  147. et proinde coinciderent dd ut 94
  148. adeoque etiam xx +am, et xxtam
  149. 43 licet
  150. +XX] = 112. 112G7
  151. contra hyspothesin

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 140r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068199:0279?run=74