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Leibniz-Handschriften zur Mathematik LH 35, 15, 5, fol. 87v

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: 0.80.

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The machine reads it as

  1. sit Lia, XFL, XEm , XIn _) = ay quaeritur asy ax quadratura rationali
  2. Quaeritur modus efficiendi ut factum ex X+L, X+m, X+n sit quadratice extrahibile
  3. ex prae
  4. si AB, AC, BC, ducantur invicem produci Quadratum AABBCC
  5. Manifestum est
  6. fiat ergo. a,X HI = AB aixtm = AC, A _ aXtn = BC X = AB - at = AC - am = BC - a
  7. Videndum quomodo assumi possint A, B, C
  8. B = 21 SaO + 221a
  9. Tentemus facere A = 11 s( + 12 fa D
  10. Erit FAB = +11. 21 aC. + 11. 22 a SOD +AC - +11. 31aC + 11. 32a SOD
  11. =ab +12. 32 a D + 12. 31 11
  12. C = 31YaO + 32 VaO
  13. +BC = +21. 31 a C + 21. 32a16)
  14. =an +22. 32 a D +22. 31 .-
  15. -00. 00 an
  16. 00.00 am
  17. +12. 22 a5 + 12. 21 4a0 in
  18. Coincidentietur primus valor cum secundo, et tertius etiam secundo, irrationales interse, et rationales inter se
  19. 2 Ex secunda +21. 32 ) + 11. 32.
  20. +22. 31 + 12. 31
  21. +12. 21 +n. 31
  22. (2) 2. 11. 32t 2. 1231- 21 (12+ 52)
  23. = al
  24. 00.00 al
  25. Ex aequ. 1 et 2 fit 11. 22 = 21. 32 seu 22 =21 (12 - 32, :, 31 - 11)
  26. Rursus a)q. et 2 eas in unum addendo fit +11. 22 + 2132 = 2. 11. 32 ande 22
  27. 12. 31
  28. 12. 21 7 22.3
  29. +12. 21 4 22, 31
  30. Et aequando duos valores ipsius 22 fit 21, 12 -32, 11+ 31 = 2. 1. 32 (131 7 - 215+1275+317
  31. 3252 - 111
  32. D.
  33. 11. 32
  34. +12ZC+ar, s+n. s + 31
  35. fiet 21 = t12 31S1- 115 =, - 32t13i5 +27325- 1
  36. 11
  37. 2fF11. 325+317
  38. - 12. 31)
  39. tn. 3F2- 31.
  40. Ex coincidentiatione prima
  41. in aeq. 3
  42. = 12. 32..
  43. Secunda +21. 31 aO + 22. 32 a D 40000a C
  44. I1. 31
  45. Et et aequio per 2., et ita aequentur inter se
  46. =HI. 31
  47. - 12. 32
  48. 2125 +217O + 00.00 h- 1t
  49. eequentur Termini absoluti fit 22 B. 12
  50. ol. 31 52 = 12
  51. fieri 21() 1l3Cl- n). si teata
  52. coinsedentiatio
  53. at 1 231912. 32 (- 17 ) l. n)
  54. si tentaremus 2A AY 3+d aY feret 22 8
  55. 32s - 12Y
  56. et debet pari jure
  57. 12. 32
  58. l. p. 72 et nr. - 11. 12. 31
  59. sen 32= 2t HV FAV, . H. ande (ir. B. 31 3 13. 31. 3dCIB. (. H_L 11. 513rL
  60. 31 A = IIV
  61. 271EIaD
  62. et evanescente fiet aequatio nova
  63. 132s ~ +21(+22212310 400005+2712V
  64. - 12.32
  65. 11 + 31
  66. 3 g1. 32 -u. 32
  67. Lu32ZCM2L. SFII.32
  68. et erit 21 +11. 31, 4VII. P + 11.32] quem Valorem subsitundo 22 = 41. 31 3l- 325
  69. fiet
  70. ex coincidentiationibus rationalium ponatur m- 1 A et pL n = V
  71. 0
  72. 2-12. 31
  73. 12.71 - 11 12FII31
  74. (12. 1 = W I)3: H + 1 +2 124- EL. I1. 12V
  75. Ne qui valores 21, e 22 sunt prioribus aequandi, nec puto permissum ut aliquid pro arbitrio
  76. seu 2. H B. 3t _ = 31. 31 (12+ a) + (12 11) r (FF1)SIB + ( c V2
  77. asumamus, quia ex coefficientibus 1, 12, 21, 22, 3, est duae aliquae tnutiliter quo ad b determinationem assumuntur
  78. cum absorberi possent ab et di
  79. a0. V. 31 + 3. s1 .
  80. 8.32V Fo 71
  81. Sic ergo (alculum resimamus A = 00 da + 00 laD
  82. ax = AB - al AC = am BC - an m l=
  83. Lam est
  84. 391.II 21+32 = 31 +32 = ov. 315 + 00. 32X
  85. 0∞uf. 31 00V-321
  86. B= 21 5ao + 2 la D C = 31 la O+ 32 +a
  87. 00 s unitas A V v - 5 = X
  88. +99+106. 24 +00. 22 9D 40051 a F00. 32aSOD ~ + 21. 314O + 21. 32 a L0D
  89. es
  90. = +00, 22 aD +00. 21 a 4) = +00. 32 45) +00 31 a Y() D = +2. 32 a5) +22. 31 a YC)
  91. 22= 00 72 (31- 00), 3132
  92. 31200). 31-34
  93. Ex prima identificatione irrationalium, fiet 21 + 22 = 31 + 32 Ex secunda fit 21. 32 + 22. 31200 (31 + 32)
  94. - v0. 00 a R
  95. -00100 ab
  96. -00.0 am
  97. Ex 1 et 2 fit 21. 32 +22 31 = 00 (21 +22). Ergo 22: 21 ~00 - 32, :, 31 - 00 Et ex 1rt 4 fit 3t +32 31. 3 fit
  98. 21+ 32 - 21, : 21 = 00 - 32; 31 -00. seu 31. 31 + 224 - 21. 21 _ - 0c 31 -ogg + ee 21 = 30 21 s 3221
  99. seu 2t seu 31+32 -1 = 00- seu 31432 = 0s-3 + 31 - 00 ac denu 21 2 31 - 00, 31432:, 31 13231 32
  100. -2,32+ 31,:, 32831. Ita enim
  101. 0
  102. 31-00
  103. 21 et 22, differcent solum permutando notas 1 et 2 dextras, ut opoatet
  104. Ex prima identificatione rationalium, fit 21O + 22D, A 231O + 32D Exsecunda 21. 31 D, r2. 32D o 00 310+00. nD
  105. 21. 31] +6000Y,: 100.32 quos vatores
  106. =n. 21
  107. Hos valores coincidentiando fit, ex constrantibus A: Y = ∞ E XC 00. 32 A - 21. 32 X = 00 321 - 00. 22V
  108. et per 9; D 1270 + 00 A, :, 32. 22. (per 10)- 00:
  109. (13) 10. 00. 32 FR:, 22 = 00. 32 (r - 1):, or 32A seu 23 00. 32H:, ooV - 32 X
  110. tiq
  111. 3 - 21. 22.32 421. 31. 32 00- 31. 327
  112. EEd
  113. Siut 31 et caleg
  114. 60. 31. 31 (+22. 31. 32 = 21. 22. 31 (+ ∞
  115. eu 1021. 72 4 ∞3231 00. 31, 32 00. 22. 3, 15 21. 22 (32 - 31) fer 21 00. 32, 2t :, 00. 21. 31 f 21. 32
  116. Ex C pro C variante ( tollenda fit +00]5 +21]32 =-
  117. abe filfev. 31i3 2t. 3
  118. 13 e ad 2 f 209 213 =60 (31 +32 + 21. 22 (33-31, et
  119. Bu Etpo C variante tullenda fit in quae qua aequatione ut et n2 servanter inter se legem justitiae, seu
  120. d-. a(e - 2 31=C
  121. 0) f (22. 00) 325) + 0000. 00V
  122. =(31 - 21) 00V, seu 21 = 0031 (V∞A) :, 00Y - 31X
  123. duos t sulore tq 15, aequando sit do
  124. M2- 00. dor 4003 = 22 (32
  125. seu 2 00. 31T: ,100V - 312. sid idem debet prodire ex 14 et 15. Nan ebe 15 es Videamu examen
  126. unde si
  127. accut
  128. 30 21. 31.92D
  129. e
  130. Ex 9 fiet d2 (22 - 32) D + 00X1 :, 31 -21
  131. Et ex rationalibus sit mdentificasis, fit (t ) 31X
  132. equa
  133. 60.00. 21. 3cV = 00. 21. 32 32 = 00. 5t. 3 ∞. 90.5 H (100, 21 31 5) Etutle
  134. frei (00 -3)2 (00+21) 3FN
  135. Ex 15est 22= 00. 21. 32:, 00.3] 71. 7. 31 t ( 32 = ( 1) 31 + 32f2t, et fie
  136. +
  137. re
  138. 1- 21.3.
  139. 00. 21 32 = 00 3131, 0931. 32 - 00. 31. 21 ( 1 31 51. 31. 37 f rl. 31 3 ((21. 32. 3( 1 31. 32
  140. 60. 31 (32 - 1
  141. fiet (00 3c)Y t
  142. 00. 2IV = 32. IY + Z1. 3IH = 0031 T. fil 21 = ( 31H. turt 31V
  143. (X =
  144. 22- Fd, 1
  145. 32.91

Cite

Leibniz-Handschriften zur Mathematik LH 35, 15, 5, fol. 87v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068207:0174?run=74