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Leibniz-Handschriften zur Mathematik LH 35, 12, 1, fol. 29v

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: 0.74.

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The machine reads it as

  1. (: paro 1676. pro h.. n conta sene rationalis quaerenqu 13. suo pinem
  2. 0
  3. +
  4. pro poneno ahae x PaB p 3a a
  5. intiquf
  6. a VH BZ et VZY
  7. V2
  8. +p
  9. VcaF Y 2
  10. VE unde hic rationalis figua
  11. 19e utius habe potest summa
  12. nan + sit Xp y + D fei ray + rab A a y +. a yb + = D. et hay pabrid
  13. Ergo Q ve 4 9 er 2ri y + quier ran +ane (a y) + 2aqu. + 29 49 1 + + ag
  14. et fiet 4. a9: y et fier
  15. et y C
  16. + a9Z + aq Ergo dindende per aq 9 debet + Z Y a
  17. + a + 42
  18. sulficii = a + ad 42 aequ van quandcato, seu: + a + 2
  19. 2 + a
  20. a2
  21. 100
  22. +3. + a
  23. + a nom quadrato
  24. atsano adcrum coincum a(dr aq - aY y , V
  25. (aquay)
  26. 2= Da. Ergo gu. Da, qu y () guadunto qui
  27. Z+ Sda
  28. quan
  29. + a + at pz0 A (+ 1 f20 quod
  30. ostis
  31. +1 - =. 1) 2 aequalio ipsarum sinquae honogeneae sunt curvae Conicae. 91 + 2.
  32. a
  33. qu+ queayt, - y
  34. et 4a
  35. qugu F
  36. a
  37. fingamus si 9+g c0d
  38. a H 2) aequatio cnvelonicae
  39. 2 +D Z
  40. aequatio ad carvum Conitam generalis figurae quae curvae conirae homogenta est
  41. et fiet y - 4 et q y p, 29 -
  42. 7+ Ba
  43. 5
  44. et prs Z Da C q 7 5 4 . fiet. Zasta (29 a 9a
  45. a2
  46. 2
  47. deuminudo ad tanigentes: N 2at + 2 t + 2a + +2at xt p 1Z at paxtz 4z at parir
  48. 1 +202 f24 r2ax
  49. V
  50. B
  51. tage dy
  52. compendit
  53. se
  54. rocurtiorpeir
  55. +1 + a E. seu a +2a +a+qX, rax + a t EZ aX
  56. cuique tH 4Z ax + 2a5 qu
  57. 11 2 2a8 f 24 X 720 f2a7
  58. per C p
  59. unde
  60. 216a
  61. ZaBa
  62. c0a
  63. Z+ sta, Z. IBa, 4+g, q y r qa. qui ponatu 9+ N2, 18a Z. id a
  64. fici ac q- y p 9a et q 3 p
  65. 29 ( 42, Z +ba. Z. iea no2e
  66. e
  67. .Ergo 29 qu 4 co ar
  68. 2+ Y8a. Z. 1Ba
  69. sei ( e 4u Z qada + co a p 2 geoz -. a D
  70. 2+ sFa, Z. 1Fa ponatur AZB 5C + d V + fa et cor det hr rla
  71. q+ tad ev + 2cLe, + dv= 1d fiv + fa- gaba + se tgnev + glaea ter hlavrVa
  72. B igec gder isa , ege +2cdge +2cfa+ dN e + 2d sagve +faege + d v ohsat
  73. 1 fa3l
  74. d+paetdr
  75. +2dflae
  76. - 296, +hv + ta
  77. +eh + la a +2cdh
  78. + 2 cfah
  79. +Ela cd aecf.
  80. Ubi habemus. v2. C3. ve. Cv. e. V. v. c..
  81. tollendi ergo termini e3. ev. et.
  82. pro e3 tollenda: Cg 10. pro e Y, tollenda erit d D+ 4h 170 2Cd9 +eh 0.
  83. 1ad.
  84. quorum utrumque non potest praestari rectius quarum ponendo c10. sed et. video hac eadem
  85. methodo non posse colli simus enim cer 9 ferent ( et evanesceret e, nec nisi una
  86. incogni indeterminata v, utaret aequationem
  87. 1a aq. list qu pone aZ B ce + d v + fa. et ay r ge+hvela. erit:
  88. qu C + 2cde v + efae + dV + 2d fav+ fa, -Da, age + 2ghe v+ Egla e+h V + Ehlaverae
  89. est
  90. viceo potuisse etiam si denominatorem nis dari ipsis az, et ayc. in queue intrassent ipsae
  91. O. et v, nec ideo ad altiores terminos ascendissemus, habuissemus alterum tantum arbitrariam
  92. adeoque libertatem destruendi magnam, at in aequatione D potnissemus quidem etiam majorem habere
  93. numerum arbitrariarum licet altius non ascendendo, onem sed ea cantione, ut ut idem sit de-
  94. minator ipsaruma Z. et saco. . Nimiram aequatio gaZ ( + co a + 29B a C0 p 29coz qab
  95. pro Z ponatur a8. pro s act, unde fiet: aN 29Ba AV p 24 a GY gaeD 173
  96. 1 6
  97. alri cetd0+ fa ac ge +hv + la. at metnorar
  98. nuspiam ascendetur ultra, v. C3. ve. Ex. v. e., ve. v. e. 0. quod si ergo desideramus, e puram. (nam par
  99. est ratio, cum eodem modo formetur ex C, quaen V. et si unum impossibile, erit et altrum). tollenda e3, etv, et
  100. x Ut excerpamus P3 fi: explicando saltem animo terminos quibus opus: quin eaMe +24 nCC C
  101. ergo aqg m +a C m +29Om C ∞ 249 9C + qB m3. Bt pro ev, fiet apntio tollenda fiet aequatiorusue negrgtent aen taectu a
  102. +248 md = 440 mnc 14g d + 493tc x 34d m n. Denique eroe tollenda siet: 4ga rqua quglac t q a cararcsam
  103. Lratnisa 24admare A 299fa + gglac + 4d3n e ar. ponendo maot Cn o. ratis fiot aequ. unde pro aegpr: 99 2 N299d
  104. n n
  105. 2d. et ex aeq. 3 9glapggza, seu la 2ta
  106. caerne artinunae et focr poperr ha et ea
  107. et s dot
  108. dvita s
  109. 13
  110. mmnuce
  111. fici

Cite

Leibniz-Handschriften zur Mathematik LH 35, 12, 1, fol. 29v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068194:0058?run=74