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Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 26v

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. fidt hu, i (Et 1eG) = Hb. Lt 1 f5 04- an alie 4 e
  2. = ma CD +unD - bh g- blq + m D L0
  3. 2bh:
  4. = hl 24 + 99C 4 - ch4q- chez 4 rtue 1B
  5. ob rmtionalos fiat th lih P ali4Z HH. abi) 0q .
  6. Aequitur medius valor, prico quam
  7. lentio; et ob irrationales fret
  8. ee GC ph (a. b) Y+mn D; hf
  9. 1b
  10. pee bhC G- bh 712 lli 2 1 G. cli 44 + Bg- si 4
  11. t.
  12. ut ex aeq. 3 explicando si, Kofilqu Ca. b) 8Y + mnumi 3D + 2 (a B) trn QD
  13. siet ( ah +5 74
  14. = h (C b) Q + mnD,: h9
  15. oberrationales fine
  16. e
  17. c
  18. fas G ul qule. Gylx t nuna DB +ih E. b) an 4B Aga (9gt b. e hq = mingus et ungude
  19. (t epaega explicano 3
  20. s in aeg. 5 si facias ff +(ba a h = o, sem f = (a- b) h, ermescant in ea co et 4, et rebidnisdiates per D,
  21. cb c)h 99 8
  22. siet m mnun D + 2h (a- b) m xQ nmfs0 + nutt G, vel mmt 3 + vnd z -mm = E
  23. Eodem modo in aeg. 6, si facias g9 + (b. c =0 evanescent in ea cQ et YL, et residuis divisis pls D
  24. tiet mmnnpA + 2h (c- b) mn q LtumggC + nnggE
  25. Et opi aeqq. 8 et 10 tollendo mmnn D, fiet - 2h (a - 1) mn Z + mn hh. 1) 0 + nn (a - b) G = - 2 h (c. 1) ma tmml . b) ex ul. 1)8
  26. et tirt -2mn G + mnC + un C =0, quod dectu in a = b + b. c, seu in a - c producit aeq. 11 sed di splicat
  27. quod il non inveniuntur. C) et Q et e intervendentibus t a, b, c..diiCi.
  28. Itaque praestabit redire ad aegus. 5 et b. et explicae caetera per D. purg. sit X 8 - 30DY2 et C = RCDF 4 et G - 30D +1
  29. lita opus est aeqq. 6. ad tolla ad AA, X, et D, _D, et s in utraque aequatione, habemus autem in eam rem
  30. hibitrarias 10, 11, 20, 21, 30, 3, F, 9 m. n. Tentemus tamen prius viam conpendiosiorem, et valorem ipsius e inventum 18
  31. Licerit
  32. Substituamus in coqu. 5, pat hhguscabi sq + mmani DB + 2h (c. b) ma 4 mmgu C) At gu (99 b.) ) 2m BC . gy lgge (b. esu mm Cd C o
  33. (1. C)t c9 ..aggnim D apragin YD
  34. 3
  35. + mn vg (gu Xb. 9) t) 9)
  36. h
  37. Comprndii sit . 1200 GL. + 1O7BH 10B2SCL IIO ZP +140,8+ 101D6=20 (tmnungu B)
  38. sint 3240+Zh et () = 304 + 3ih, Et ex 4eg. 13 fict 120078. + 1020. 20. 2098 17 1020, 2d. 21hG + 1020. 21. ahh 4
  39. Ubi H aequando nihilo coefficientes ipsorum
  40. e
  41. L
  42. +∞2 3030..2. 1002. 30.31 ... + 1002.31. 31 th
  43. +1110. 20. 1 21110. 21.
  44. IIN 30 , +1101. 31
  45. 1011 20. 30,-1011. 20.31 .. +1011. 21. 31hh
  46. 1011. 21. 30 1
  47. Sed quia is calculus paulo prolixior ideo redeundo ad aeq. 13, faciamus O = 210 4 + 201 D + 200h,: 000
  48. 0f.8) -7 210 - 1002. - + 20, 2. 1002D7+ 2. 20. 201 1002 - . + 2. 40 2001002. ( + 2. 201. 2902 D h, 200 L 602 it
  49. et ex aeq. 13 firt 000: 12008 + 800. 1020D7 + 9002. 111087
  50. O4 20. 1101 ..
  51. 000. 201 .1101. 300, 200. 110. 1
  52. +000. 200. 1011Jh
  53. uti tollere spaptet tres ter minos summos. fit ob X4 210 4 00e. 101, 210. + 0002. 1105 = 0015. 1101 - 4, 1200. 100Z. OV0
  54. l s
  55. 800. 241. 1011 DP +000210.1011..
  56. 1002
  57. 4. 10021∞o fiss 4. 1002
  58. adeaque 210 - ( (1101 - 4. 1200. 1002) 110I, 00b et eodem nodo (20 (10112 - 4. 1020. 1002) F 1041, 1 002
  59. superest ZD et fit 201 = 000. 210. 101 + 000= 11107:, 2. 20. 1002 + 000. 1101
  60. seu =2 L 000. 1011 (+ (1101- 4. 1200. 102) 1101) + 0c 0. 1110
  61. (2, 2. 1002
  62. 201 =
  63. O (105 - 4. 1200. 1002) - RCoc. 101 + 960- 1101
  64. vuo
  65. (25)
  66. (2d L (101, - 4. 1020. 1uo2) 1981 7 2.1002
  67. 1011 +(110 - 4. 1200. 1002) f 1011 . 101 - + 2. 1002. 1110 == L (1C11- 4. 1020. 1002) 1V11, V1101- 4. 1200. 1002)
  68. Emotandem 1aH H (ctO H02).
  69. et firt - 1011. 1101 + 2. 1002. 1110=- 1(1012= 4 r1020. 1002, 1101 - 4. 1200. 1002)
  70. quae aequatio explicatis significatio nobus pumerorum patiticorum, praestanda est ope residuarum, arbitrariarum m n, g
  71. et ex aeq. 18 sublatis 2Z, DD, 4) sperest 2. 20. 200. 1092 CB + 2. 20: 1002Y + 200. 1002 h0
  72. 000. 700 H1C1I
  73. undem redacta sunt ad per valores simplicissimos
  74. en
  75. (1611. n. 1101. + 4, 1002. 110 4, Per. 1101. 11O (122) = (1011. 1491) - A. 1020 (1002) 101 - 4. 1200 (002) 1011 +16. guor 1200. lest
  76. iaque superest explicatio numeroum fictitiorum
  77. Seu A, 1002. 111O _ 18H. 1101. 1110 = 4. 1200. 1020. 1602 quae aequatio servat leges justitice et potest inservire pro lanone
  78. 1020. 1101
  79. e 1200. 10112
  80. astenus vene nor culculi
  81. ll
  82. se nerali, aequationis trium literadum legis homogineorum inter se servantium
  83. reducendae per mtires simpli seu reddenda identicae per valoces simplicissi
  84. 5
  85. duarum ex his ex tertia
  86. 1200 = heb. 9 (hb. 9 +a0) 1020 = mump C h Ca b). B) toot mngs (9or hsb - c)
  87. h (a- b
  88. quia g9 +. (b- C) h. tam saepe occurit
  89. 111O = 2ma (9gth cb. c)) HIOC =mng Cgatib. Gh) _ 1011 = umgque (gg + b. d6)
  90. ideo compenvia vecetur hp et Hba
  91. (29)
  92. ha. 6)h
  93. Et exaeq. 28 fiet: ahm sipinta ahemingu hxmmnntilipp hCa.b)
  94. munt esthe man hegomnunaF ahena muhe mngghemmgglp = ahenn tb. c hpmnanche go) napetip
  95. (bnc)
  96. Mhib. e)hp mgh
  97. vil alegninp + h ccg aen p - ke genenpp +
  98. (et divisrs onnibus per nggm n pp, sic et mtu tistu
  99. Thecgsque porco pro hp - is(b. C) reponento g sit - a
  100. et contrari, fietque -3nee + egg - 2he ( 4+
  101. htegp=-gheegmn p aie(. ma pp
  102. s eheegu -eg + h( b. cg ep L rt eg ep = - 4thev (-c) + 4he (b.) 99
  103. )u +2egt = 2 helt- 1)gg = 0 quae divivi potstael g
  104. et explicande e per a- l, fiet
  105. hra + 6hab - 3hbb + agque - bg9 t B ∞ gb C Et c eticb B lb + hcc = 2hbc = 0
  106. gg: h = + ua + 3a
  107. unde tandem fiet
  108. ct 40b 108+ aub. sed clculus resumendus
  109. 2eng99F 2eggti(b d
  110. acogtsb
  111. siet
  112. = 17) =0

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 26v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068197:0052?run=74