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Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 24r

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. 25v); this page is its right half.

The machine reads it as

  1. mo cedit iatius mndr sis
  2. quaritur Chytha, hy +. hb, hy +. hc) aessumatur Thyaha) L l.H + s. CZ t t CEy atib) L n D n t Z t Hipu 1c. A q 0t
  3. ntitu t + ff0G
  4. (2) pmmoDtun DE
  5. +hb EE - hb C
  6. (2) pahh 42 +g9C4
  7. L.he GG- hc04
  8. +2hftur VOG nitres ipsius 2E+02+ 24 10 valores valores ita dven, ut primus
  9. = 2ha 2 10
  10. +2mn D 1CG
  11. + 2h92, 102
  12. =2 hc 8 10G
  13. fiet: munndD qu (a -b) 43 + L (a. b) ma D
  14. et mmunD D+ H qu cab) 4E + ahlc. b) mn D Z
  15. et tertius item secundo; seu extremimedio; fiet ex irrationalibus aequa
  16. ht m
  17. Ex rationalibus aequatis fiet
  18. hthih+ A = m BDran Z = EE 4 4 +99 8G fb. ct 47
  19. Et in his dluabus aequationibus explicando lonondim
  20. ht et h2 per ag4. valores ex aegy. 3 et 4,
  21. +5 O2 - ffmnO D - ss nn X) = 0
  22. 9+ c9 49mm C 3 99na 34 6
  23. abest hic 00 et 88, 07, 48
  24. non licet sunui eodem movo tactar
  25. quodsi in aeq. 7. ponatur ff H(b -a) h 20, evarescet in ea Oe: quin evanescet etiam ZE, itaque residur
  26. diviso per D, ex aeq. 7. fiet mannD + 2 Ca: b) hmnq-fmmO- fsnn E, et explicando ff per aequ. habebitur
  27. 2 + 2 m 8 =mm C
  28. + mmun DD + hhqul c - b) 4G
  29. + 99n (l. C)..
  30. is valor substituatur in aeq. 8 fiet
  31. +2h (C- b) mn D Q(= gmmOD)
  32. iam (1D +gt
  33. golb. dh a. D h
  34. Haec aequatio 12, compendio et generaliter sic exprimatur
  35. 489b. chs
  36. 12004Z + 1020D) + 100291 + 11083 + 1101 3( + 10113020
  37. faciamus jam C) = (14) = 21C8 +01D + 200h,: 000, fet 10o Z4
  38. (15) (000. cro. 1700 98 + 000. 000. 10203) + 000. 000. 1II0 ZD 2ro AbL..
  39. +80o oro. 1820DD + H10SD
  40. +P ret teonsx +2 pot. rerveo nortf
  41. 210. 210. 1602. + 201. 201. 1002.. + 2. 210. 201. 1e02 - - + 2. 210. 200. 1002h8 + 2. 201. 200. 1002h7 + 200. 200. 1002 hh
  42. 000. 210. 1131-.. 40
  43. + 000. 2811101.. -+- 000. 200. 110Y
  44. 4000. 20l. 1011.- +000, 210. 101..
  45. 4000. 200. 1011r
  46. siant sam cdeficientes termindum Y Z, 33, XD = b r savit b. 2. 20. . 1002 Z + 2 201 po. 100 tyt 4 200. 1eb 2 b
  47. ob 77 fit pi 210 + 100. pe 210 4 voo 101 2 = 005. 1101-u0v. 1eobi1 200. hin 2ol sceuri tromi Mer,
  48. seu 210 (NO- 4. 1209. 1002) -1101, 000: 41002 . 190
  49. Eatem modo ex D) siet sublato
  50. fiet 201 1 (101r- 4. 1020. 1002) = 101, 000. 7. . Capli est telli. ), in qua a unde fit aequatio, in
  51. qua pro 210, 201, substituendo valores, fiet
  52. 3. ∞ob. 1110. 1002 + fL11 2- 4. 12v0. 1002, 10112- 4. 1020. 1002)uo 1) 101 F( 1 (1o1 2ete) 110, L ry. 1101. 1311)
  53. X 1 (10n t) 1101) = 1011. 101 + V (, poi h) 1BU uot II)
  54. Seu sublantis Lllendis I( - 4. nov. 1002, 1011- 4. 1020. 1002)-
  55. 10OL. 1011 = 2- 1110. 1002
  56. et quadrundo utrobique (APP2 1013 4. 101. 1020 (1002) - 4. 1011. 1200 (100716. od. 1020( (101. 102+ 4. 110. 120- 4. 101. 191. 1 sed
  57. quam aequationem purgando et adinando firt tandem 4. 1200. 10d8. 1002 4. Hvt ry. 1110. 1101. 10, y10. 100L
  58. quae aequatio legem justitiae pulchre observat e a es nit aitem t e
  59. Exphlemus jam numerus hujus aequationis ex aequ. 12 vel 13, compendii autem causa a + h(t. c) vocemus tp, fiet
  60. 1200= tb c) lisitie 1020 minua Chtarb) = 99) t mmnnXq ( , 1002 = - tp gomn 89+h b -a vocemque h9
  61. 1D LD- 2mahp et 1101 = 2mgghip et 101 2= mm g p um 99 P
  62. et exaeq. 20 fiet Ahtitpmmnuqueupugum, 4mttip myghp mmgop:
  63. Dividitur hac aequatio per thpperta, et nultiplicetur per e, 3C
  64. fiet =ek9 + 4 ep9g = = ahp ee + 4 e999 L Kpg9
  65. ammontulitipoam heb. C) vocemus tik
  66. 4 amoetitip pmmtriq
  67. in hac aegpntione pronbisat pondatur multiplicata per h, loco tp, et h9 ponantur valores
  68. fiet =AheK 99 = ahek hC) + 4 eg90e aegghK =. ( 4heegos- Ahoehk (+ 409999 t ci 19h0 + 99k99 +9G ht
  69. Unde tandem fiet Kg+ + h k kgy = d
  70. Sed K non potis
  71. aliaqui in aeq. 12 omnes tegmini destruuntur, praeter equm sed hos
  72. iosers HG et fiA V =b
  73. ergo t
  74. ibidem termini 1002, Hot, loi, seu termini continentes
  75. et pracepib simunter D 24 F5 de 8
  76. 112DD + 1448Z + 114)8+ 123F+23O+23C)O =0. pro 3 sculatur V, et fiant
  77. e monnt editraria quaed saedible
  78. ntata compentiao
  79. el
  80. hon hecse tatabitur tatu inter nisi etiam velimus
  81. evanescere termunos DD, fY, YD quo non licet. quod si ratio datur inter Y et 8, ontato
  82. et viter it ti et sed
  83. R fumatur aeg.
  84. = 20V + 21H: C = 30 v + 3ch: 6ol 4= 40 v + 41h: deh, et fiec moovv
  85. uet tollgatur ex invenictur 30, ut tollatur v, invenintur 31. et in aeqvotione
  86. simparan ad tollendum hv, puperpunt 20, 21, 4C, 41. Endem faracnvo pro
  87. 9. facta ex 8 erit similis calcutus, x pro 20, 21 40, E1, nisi quod per
  88. pro 11t et 14 ex. pontur 211, 24. + etC. quam duau auus a
  89. tollatum 20 pos
  90. 2. 144. 40. 41 l.B + 144. 41 hh
  91. obB + 144, 00. 4(hV
  92. L. 00 2d 144 60. 21 p
  93. es rdotio
  94. s p t
  95. 113. 00. 35VH + 113.00.9. hin
  96. maju
  97. qviis
  98. NN van ns
  99. ng..90+ he
  100. requamb.

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 24r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068197:0047?run=74