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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 389v

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: 0.78.

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. 390r); this page is its left half.

The machine reads it as

  1. mo) X =
  2. Gpehpy Aipp yr4. vat (Edu) srm =
  3. +92 y+s, y+W
  4. Aequationes assumtae et praestandae
  5. (mo) X-
  6. dyyarabyraC, via
  7. 3rb, p, ytq ver, yts
  8. Aequatio ex 1. deducta, (4to) X+m =
  9. debet esse (O ∞ D
  10. ayripcyrece
  11. ay + 2acyy+ acc y
  12. r ap.. + racp. + aecp
  13. cenence
  14. m
  15. y+4
  16. 31b, ytr, y+ 8
  17. et ex aeq. 2. fit similiter Cto) Xtm= egytresyt ess. yrp, 325
  18. (6t0)
  19. ay+ 2acy3 + accy
  20. ap.. raep racep.
  21. ag. +racq. + accg.
  22. apq. tagpu. + accpq
  23. non, (, p. 2) mi + 2mb yt + mbb yy
  24. mr. ambr. mobrus
  25. ms. Embs. mbbs..
  26. Mrs. Embrs.. mbbrs
  27. Eodem modo
  28. (imd) e= a + m
  29. 3+b, y+ Y, y+5
  30. SQ et fiet 6 ex C pro m ponendo n
  31. F
  32. D ex Q pro se e, foB, Y Ib etc sunt communes ett ( l commuris
  33. ponendo R, 9,95
  34. itaque aequationes identificatrices jam instituomus.
  35. (2do) h = a+n itaque e, et h, haberi possunt pro datis
  36. 3ti) pS racF an+ aq = (2 ef + ept es -( per 1) 2a 5 + 2mf + apmp + a S m 5)
  37. fit mr n (4t) a5 - mp = + 2ac, +aq
  38. curi jure
  39. 11. 1I1. 110. 101, 100, 3H.510. frl.500
  40. +
  41. multiplicetur aeq. 4 per n, et ns et aeqis per a, et producndaddantur invicem,
  42. simstra simistrae et dextra dextrae, fiet ibto) aat- mnBn = ranc + 2mub-rans 2mnstanq- mnp
  43. raa c + 2anb = 2aag- 2ang t aap = anq
  44. et pari jure multiplicetur aeq. 5 per M, et aeq4 per a, et productae addantur invicem, sinistra
  45. simistiae, dexta dextrae fiet ua-mn 5 = +2ame + mnb -2amg - 2 mng amp- minq tubemus ergo r et S
  46. 42aac +ramb- 2a a t-ramf + aaq am
  47. Hactenus coincidentiavimus terminos primum et secundum, quaera idem quaerendo r et s
  48. nunc rursus coincidentiemus ultimum et penultimum, quaeriendo p.et g, subsditutis pro
  49. quod unt fiat commodius, et ne calculis prolixioribus involvamur, aequa
  50. tiones 6 et 7 tam compendiose exprimemus, ut solum appareant, ri s, p, q quibus et ex aeg. fiat
  51. r et svaloribus inventis:
  52. et naito + p e s traito +9
  53. dlotaxilo Xu. nagnoi
  54. Ex termino ultimo estu eff ps = a acepg + mbbrs seu per 1, est afsps + nHps. semque
  55. modo ex aeg. 7 fiet _ (omo) 104 s-q = 12 ap
  56. pari jure fit (2mo) hgggr = accpq + nbbrS unde (3() fit efs ps - hg9 qY = m -n bbrs
  57. sed hac q. non est opus. Bllamus s, et ex e2 fiet est ps = acepgs + mbbsnaito a mbbsp
  58. Ay agq n et 12 tollamus Y et S, f et ex 11 fidt efspus + efs p12a 10 = acepq. + mbbpus + n bb pagnrap, mb11. 12aa
  59. (15)
  60. et ex 12 Galo) hggDG + RBgraO = a ccpq + n bopq + ebb naptaq + m bb. H2 aa
  61. n rahc +2 enb - 2enf - rahg, iaa copendro A. 4 1010 f +10019 + 1000 a 1a 10.c
  62. ubi 10 est data nam 10 = aa- mn, : a
  63. Follamus etiam ret s ex terminis penustimo hacc + numbi Amg -raeso
  64. et fret
  65. ext penultime q
  66. i
  67. as accsue a amque rrachus + mbbB t mbtetasio t orttus t tlreus ubpus +peb aq Lmtnaro pae en buagrnax F rmbuinaa esse t e es + esfu te nanores p trespnaio
  68. et medio
  69. anc acq ta tracpus + mblsque + nbbserazio tnlbo tntbram + ub pu ee
  70. C C motaxinaque + unb muna (L hoyot E tggP + hgg 1a 10 tahg p9 + etge qua . 10
  71. du tagi amqu tape umdb. anties siud ittuea tu pyt B engterae nunaa e etst resue t resium rex eap ue )in li d es qntimibs sognit ut cont
  72. +obb trat uatua +an sasta) An nous nogt atique tangnario + paquio 5
  73. Assemus jam ope aqu. 20 et 2I invenire p et q. et earum ope tollere has literas ex aeggs. 13. 14, 18, 19, Sed idem tamen faciemus pouto compendiosius, si prius
  74. ita ex 13 et 14 v nastetur 59. 2t sine pus, et ex 18 et 19 nascetur aeq. 23 sine
  75. t, tollendo B3 a 14, itemque 18 a 19. haber
  76. Ai ac +eI
  77. tollams itiiem, 0g ex 18 et 14 conjunatis, et atidem ex 18, et 19 conjunctis
  78. quo
  79. quae aequ
  80. pro cegq. 13, et, 18, (9 rese Betive suibumus. 1MBF et soq o 2 rup rrioap Copaatrova Ld, At 3upg + Sroup + Joaq r ovao et An pus E urapeo aytaa
  81. et
  82. ebit
  83. Envetia fil e) on noru s tioma oaita Et exIi sil BIoGnA F oN AUAq + 300. du pa So copendio rp
  84. compentio sp + a (p + (0 9 + (100) a = o et (2,10 +o +2 oda -unde seu 4 113L201 p L (101)20) 4+ 400lepia C = 0. et
  85. Yo1. 311
  86. et prr his fubsti t. Eado valores fit 410. 217(301. 411
  87. 10. Mi St ro1. Sii lp
  88. 1100. 21125301. 4119
  89. 2 100. 111S2 ac1. 31 fa
  90. ∞5101. 211(300. 411
  91. (+)
  92. 0
  93. 21D PC 1101) 219- 10eosa
  94. in aEp+ta
  95. t
  96. 5. 211(310L4 11)
  97. 5
  98. ithaco uta=
  99. a, m, n dats
  100. hwy teligyshigae, 32
  101. xin-
  102. extassi oepu
  103. Eto
  104. 260) tam
  105. ytp
  106. +b 1
  107. agypracynace, 9. p, ytq +myytumbyyem bb, vi y1d = C
  108. 12. 2. 20 201. 300 4 11. 410.
  109. (25
  110. 3
  111. ep.
  112. 2055.
  113. + efsp
  114. 5.
  115. ep s.. 2 es p.. + ets p.
  116. 1821115300. 4 11
  117. l201. 1115400. 211
  118. =1 101. 2IIY31O.HI (I
  119. pis
  120. 9. 1II.41D. Si)
  121. aetimumi erit hos vaotes p et p substitui in a49. t8+ 19 13. 14, 18, 10
  122. episa d se

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 389v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0774?run=74