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Leibniz-Handschriften zur Mathematik LH 35, 15, 5, fol. 22r

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: 0.79.

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The machine reads it as

  1. AF, a. CF
  2. Ce-CA
  3. AV, v.
  4. KanvVa.
  5. Ad Epistolam du. Barons Bodeni. 23 jun. 1691
  6. a
  7. puncto, recta et circulo positione datis; invenire minimam interceptam
  8. inter rectam et circulum fa quae producter transeat per punctum
  9. Neuipe dato centro C et radio CB, adeoque circulo, dataque p recta cB
  10. popositione recta GH indefinita cui producta CB occurrat normaliter
  11. in G et dato puncto A, adeoque rectis CF, FA, quaeritur ducenda
  12. AH, secans circulum in E, sie ut EH sit omnium possibilium minima
  13. quaer sit GHx sit CB, b, e CG, g. CF, f, AF, a
  14. GH, X
  15. gatur
  16. Ex puncto E deillatur EM normalis ad cG
  17. et CM sit m et Cm sil C. fiet eet mm = bb
  18. a - e, : M = f :: a -X, : 9 - f
  19. postremo et
  20. ita determinatum est punctum E per intersectionem recta
  21. AH, et circuli BE.
  22. porro HE sit y minima eritque
  23. ce HE = cG. Cm + CM - GH. seu yy = g9 - 29m + mm + e- rex + XX
  24. 55 ag. 1 est cde = = mdm, et ex aey. 2 est - de g. f= dn a -x = dx m. f
  25. erg. 3 est Rydy = -gam = edx + xdx et quia du =0 ub mimimam
  26. s fit: de 2 gdm + Xle C Xdx - e dx
  27. A
  28. (1
  29. EBBaBa rursus AF = EM ad CM - CF, ut FA - GH ad CG- CF seu
  30. 2
  31. 2
  32. porro ex aeg. 2
  33. F
  34. fit a porro, g- f. per compendium vocemus p, fietqu e
  35. aeq. 2.,
  36. 10
  37. act ap - ep = ma = mx - fa + fx et per compendium
  38. 11
  39. sit ap + fa = 99 fietque que = epa mx+sx, et
  40. pe ita compentiosius pro sg+ habebimus +xam + max = p de + fdx quae coincudit cum aeg. 5
  41. xoe e= 4 94 - fx + xtam,: p =bb - uim ex 12 et 1
  42. porio, jungantur aequationes 4, 12 et 4, ad tollendas differentiales, fiet
  43. de =-mam: e (ex 4) N- a dm + im dx = f dx 3: p = (ex 8) Xdx cax- gam: X
  44. (19Y
  45. c2
  46. ex 1b et 17 fit dx = - pmam: C + a = X dm ,:, m- f = (ex 191) et D) - xmam: C + gi i29.
  47. ergo ob eq 20 evanescente am, fit . pm + a = XC X - e L =xm + ge m- f
  48. e per 14 et 15 sit ge ex Ex 3 ope 14, et 15 sit
  49. + gg 29m. 6+ x C R 2Ab minX ex is est X
  50. + Y
  51. 23
  52. et ex aeq. 3 sit gg rr - xx- rex 2gm et ex
  53. sit gg. t bb2
  54. aeq. 14 est pC - qq am, m quem valorm substituendo
  55. et quia a= C p: f - in + a = X
  56. e
  57. e
  58. m. mafnt gen
  59. seu X= a na -pa -e,: n
  60. sit f+ m = n t et ex ag. 22 fiet
  61. (25)
  62. A-nes pn + a epe, al Ha-e Bn p= ar Bon
  63. = un =na + pa-pe ntf + gen
  64. et a-e faciendo v. fiet
  65. =n + f Pn + V pa B, v. np = un - na + pP ntf L gn a- v
  66. s seu, = pnn = pnf + PaV = pPV, vn-vp= un exentannatutgann
  67. bbacoco et quia. Ce+ um, sera aa - 2ar + vv + n + fn + f =bb fiet utr
  68. es
  69. vo + nn = bb - ff - aa - 2fn + 2a0. sit bb - ft = a a = BB et
  70. fiel en+ nn= BB - 2fn + 2 aV et 6g. 27.
  71. =pBB + p fn, - p avC pns) pav
  72. siel
  73. et quia p - g = - f per aeg. 9.
  74. =pBβ +. (2) p fn = (2) p av (= pr F + paD, vn - xp = nn gf Vn Fann xso Aan
  75. et problema solvetur ope duarum aequationum, quarum una est aeq. 31 ad
  76. circulum, altera est aeq. 32 ad lineam duobus gradibus conica altiorem
  77. vnp B3F pt. Vnn = pavOn +ppCBVC +ppavv = - fVN- an tEp f Vt par
  78. BPF
  79. c’ et pro vn substituendo valorem ex aeq. 31. fiet:
  80. pes Vn + pp BC V + fvH + an pan= (pan-ppa PB + 2av - nn - 251)
  81. ppa ((3 - 3pp a a V + ppann + 2pn fan + 2paavn ( pan
  82. )(34)
  83. 2p af nn + pa βBn
  84. Eergo v a ia eB= riptan
  85. quae est aequatio ad curvam
  86. lecet per numeros ratianales
  87. 3
  88. Lpatn
  89. B(B
  90. PB1
  91. 22
  92. rationalem quarti gradus, quam etiam Peuiu puncta invenire
  93. habit solutionem problem abi
  94. Ruoe arqu. 31
  95. at=at (e SBe-2fn. nin
  96. groblemta est impossibile solum et semper sit BB+ ac- 5) sentb. aa, sit minor quam f+n seu minor
  97. qu a fubtco sorocib quam nins bb dib, es, in rins qeao dibilitas eitandu est s. d a tiem ns aalemi, ut 35. abile
  98. n.
  99. ud aet
  100. blaitu
  101. 31 un segus
  102. nur das gua
  103. caerie
  104. 3 taustrgus negativa
  105. c
  106. c
  107. e
  108. Ec
  109. 4
  110. eu v. abb facns fulbio
  111. sed non video,
  112. quid hinc lucremur
  113. Contraretur Magis
  114. calculus si in valore
  115. ipsig. V aeq. 35 siat
  116. numerara et nomi-
  117. nator yndivisibiles
  118. g. f = P pf- 95 t)
  119. BB= bb- aa -
  120. (Ex aeq. 32 si
  121. 3B + 244 = bb ta +- g
  122. Pa-2af = ga- fa
  123. BBtpS =
  124. 31
  125. seu v = atrbb - 5+R
  126. at sba ta

Cite

Leibniz-Handschriften zur Mathematik LH 35, 15, 5, fol. 22r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068207:0041?run=74