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Leibniz-Handschriften zur Mathematik LH 35, 10, 1, fol. 12r

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: 0.84.

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. 13v); this page is its right half.

The machine reads it as

  1. 2x-4-
  2. =4
  3. Elementis radiorum
  4. Calculus de crentis adioum Ellipseos ex umbilico eductorum
  5. x radies velocitatem circulationis inveniendis, et speciatim de casu quo circulationes
  6. rectangulum
  7. Ellipseos ALGV iaxis major AV. foci OF centrum C triangulum characteristicum GDL
  8. e descendendi impesus, versus
  9. Goccurra
  10. irmportionale
  11. in quo GL velocitas in curva, Gd circulatio, D L descensus
  12. focum O, _ seu decrementum radii LD. Cducta ex Fbisecanti e angulum FGC perpendiculanter
  13. occurrat in , et ipsi OG in M, patet triangula GMH, et GDL esse similia. quaeritur
  14. ratio GM: MH seu GD: DL. ex OG. Habebitur autem FM si drea trianguli OFG dividatur per OG.
  15. habetur et MN ex FM et GF (seu AV-(,OG) quia sinus anguli dimi MN sinus anguli dimidi MGN
  16. habetur ex simu toto GF, et FM siu anguli integri MGF. Area autem Trianguli habetur ex tatvibus
  17. quod hic peculiaria involvit toremata compendia sit (0g, , AV, 4. OF, e. OG.r FG r. q
  18. summus laterum +C
  19. differentia prima je
  20. differentia 2da AC
  21. differentia 3tia -e
  22. +4 - Y
  23. = +e+ q
  24. +Y - 9+r = + e-9+21
  25. -Y +q. Y = +C + 9 - 27
  26. +r +g. Y = -e+ 9
  27. Ergo area trianguli 49 - ee, in eC - 2r - 9: 4 = OFG -
  28. Ergo erit FM- V . LuI
  29. jam ob angulum MGF ab ipsa GN bisectum erit MN ME: MG: MGGF
  30. et GM= P GOFG FM seu qui 4F.Y agrra
  31. Ergo fiet SpN. A 2X = jam quin MN: Et quia MN= MF. MG jam Et GM. M N_ seu GD: DL est:: MG+GF: MF
  32. ergo GD: DL:: FG _ = FM + FG,: FM. seu Gd: DL:: r-g - 4Y: Y + q. Y
  33. jam in eo casu quo circulationes sunt radii reciproce AG posito temporis incremento , ducto in aestarie
  34. sut est GD = aD: Y ergo fiet D L = 2Y. aD: . r9- 4r. r +9- Y, seu
  35. postremo DL = aba 14 ee in ∞ -2r. g+AY (4r-9 r - 49- ee. ec- 2r. q + 29 Y r.
  36. nR: Y = 0
  37. Ergo 0: D.. M: Y
  38. Eandem quantitatem ad huc aliter quaeramus alia via. Angulum OGF bisecans axi occurratim
  39. et ex F et O eductis ad ipsam normaibus in Q et H. sunt autem Friangula GQF GHO,GDe, similo
  40. et triangula RQF, RHO etiam similia, et ex natura anguli bissecti FR: FO: FG: AV.
  41. et OR: FO:: OG: AV. quaeritur GD: DL seu GH: HO. Et primum GE: GF: GH: HDGC
  42. QR: RH(:: FR: BR (per 4): re BGF FG: OC (per
  43. 1092 Et 3
  44. 5et 6) et similiter per 4, 5,6, F. Q: OH: FG: 0
  45. Ex his quaerendae GH, et HO
  46. denique FL + Gq= FG2 et GH + HC
  47. Ex9 et 10 fit FG. DH: OGFG Gq et cessat aequasio ex duabus difficilior, 10, substituta in
  48. ejus locum 13. in qua tollatur GQ per per fiet FG CH: OG- FGaFG. GH: OG
  49. in qua tollatur OH per 11. fiet FE. OG- GH OG GG2 et habetum GE. K
  50. FG = FG- FG. GH: 05
  51. G2 G FG. GH: OG et per 10 F
  52. Rursus H per 7 fit
  53. et ob i fit HO 05 - OG GH: et RQ = FN - F 92 seu ob 7 RQ = FO. FG. 5
  54. =FG + FG. GH: OG, et ob 4, 5, 6, RH = FB ∞G 0G-G + EBG. GH: 9G
  55. RH2 F02. OG2: AV - 0G + GH:. Ergo peraequ. 12. cum 13. 16. et 17 con-
  56. punctam, fit: FG. GH: _OG + FG. VFO: AV - 1 + GH: 65
  57. +OG. V FO: AV - i + GH: OG = GH. unde fet.
  58. : (FG+ 6G seu) q = FO: AV - 1 + GH. OG
  59. 1-2FG+F
  60. seu GH = B S - FS: AV : Y1: 0G, - _ 1 : 1 - 2FG + FG = 51)
  61. 03 dist
  62. BH = OG TAV = FO :AVY 1 = 0G: 0G -. OGFG+ FG et substitutis literis
  63. GH = Y sgq- ee: 1 - rr: r - g. 1 = r. 2r- 999- ee: 4 ar= a9r + 99a rv
  64. c jam OH = (OG =GH et Ergo OH: GH seu A DL: DG:: (OG - GH: GH. jam
  65. DG = ab: Y. et fiet: DL = a SC GH: YSH ad Sr= GH: r.GH
  66. seu DL jam si compendii causa Erq vocemus p, et 19q ee vocemus h, fiet
  67. GH = rph: q S pp- rr. ergo r = GH = gqrr pp. rr- hhrrpp: 49. pp. YV
  68. seu = ee rrpp - 99r: 4qpp - rr et fiet DC = aD eexrpp - 99rt: hxrp
  69. seu DL = aB seepp - Ggrr: hrp
  70. In numeris sit g5 e = 3 erit h = 4
  71. Eautem quantitatem ad huc aliter quaeramus flagulum OGFbisecans axi sccurrat in A, et
  72. h =, 12
  73. 4- t3. ex 5
  74. ex F et O eductis ad ipsam normalibus, t occurrat in Q et H, quaeritur GH: HO:: GD: DL. sit AV, 9
  75. et FB, e et DG, Y et FG n = q- Y. et GH, sit X, et HO y. ob angulum bissectum cunt
  76. OR: FR:: OG: FG ergo OR+FR, seu C,: FR:: OG+FG seu q: FGsO n. ergo FR = en: 9, et similiter
  77. OR = er9 ob AC Ob RQF sim. RHO est FQ. FR:: OH: OR dver seu FQ- en 9 y; errque = ny: r
  78. Q: OH seu y:: FR: OR:: n: r. Ergo F9 = ny: Y et G9 YFG - Fq2 = p TrKyy∞: et QR = FR -F =
  79. 49 + nn -9 + 29u -nn) Seenn: 9q - nnyy: rr = n Seerr - ggyy: gr = eR et RH = SOR - H~ - cerr: 9q - yy = Seerr - 99yy:9
  80. 4+ p= (2Y
  81. 49 + G- 29r + rr
  82. q- p = n
  83. un-rr-
  84. Ergo . G jam GH = GQ + eR + RH. ErgolX = n Frr-yy: Y + Seerr- qqyy n: r F 1: 9seu) R: Y
  85. sed rursus X2+ = rY, quin GH + HO= OG. ergo fit r rryy=rrnn-nnyy+ eerr-qquytrry. er. q
  86. H rrnnt eerr vocemus AEY, et 99 + nn =rY vocemus B, et fiet Byy = AEr + 2S.. seu
  87. B1t = 2 A B ry + r A+ = a r- gy. eerr -qqyy = 4 40r4- 4ggrryy -4 eerr yy+ 497,
  88. jam nar=q et r-n = p siet B- 9 q+ P et q+p nn -rr = pG et B- 9 - 9. 9p. sed 4 - 2r.
  89. Ergo B 2n sed q. p = n. firt B = gn. Aursus Et A2 - ee -pq et fiet: . (+qqui
  90. (99nn y= 2 gurryy ee + Egurryy pus + rt - 2r eepq. + rp 9= 4e rn ggrryy-Anneerris
  91. Ergo denique yy = 4Cren etr+ cerq reerpq. rpq: aggrrunt aeerrun ycern
  92. et dit i. vi dtubus
  93. F- F
  94. Y = q = 2Y-
  95. Pr
  96. 4n qrqtq
  97. Ser 3r 4 p 4)
  98. nam si

Cite

Leibniz-Handschriften zur Mathematik LH 35, 10, 1, fol. 12r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068154:0023?run=74