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Leibniz-Handschriften zur Mathematik LH 35, 6, 11, fol. 15v

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: 0.83.

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. 16r); this page is its left half.

The machine reads it as

  1. sit grave quodcurque rigidum A MG, une quidem puincto A mobila cira punctum
  2. fixum A, altero autem
  3. sit grave quodcunque rigidum ec MEN cujus centrum gravitatis G.
  4. suspensum ex duobus filis LM, PN, fixis in punctis datis L, P, quaeritu situs
  5. suspensionis. per L summum punctum fixum agatur horizontalis LS
  6. cui ex p normalit et occurrat ps, agatur huic parallela GX, debet situs esse talis
  7. ut sit eX omnium possibilium maxima, seu ut centrum gravitatis maxime descend
  8. dabitur autem situs quaesilus si detur punctum H, in quo L M, et pN futa
  9. concurrant. Datur porro Ged, et NCo. Ex punctis pGet Co, agaaturm AN
  10. (normalem ipsi LS) re normales MW, C0Z, G1. Erit G ut Ged data
  11. ad Z V, ut MN data ad Mu se QR. daturus ratio Z P ad ZR quae Gcd ad M N.. rr
  12. ZV eta ad AZ ot Z P adjuncta a) AZ id est ad. Rursus ob tiangula co Z N, et MH N
  13. similia est ca Neo data ad NZ ut MN rata ad WN Est autem
  14. CX = NR - NZ GX seu VR V Qxe AN - N4, et NI = NZ- Z i
  15. ergo GX fit aequ. RN - NZ + ZY. sed ANaequ. SNdat + PF
  16. sed RN aequ. 5 P (dat) + pF. Jam si habeatur punssum H habebitur L
  17. C
  18. Psa LR vocetur y et Bey HY vocetur E, et sit fet.
  19. reducantur;
  20. et LH vocetur l. patet esse H- gy + hh. et fiet
  21. LM= Q= LM y: l et MQ = LM h: l (oMW PF = PN (AY. SPsen) E. Sp: Y
  22. _RE CPN Exg. CBG Est autem LH = LY + HY. porro similiter
  23. L=CQM = LM. HV: LH PF pN. PK: pH Est autem
  24. PK = HY = SR et PH = PK + HN. et HK == L5- LY. Quoniam
  25. ergo ex 5 et 6 est GX = si + pF - NZ + Z P adeoque i
  26. ad (per 11. 1012 a yfit PH = HY + SP = bis HY. SP + L5 + LY = bis LS. LY. unde
  27. (per 9, 10, 13. fit pF PN. HY- SP: SHY + SP - bis HY. 3P 1 L + 1Y - bis B.LY,
  28. porro ex 5 et 6 est GX = sP + PF = NZ + ZP porro NZ = XCB. WN: MN
  29. et M W N = (A N seu) sP+ PF - qM. Ergo per 16. 17, 7. fi et
  30. NZ = NC SP+ PE = LM. HY. LH: MN et per 1 fit ZP = GCOrMN QR
  31. per 1 autem est ZPE QR. GCo: MN et QA =Lf( CG sA) ren
  32. 20
  33. FN= PN - PF. Erx ER = 1 +1 m et Zp = L5- DLmOL Y: LH -pr. L5Ir PH
  34. Ergo denique ex 15, 18, C3 fil GX = SPA pF = ACO: MN SP+ PF - L M. HY. LNHLS - LM. LY. LH - pN. 25- L Y. pA GCS: MX
  35. seu sE GX LSER GX. MN = MSPKPF MCD = LM. NCB. HY. LH + L5. GCD - LIT. GCI. LY LHP pN G( L5. PH F eN 5 0. IY. pH
  36. A SP EntPH. HNBM. N , - GCd. L5. PN OH + PN. GCd. L.Y
  37. Exassit 0 = SPF - d NZ + d Zp ApF = ( H PA apC PH PN: PN PH SPKD. PK spA
  38. (25
  39. (26)
  40. A eK = dHY PH ApH = PK LHYBHK ALY. Ergo dpe = p
  41. Erso p F =7 ex AHV: pH - VX pR AB Y. BH3 + PX. HK aLY. pHet
  42. s
  43. ...
  44. W
  45. ..
  46. p
  47. tn

Cite

Leibniz-Handschriften zur Mathematik LH 35, 6, 11, fol. 15v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068056:0030?run=73