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Leibniz-Handschriften zur Mathematik LH 35, 7, 18, fol. 17v

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: 0.91.

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. 18r); this page is its left half.

The machine reads it as

  1. sporantur instatione applicatarum vel potus parallelogmnorum
  2. 662 respondentum (h. figurae ACF ad exempositoe sentin
  3. maecedentibus AH, X. A, B, y. M, F. spatium AHC (Quod pondis desirnat
  4. scatena Ast B potentia constans in infimo puncto A, aa au
  5. evic ut do ad dy atus pondus catena ad aa erit pdy= andx et
  6. as
  7. y = aa (ax: p. si ACF recta et parallela Axi AE erit p = ax
  8. et fit aadx: p = adx: X = du vel adx = Xdus quod ostendit
  9. miva Oalenariam ABG esse requi thinicam cujus sublangentiralis
  10. nunc ACF linea rrectum angulum
  11. facient in A, cum laxe AE, ratio AH ad He, ut a ad b proinde
  12. sit a
  13. 1 C- bX: a. spatium AHC = IXx: a = p ideo aa ax+p =
  14. 203 dx: xX cujus summatio 24d: bx =y quod indicet
  15. curvam nam Catenaria ABC, ese (frg. 11) esse Hyper
  16. volam, sed ab altera parte positam ob quantitatem regativam
  17. v quod scuper accidet, quolies, grre e ACF vertex est in A
  18. curva enim aBG, una ex hyperbolaeidibus eut, sed ex anverso
  19. ta uno est vertitalis, altera vero laorr fontatis
  20. Cum autem aCF est ex Huperbolicarum Genere (rit atenaria
  21. ABG curva cuius vertex in A. si ex. gr. _ eF est tali ut CH vel bsit
  22. aa: Vax erit spatium a CHA vel p = 2a tax. proinde aa ap: p =
  23. adx: 2Vax ejusque summatio, tax =y. inde iprva funitularia hoc easu est
  24. narabola ABG cujus parameter a Problematis inversi solitio etiam
  25. nullo negotie habetur si nempe ex cognita natune funicularia ABG
  26. inveniendasit curva. _X CF. Nam quia p = aadx idus eorumque
  27. = aa )(dx :dy): dx, ex
  28. afferentia ap seu tax = aa dxidus ideo
  29. quo itidem patet, quod existente ABG otgebraica, curva XCF etiam sittalis
  30. Cixur. ABE parabo param. a, Erguu Tax et ius = adx . dax
  31. ergo aacxidu= ratax ejusque diff aaax: sax: quae diorsa
  32. ut ante
  33. sit ABe
  34. per dx dat aa: Vax = f = CH
  35. circulus radius a. y = ap x et dy= adx - fox, : ax A
  36. Cut aadx: dy = aa 1 (2aX XX): a - x et ad dx: dy = cx
  37. Qu. (( -X) Ea X - XX) proinde + seu HC = a . (a - X) iux axx)

Cite

Leibniz-Handschriften zur Mathematik LH 35, 7, 18, fol. 17v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068089:0034?run=73