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Leibniz-Handschriften zur Mathematik LH 35, 8, 30, 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: 0.88.

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. 21v); this page is its right half.

The machine reads it as

  1. sit divisor ipsius p, et secundum residuum eundem, qui sit divisor summ
  2. termini aequationis data veluti w; hi residui erunt ille b, huc c
  3. et dividi poterit aequatio data per b + cx. Quod si quocunque assum
  4. d
  5. to h semper habetur aliquis ipsius in divisor, qui dat residuos eosde
  6. s
  7. b primum, c secundum, d tertium, ita ut b sit divisor ipsius p, et
  8. d divisor ipsius w: Poterit aequatio data dividi per b + CX + dxx; Et
  9. Nempe itat
  10. porro ssi assumto quocunque h semper habetur divisor respondentis m
  11. qui snti verbique ratia B
  12. eosdem: oprimum, c secunduma, d tertium e quartur
  13. plares aut paulciores ita ut primus fb sitdivi (b) sit divisor ipsius B, et altimin
  14. ita ut b sit dritor iohus o, et e divisor ipsius n poterit aequatio drvii per
  15. per
  16. sit divisor ipsius W; poterit aequario dividi
  17. b+ CX F dxx + ex. Et ita porro. Ubi notandum, si talis consensur
  18. residuorum pluribus modis obtineatur, pluribus modis succedere divi
  19. sionem Formula datae, et semper rem, si semel succedit, bis succedere
  20. debere. Nam si aequatio divisibilis est per aliam, etiam divisibilis est
  21. per prioris divisionis quotientem.
  22. Ratio horum omnium facilis est. Sit aequatio vel formula p. F gX
  23. t. FXX + 5 X3 + FX4 L VXS = WX6 = O: quaeritur an sit divisibilio
  24. per aliam b + CX + d XX + ex3 = D. Utramque si explices per y + M
  25. vel per y + (4) vel per y + (Chd), erit ultimus terminus aequationis e
  26. e
  27. O factae, p + qh + rhh + 5h3 + F h+ + vh = w h- m; divisibilis per
  28. s
  29. ultimum terminum aequationis aD facta, b + ch + d hh + etc=
  30. Itaque patet fore
  31. F gh F rhh + 5h3
  32. AF+ vhs 1 wh= m divisibilem per brcha dhhred

Cite

Leibniz-Handschriften zur Mathematik LH 35, 8, 30, fol. 22r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068124:0043?run=73