Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

An Introduction To Algebra, fol. 155

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: 0.80.

Original at the GWLB · Page image · Annotations (IIIF) · Download text

The machine reads it as

  1. Resolution of Problemes.
  2. ASche lesser limit helped as 1o 1, 4, 8 For common Divilors OF A. B
  3. Sochis ercater limir givesus 2, 3. IE chese mulripls thole FOrmer, we
  4. tave 3. 12. 24. And (0 we are again Fallen upon che six Divisors
  5. (2. 3. 4. 8. 22. 24) Pa8, 252. liV. 26.
  6. The Reason oF thac ACultiplication is ehis
  7. X.) When(OeVeF = -- 3y - 3C OF 37 + 3C, ic maties A. B. K. D. div
  8. by 3. IF che same Z BC aI(O 27 - + 4h (28 7 = 7. 2 = 28. p =- 27. 2 -
  9. ic makres them divisible by 8. Andcheretore cheir grearest common Divis
  10. 3 cimes 8, that15 24.
  11. 2.) ButiEche same Z DC (BOF 27 .t AB, buE) 27 F 2B, it makes therr
  12. divisible by 43 and cherecore cheir grearest common Divilor I5 3 cimes 4
  13. thac is 12. A5 When p =- 5. 2 = 12. OFY = 7. Z =24.
  14. 3.) BucIF Z = 37 - 30 Or Z =3y + 36, DC al(027. 1 some odd number,
  15. it makes them noc divisible by any number Greater than F. S0 chat cheir
  16. creacelt common Dirilor is 3 times X chac is 3. AS When Y = 4, 2 =9. O
  17. Wten y = 1O, Z = 33.
  18. 4.) Wrhen = is noc cqual 10 37 - or - some cripled Inteoer then it
  19. makes HOC A. B. R. D divisible by any muniber greater than P. S0 chae cheir
  20. common Dirilor is no ocher chen was deligned betore Dy Z = - 2Y t h, 27 1 2b.
  21. 2y + 4h, a5 IB P2G, 253.
  22. Whieretore nom chere is no place lese For that suspicion (pa3. F52 lin. 28
  23. Chat A. B. K. D con have Come orter orearest common DivilOES chan one Ot
  24. chose siX 24, 22, 8, 4. 3, 7.
  25. Lec the rationes OF y ro = be distinguistred by chese six Divisors into (X
  26. Rantes, Whose Lcaders may be Found by chese 3 last PaBes, supPOsingB =2. 2
  27. c = F Or 0, and chen lagine
  28. ad
  29. 242 =- 27 + 4 -- 3p - 3,. y = 7.. 2 = 18)I
  30. T2 2 = 2y 1 2 =37 - 3..) =5.. 2 =12 II
  31. 8 2 = 27 1 4 = 37 1 1.. ) =3 ,. 2 =20 IIL
  32. 42 = 27 1 2 -37 - 2.. 7 = 3.. 2 = 8 IV
  33. 3
  34. 2 = 27 1 F =-37 - 0.. 7 =T.. Z = 3
  35. V
  36. 2 2 = 27 F 1-37- 2,. 7 =2,. 2 = 5IVI
  37. u cact Rank reguires muchi more work to tind it.
  38. E2

Cite

An Introduction To Algebra, fol. 155. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/827130880:0171?run=74