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Leibniz-Handschriften zur Mathematik LH 35, 13, 3, fol. 139r

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. 138v); this page is its right half.

The machine reads it as

  1. magnitudine
  2. centro D radio DE describatur arcus circuli E2. centro IB radidat
  3. radio BE arcus descriptus sccabit EEE in 1E. Sumatur alud punctum 2E. et
  4. jungatur et centro 2E radio EB descriptus arcus secabit: E1E in 2B.
  5. jungatur 2B2E et sumta 3E velut centro radio EB descriptus
  6. arcu secalit 2B2E in 3B. jungatur 2BuE, et sumto 4.E
  7. +
  8. 1B3C
  9. velut centro radio BE descriptus arcus secabit 3B3E in 4B
  10. et ita porro; posito intervalla essequatum
  11. ucpuncta cB2B3B+ B. constituent curvam seu potysgonum
  12. infinitangulum cujus lat langens BE est data magnitudine
  13. data occurrit circumferentiae. EEE centro D. radio DE descriptae
  14. Hinc patet curvam hanc describi posse, si dum DE movetur
  15. circa D. ipsa EB moveatur circa E, ata, ut B percuriat punctu
  16. 1B2B. 3B. consideremus ergo, quae futura sit motus relatio motus
  17. EB circa E ad motum DE circa D., id est quantum angula 1B. ED
  18. 2B2ED, 3B3ED ietc differant.. ducatur 2BEC aequalis et
  19. parallela 1E.B. et 3E3C aequ. et parall. 2E2B, et 4E4C.
  20. aequ. et parallela 3E3B. et ita porro erunl omnes aequales destanti EB
  21. anguli autem 2C2E2B. 3C3E3B. 4C4E4B. pempe in tria ad
  22. vertices in triangulis. aequicreris.) erunt angulorum 1BIED. 2B2ED etc.
  23. ifferentiae jungantur 2C2B. 3C3B. +C4 B. bases in triangulis
  24. equeruris quorum cuisasem semper constanti EB aequalia
  25. ponantur et 1E2C. 2E3E. 3E4E, etc aequales adeoque et ipsae
  26. 1B2C. 2B3C. 3B4C. aequales ipsis 1EG, et in 1E2E, et inter se.
  27. quaeruntur ipsae 2B2C, 3B3C. +B+C. Chordae scilicet sive
  28. arcus sriam in infinite parvis idem est) angulorum, differentialium
  29. seu portionem motus circ EB circa E.
  30. pro ducatur 1E2E aliquonta in Z. erit ang. 3E2Eq. aequalis angulo
  31. dimcidis
  32. 1ED2E nam ang. 3E2E1E aequ. angulo 1EDF (ad cinumsrema
  33. ferentio ad centrum) ipsi autem 1EdF sumplementu ad 2ret
  34. 2 rectos est 1 1ED2E, et ipsi 162E3E suppl. est DE2EZ. ergo
  35. ED2E et 3E2ER. aequales anguli
  36. Rursus 2C2E2B ang. aequ 2 2E2B, E
  37. Jan 2C2E2B + 2E2B,C + 2E. C 2B. aequ2 rect. equ aBb4
  38. aequ
  39. gei
  40. EE2B,E + 2E2BEC +C2B. B aequ. 2. rest.
  41. Ergo 262C7B. aequ 2C2B. B.
  42. differentia inter angulum DB DE.E et D2E2B est ang.
  43. 2B,5 2E E 2C2E2B, ergo et huic aequalis 2E 2B, B.
  44. imo errutum, non debet esse 2E2C aequatis paralleta 1E1B, sed
  45. debet eunde facere angulus ad radium DE, seu 2C2Ed aego ang. 1B, ED
  46. f figura ergo aliter delineanda nempe ut in N. uti hic calculus
  47. 1E25 e. DEHd
  48. F. EN DFd -C, DE,EH ESd- e area Ili 1Ed,
  49. dividatur per dimidium basin D. Ep, L habebi fiet Sa2 C C s d a quae
  50. aequ. D a 2EG. 1E, EH = 2 EG( 1 G15F 2 seu e - erd +. et
  51. fiet: G. Eaequ e. pono G+BB 2E2B( - e1, + d g 4 q
  52. DE D.Bp, D, E =G2B = G.Ep, d + f6- e+ et -
  53. e
  54. d 4d G2Bp Nb- C4 0
  55. mulle. per = C5 fiet. 4d
  56. 4d 2d
  57. 2d aC + 8 (62 C+ , 1. 15 - 1 e fde e area Al. 2ED2B quae
  58. d
  59. 4
  60. dividatur per dimidiam D2E fiet p L. firt: Fd po + fC . 2e .
  61. po cea laon ali cireo untta peo 1us et et abionitu.

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 3, fol. 139r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068200:0279?run=74