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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 426v

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: 0.84.

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. 425r); this page is its left half.

The machine reads it as

  1. sit ∞EBp rectangulum, ejus appositum tifineum BEYB
  2. X centrum commune
  3. M centrum trilinei
  4. juncta CH. cadat in H, punctum re baseos XY, quod sit sit ut se XH minus quam HY
  5. Hea H cadere in medium ipsius xYs quia alicubi supra
  6. L centrum rectanguli,
  7. nempe proxime ad C, cedidit inter medium et Y, t sutrans medum versus 7
  8. sit ABCd rectangulum, huic addatur odE triangulum male a n: m=
  9. centrum ipsius rectanguli sit F, ipsius trianguli G centrum
  10. Commune H, juncta AH occurrat ipsi et producta
  11. occurrat ipsi BE in j (et FHad FGut ECEad veri
  12. F. H est ad Gt, ut BE ad ABCd seu ut L CE ad BC
  13. AB: BI ZAN: NH AN = = AB+FK. VH = EBC+KL
  14. FL = EAB- AB = = AB
  15. LG= ZBC+3 CE FK AY: FL = ZCE:, BC+ = CE
  16. FK: KH = FL: LG
  17. seu FK = BAB. L CE:, BC + 2CE, Et XH- LB CaL. lE )C
  18. et AB B L 2AB. BC + AB CE+ L A1B. C23
  19. BC+I ∞
  20. Bi = LBC. BC + 4BC. (E + BC. C2 + C4 e1( BC13
  21. quod si jam sit BI = iBC+ hCE finet (Bc+ CE = _B Equ + _BC. C2 + CEqu, :, LBC+ E
  22. senfiet ZBEqu + 2BC. CE + ZBC. CE (+ CEqu) = BCqu + BC. (E (+ C5qu seu fint
  23. EBC + 3 CE = BC + CE, seu C fEBC + L CE = 0 se BC = ECE
  24. seu CE = - BE entus Esumenda intta B et C. sed suspicor eriore esse in cutculo
  25. sine cum C endis tendendo versus C, cadit tandem in e, ne tunc quidem tunc etiami cadit
  26. graritur centum figurae per momenta ex duobus axibus AC, et AB, sit centrum partis
  27. B in C. Ergo non in dimidium BC se BE
  28. priaris K accedit novum rectangulum Elemenitare, cijus nebrum g. patet recesse esse ut K sit utrique
  29. axi propius quamZ. ut possut A, K, q cadere in directum
  30. sit hilineum AXYA, ubi simul crescunt ord inatae et abscissae. sit trilius
  31. aaliuli centum L
  32. ipsius ansungeah X). seu terulundem abest ab axe AX sed M cento vil trilinei est propius Axi AX,
  33. sit i rectaguili circumscirphicentum L., quod imminet medio ipsius
  34. idem est in
  35. ona cujus ordinalae
  36. crescentibus.
  37. crescunt raedenda abscssis a centro A
  38. y = La Max- A∞) hssyax = S, 2 raxdx - 2 XXdx = (x r. - 1 X
  39. sit A X: 29 = sx dex Sem. 21): har . LX
  40. (X dx (1aX- XC) :, XX = X
  41. Xyax = (Xdx VCrax - X1).
  42. linea centrorum proctatis MM) sit AP, Z et PM, v eit eritus
  43. siu X. y = X: Hrax XY) =
  44. px - 3
  45. fatax) Xax Crap XB) (cx eax XX) = d x Herax- p2) sX ax VCrax XX), :, qu (dx ACrax -XX)
  46. et v =,
  47. AP= Z = SX ax LC Lax - xx)
  48. Ax S(ac XX
  49. de -d (xax = XX dX) Sdx ICrax XX) = (ZXX = = ) dx SEax X),:, qu Sax MaX - XX
  50. (dx (ax ∞)
  51. Ergo dez ed = X Y(rax- XX) sdx spax- x+) = + (2ax XX) S Xax sCrax XB)
  52. (X = L XX) (dx (Crax - XxX) = (1. xX - L X3) (2ax. XX)
  53. ax -X1)
  54. Xx - X
  55. nan yd a- X nam : Y Zqu dy Qu YZ = 4 dy, aa gy
  56. et summando aau - + eß. Ergo monentur hilinei AXYA ex CB est mon.. ipsius A CZ YA ex CB, dento
  57. momento ipsius rectanguli XZ et CB, quod 1 (a- X) ; (a- X) seu Ly, aa + XX- 2aX seu L’aay - 2 yt
  58. sed datur mom eatu hilinet AX IA ex vasi CB
  59. (dhax. H)
  60. Ergo momenum hrilinei, AXYA ex ape BCest h aay - L est = L aagu + 1 y = )
  61. ea iyr (yex- ixxca ix9
  62. inde non orctetur aeqi utro
  63. qusesitre d pelitur calcutus
  64. sed Ex summ momenti ex AE + mom ex BC est, ACsis rax Xx) Ergo a (dx M ax - xX) - + G=(Xtx posito a esse Es, et psat
  65. in Xy syiX - 4y sydx + L et
  66. Ergo lict exprioibus X Rhax XX) Fdx ICan. X) renax x) a (Ex sCrax- ) + sC ax- Xd 3 (ax X∞) Ccap X) Y atd, 0, Di C
  67. (x - 1 XX) (dx 1 (rax - XX) (1X- 1 p) (C a XF)
  68. asy dx = fy, quod
  69. na a- 3x
  70. et KH: LG= CE:, BC+ Z CE, son XH- EBC C Eide rursus seu C
  71. seu RH = ZCE, 2BC+ ZCE,:, BC+ ZCE
  72. que
  73. minus
  74. si magis cresca
  75. horforda lis figni
  76. quam recess
  77. CBEYB
  78. Sxdxtuxne et QA = n B: 5 et GA - M-
  79. D Xt Sid s ma
  80. FCrX) sI
  81. seu cadal H versus t. citrca mes portet alicabi inter B et Y

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 426v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0848?run=74