Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

[Johannis Wallis S. T. D. Geometriae Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica] Johannis Wallis S. T. D. Geometriæ Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica, fol. 771

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: 0.83.

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

The machine reads it as

  1. PFOD. XVIII. DeCalculo Centri Cravitatis.
  2. Porro; Si intellivatur Solidum inegrum ita poticum, uE Za n planum sic in sieu
  3. horizontali, adeoque A ra (super illo crectum) in plano ad Florizontem recto:
  4. Momencum Tolidi corius, respectu za rectae; erir Duplum momenci Ongule (c
  5. micirculi aciens habentis A ay respectu iplius A a. (Bc linsiliter in parcibus respe
  6. etire Tumpris.) Sunc neique singula b eo Parallelepipeda Solidum hoc complencia
  7. (ne ostentum eltSA,) ad respectiras Pyramides a D Ongulam illam complentes
  8. ut 3 ad T. Porumque Parallelepipedorum à perpendiculari plano r0 A distantix
  9. Cenri GravitatS, hoc est Z Bo respectire, (per PrOP. 2. trujus; ) ad Pyramidum
  10. illarum diltaneias Ceneri graricatis a perpendiculari plano Ra ZBV, (distane Uci-
  11. que ab a, 3a B, per proP. B hujus; adeoque, ZBV, ab A∞;) seu 2B0; U Z ad Z
  12. Ieu 2 ad 3. ErBO, (PrOPteF ZX 3 ==E,) momenium cujusque Parallelepipedi, (adeo.
  13. que et limul omnium,) ad respectirae Pyramidis (adeoque et simul omnium) mo-
  14. mencum; ett Ar 2 ad L. Ouoll quidem momeneum, ell aggrexatum Omnium ? SB
  15. sire cocum Solidum, live iplius portionem, spectantium. (Sunc urique masnicudi
  16. nes, asgresatum Omnium sB: diltanciae que Cencrorum grarieatis respectire, 25.
  17. FIL aurem Ongulae Semicirculi A Da ZC em habentis Aa momentm respecti
  18. A_, 16 R3 P; Onsulaeque Sectoris Ba A, BC R3 F 55V K2 F 153 R; (Der SP, R,
  19. PrOp. 16.) Ergo Tocius Solidi aFa (Pieu illo polici) momentum relpectu a 7)
  20. est S R Z; d porrionis AbBa, momentm, LC R3 F, sV R2 853 R. AIGVC
  21. hraec momenta, per respectiras magnicudities divila, (hoc elt, pet 2 R3, e V R 2 +
  22. 252 R, Ut ad S A.) extribene Cencrorum gravitatis ab A + a platio distancias:
  23. nempe corcius solidis etP; et porrionis Solidi Pibca, 3e + 350 X f 2 5
  24. 120R + 65
  25. 1a
  26. Si vero ex eo Solidi Ab ea momenco; auteracur momencum iplius bB d R: se.
  27. stac momencum Solidi ABB.
  28. c1
  29. Est aurem Solidi BBa B magnicudo (per SB.) s R = vB se; ejulque Cenrei
  30. Braricatis ab Ara plano diltancia, (quanta plani ABv d F a Der GCi. DEOP. 5.) ell
  31. eR +52
  32. Per SO. DrOB. 17. adcoque momemum (in co situ) relpectu r a,
  33. ZCbR2 = 4 5VBR = d eB R2 + 253R = = C R3 = = ev R2 + 4 53 R = C R -
  34. 2a0R = = +5V R 2 F +53 R: FIOC itagHe ex FOTIIS A B Ba MOMeNIO, ZCR3.
  35. 25V R 2 + 353R, (SC.) subductum; relinquit = =P _3 + Z a V R 2 = 1 53R
  36. momencum Solici Ab B ( super Planio abo erecti) relpectu ra. CQua est sum.
  37. ma omnium 2 R Colidum complentium in suas respectire distancias ducta
  38. + 2
  39. rom: seu, omnium : c RE. + + 5V R; sumpris v acictmetice propoccionalibus. H
  40. Judque momentum, pes magnicudinem dirilum (S B. cradITam) V R2
  41. Ev R; exhiber ejuldem AbB, Centri gravicaris a plano A r a diltanciam
  42. =3e R + 3a0R - 5
  43. 220R - 652=60
  44. Idem eriam per le (absque ope porcionis ABB a) sic colligitur. Cum sinoula
  45. plana rectis bB insistencia, Solidum complentia, aequalia lint iplis respectire a B0
  46. =2 _, (ut dictum est;) lincque eorum Cenira gravicalis in eadem ab A r a plano
  47. distancia, qua ipsorum a Bv d ra; hOc CR F respectire: Prunc singulorm
  48. momenta, respectu ipsus Ar a perpendicularis plani, Le R= = 5V R, seu ; a R
  49. R2 = =5VR. Adeoque Solidi AbB momentum, eri Omnium Summa; hoc
  50. C, Omn. = a R2 = = s R2 f =5V R: Tumpris v arichmetice proporrionalibus.
  51. Sunt autem, Omnes a, (lumptis arichmetico proporrionalibus,) ipsut ABB
  52. planum; hoc est, = e R F a V, (per SB. PrOP. 17.) Adeoque Omn. L a R = = i∞ R
  53. +aVR2
  54. Frsimiliter, Omnes s, (sumpris e arichmerico proporrionalibus) sune iptum
  55. in semicirculo ABVY planum; hoc esti Ze _ f 3 52, (per BP. prop. 15. ) Adeo.
  56. que Omn. = 5 R3: = de R3 4 5VR2
  57. trem, Omnia sv, (hoc sentu,) Cunc iptius, in semicireulo, plani ABV, mo-
  58. mencum respectu P A, C est enim ingulorum s, d Y A diltaneia v, respective;)
  59. E eecc2
  60. hoc
  61. C
  62. Fi8
  63. 69
  64. 170.

Cite

[Johannis Wallis S. T. D. Geometriae Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica] Johannis Wallis S. T. D. Geometriæ Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica, fol. 771. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/851387705:0791?run=74