Leibniz Legible

Machine transcription of the Leibniz Nachlass

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[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. 811

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: 0.77.

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The machine reads it as

  1. PFOP. XX. De Calculo Centri Gravitatis.
  2. 32~ 3 = 3R3. Solidunque convertione tactum (pirpoce ad Ongulam ut Z ad PB 168.
  3. s) circa Aa, 8P3 = 3 RZP; ed cirea r T 16D 3 A P: Semi sOlidaque H0. 269, 170.
  4. rum dimidia.
  5. Lademque Momenca, ex retpectiris Paralletosrammi A ax F moinencis, hoc. cst,
  6. (DTODIEF, a = LP, et A a.=7 2R, diltanciamque Conori gravicaris d Cre d = Psive
  7. ab Aa, 274 == +7,) ex = RDE, lubdueta; relinguunt Complemenei Semiercloidis
  8. AZ P, momentum respeetu Aa (seu correspondensem Onsulam Semiguadranta:
  9. lem) a6 R~ 2 f L R3. e relpectu r d, 16 R
  10. Ct es (lic Solica Semilolida-
  11. que correlpondenua, ad hac Momenca Ongulatre, ut D seu ZP, ad R:) Fadem-
  12. que momentaCompleniene senriquselgidtis, ecr magnicydinem, R P (per 5B.)
  13. dirita; extlibene ejuldem abst a ctamiaui centri graricaio +P +
  14. La des LBKIL HI
  15. 12
  16. 26K2
  17. Clii 331.
  18. 5i
  19. 6X
  20. 19X.
  21. 1s1 AHIi et _) GCIBI HBCL 1C SBI (1IS
  22. et arF.
  23. Sutiluer, in Semieyeloidis portione Be a V A. Momentum hujus) ad momen.
  24. rum Sectoris in Semicirculo chrrespondencis, D a R, respectu iptius Ro, Cut modo
  25. oltentum ell,) clt uc 5 ad 2; aeque insupers ut Triplum momenei correspondenus
  26. Porconis Frilmei rellicuti b RaB A, ad Duplume momenci. dectoris Semicireuli
  27. Ba A; respectu A a.
  28. tlt autem Momencum Porrionis Prilinei Rellituti B BaB A, respectu A a, = a2 R
  29. F asR = v R2, (per D EI. prOP. 17.) adeoque ejusdem Priplum 3 dR F 3a5R
  30. =ZVR_ omencum SectotiS B a A, respeCtILA a, ZV R 2 = 352 R, (per 55.
  31. DTOB. 255) hujusque Duplum 3.V R E f F. 5E PP. B. Racio itaque quam haber l’riplum
  32. illud ad hoc Duplum, hocelb B a 2R 3a sN - 3.2 R 2 2d 3~ R 2 +- + 52R, lCI
  33. 9a 2. F. 28a5= 18VR, ad 40X Y252: dalisni 8 2d 2, lcu 100 R f 5522d
  34. 42 R +12 152 P acdetos Consdeiaca; extriber Monienui Porrionis semieyclodis
  35. bP a V A ad momencum cortespondcurio Sestorts: (B a A, relpcetu a a rationem
  36. Dat 845∞ 8V R + 15 5 d A ~ R F. 252 Cum itaque Sectoris momencum
  37. illud lic 5V R + is s Cinnatioco dictum; Jerir Porrionis Sanieycloidis bea V A,
  38. momencum respectu Aa, (seueorrespondons Cngula SemiguadrancalIS) 222 k f.
  39. 2a5R = 3V R 2 + 35 2 X
  40. Acque hoc momencum, per Porcionis Semiexcloidis b Ba V A magnitudinem
  41. 3fR = 3a R + ESR, (Per SB.) dirisum; extribet diltanciam Centri Graricacis ab Aa,
  42. 94 + 18, 1= 82 R + 55 st 5
  43. 1 sc 1Ba AEBS ui
  44. 03CH.~ ( 2521. d 4u_ + 25
  45. 0a +95
  46. . Unde cciam en
  47. jusdem d h. L et b K diltancia tacsle colligicur; de momencum respectu illarum,
  48. Icem Solidu ejuldem circa Aa convertione factum, 3a 7 P A. Ba5P = ZV R ∞
  49. F1552∞: e lemitolleum, hujus dunicium.
  50. Si aucem ex iorius Semlercloidis sespectu A a, momento, 3 X X 3
  51. 3R, sulodii.
  52. catur hoc potiionis b B a. V A momencum 3 a2 R + 3 a s R = ZV R2 +. 3S2 R: RC
  53. lingnitur, Scemenei b 6. 5 momencum respectu ejuldem Aa, 1 R P. E- 1 3 R3 -- 312 R
  54. 2a5 R + 30 R 2 = 25E R; TeU (DFOPICF a = 3 P = a, e B = 2R - v,) 3 a p
  55. =35R~ (3 a 2 R + 3 4. s R = 3 B R2 = 352 R: OuOd per MaenicudIneM 3 a R -
  56. 35 R; (8 B.) divitum: Fxhibet Cencri sravicacis ab Aa distantiam, 5 P - : a. +
  57. 55-
  58. 3
  59. -05
  60. Adecque d Y+, 1a - 35
  61. 9a - 951
  62. du -os: Ejulgue, cespectu F +, momencum 3 et R - 3 a s R. + 3 5. R + ; V R.
  63. EX illo aurem Porrionis Semiexcloidis BBa V A Momenio (Ongulave) IC. B
  64. spectu Aa; Si subducatur Praperii bBaV, respectu ejusdem Aa Momencum
  65. Onculare: Relinquicur, respectu ejusdem AC, Momencum Ongulare Sexmenci
  66. Semcercloidis ABV
  67. Componiur aucem hoc Fraperium, ex Parallelogrammo bBa B, et Friangulo
  68. aB V. Parallelosramnni magnicudo (propter baln BB = a ee alcicudinem
  69. V a ==B, elt aB; Centrique Pravicaris (mepore in sui medio polici) ab A a di.
  70. K H H H K 2
  71. llantiam
  72. 8TF

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. 811. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/851387705:0831?run=74