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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. 171

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: 0.92.

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  1. Cap. XXXIII. GEOMDL LICA
  2. Primo) aequacur illorum indicibus simul
  3. lumpeis. Sic enim, verbi pracia, cermi-
  4. norum invicem mulciplicatorum unius in-
  5. dex m, alcerius n: erune ergo cermini illi
  6. A AM eC ARN; per proP. 2. horum erso
  7. rectangulum A Rm X A R. = A~ Rn Fn,
  8. quod per A dirisum, extribet A sem +n
  9. AR R R = A B3
  10. XARR = A R2
  11. RARRRRR = N R
  12. hoc est (per prop. 2.) cerminum illum cujus index est n f n, indicum illorum
  13. 288rC8at0 aequalis.
  14. 22. Eodem modo; Si cermini cres, quacuOr, quinque, aut plureS, concinne
  15. mulciplicentur, productum eoc vicibus una minus diritum per cerminum primum
  16. (sirc ea primi pocellate dirilum quae uno gradu minor est qua nuIerUS termi-
  17. norum sic continue mulciplicatorum,) exhibet terminum cujus index illorum
  18. indicum agBrCgaTO aequatuT. Puta, li continue mulciplicatorum indices (inc L, M, u,
  19. TETMINI CTUNE ARI, ARm, A Rn qui invicem ducti FaCICNE A A A RIFM FN
  20. quodti diridantur per A A, vel A2, prodibir ARIFmFn, cerminus nempe cujus
  21. index l. F m Y n. Der PEOP. 2
  22. 23. Si itaque concinue proporrionalium primus cerminus sit F; (quod in ca
  23. bulis Losarichmieis ponicur;) duobus, pluributre, continue mulciplicatis, pro-
  24. veriet cerminus cujus incex illorum indicum aggresatO aquatuT. SequitI ex
  25. PrOP. 21, X 22. Ouia nempe qua illic imperatur divisio per cerminum primum
  26. (sire semel sire laepius tacienda) hoc calu (CUM PTIUS TETHINUS DONITUE L,)
  27. nihil immurabit. NIaM LXLXZXR = FXZXR = TXR = R
  28. 24: Icem; numerorum ab 2 concinue proporcionalium; erie quilibet terminus,
  29. ipsa poceltas racionis communis, quae cermini illius indici est cognominis. per
  30. DEOP. 2. Nam (I A == F, exit A Rd =- = Rd = Ra
  31. Acque hinc pender Regula de Mulciplicatione L osarichmica. Nempe Darorum
  32. numerorum Foearithmi simul addici, aequantur Zocarichmo numeri ex datorum
  33. invicem multiplicatione producti. Per pE. 23. Sunc enim Logarichmi, numero-
  34. rum ab E concinue provorcionalium Indices.
  35. 25. Continne proportionalium; si duorum alter per alterum diridatur, de quo-
  36. tiens in cerminum primum ducatur; prodibis cerminus cujus index aequatur disse
  37. rentia indicum cerminorum expolitorum. Sit majoris index m L n, minoris m
  38. adeoque eorum difterentia n; Crunt per pr. 2. ipE termini ARm F2, d A Rm
  39. facta itaque divitione, A Rm) ARm Fn (Rn, Si quoriens ducatur in A, habecur
  40. A R~, terminus cujus indCX N PEF PF. Z
  41. 26. Si iaque concinue proporcionalium primus cerminus sic Y; quoriens cu
  42. jutris cermini per quemris alium dirisi, clt ipse cerminus cujus index aequatur
  43. illorum indicum ditterentix. (Intellise, excestui indieis dirisi supra indicem
  44. dividentis; et propterea si hic major tueric, quorientis index exit negaciruS.) SC
  45. quicur ex praeced. quia ( A == E CxIt R~ = A R
  46. 27. Tiem; numerorum ab Z concinue proportionalium; s aller per alcerum
  47. dividatur, eric quoriens, ipsa porestas racionis communis, ditterenciae indicum da-
  48. torum numerorum cognominis. nempe Rn. per Praced.
  49. Acque hinc pender Regula Diritionis Logarichmicx. Nempe Si ex Loga
  50. rithmo Dividendi auseratur Loearichmus Divisoris, quod reliquum est, est Lo
  51. sarithmus Quotientis. Ouippe Logariclimi sunc numerorum ab F continue pro.
  52. vorcionalium indices.
  53. aliae propoliciones de operacionibus Lopprichmicis; pura, de excractione RA
  54. dicis Ouadraticae, per biparcicionem Losarichmi; de Cubica, per ejusdem cripar.
  55. ricionem, ecc. aliaeque consimiles; ex Propoticionibus jam cradies dependent
  56. Nec opS CH l sulio ex prandis jam immorari, ne nimis digresti videamur.
  57. dibus ab unO ExEremO, quoL Lelus a reliquo, distat.) Cum enim sIc termino-
  58. rum alter A R C pet plOB. L. auL R a) V, per prop. 5. Lucque distania D uirobique
  59. eadem:
  60. Susticie dirico foncem indicalle.
  61. 28. In quancitatum concinue proportionaliun quoleunque proprectione; Ouod
  62. sit ex ductu cermini primi in ulcimum, aequatur facto ex mucuo ductu duorum
  63. quorumris terminorum ab excremis aequaliter verinque remotorum. Vel, Rectan.
  64. sulum sub excremis, aequatur rectangulo sud cobus Gebustibet incermediis ab ex-
  65. cremis ucrinque aequaliter distancibus. Incellise; quorum unus coc praecise gra

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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. 171. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/851387705:0191?run=74