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Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo, fol. 268

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: 0.90.

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

The machine reads it as

  1. 268 DE V EREBUS EF MOTTBUS CORPORUM. L IB. II.
  2. TI. Elementum quadrantis 8 aequabitur lincolae BB. Nam 6e:
  3. re velEf =OC: CII = AO: TO = H O: AO, acquicciam BB: Ff =
  4. HO: AO, ergO GB: Ff = BB: Ff, atque adco 6E = BB.
  5. TIT. Figurxe similes boBB et BETV, utpote qua circa candemre.
  6. etam bT constituta, ec e triangulis similibus b0B, BEI, e bBB,
  7. BTV compositae Cunc, praebent analogiam bo: BB vel (nuM. TF. Bu-
  8. jus) C8 aut (nuM. TIT. 5. 463.) ea =EB: TV =EO: TO, atqui
  9. sa: Dd = GFI. (nUM. T. hujuS) OI: Od, et Dd: Dd =Od: OL. vel
  10. OA, erSO ex aequo habetur bo: Dd =EO: AO = AO: TO; atque
  11. 2d00 b0. IO = AO. Dd = AO. Cn.
  12. IV. Est vero duplum trianguli BTO =be. TO, duplumque trian-
  13. suli BTO =BF. FO, ergo duplum triansuli BOb = b0. TO (num.
  14. FTI. hujus) = AO. cn, et per consequens eriam arexe B AO duplum
  15. xquabit rectansulum sub AO. DC. Quod erat demonstrandum.
  16. C OR OL L A R F U M I.
  17. 465. Ductis ex logarithmicae puncto C ad puncta A et O rectis
  18. CA ex CO, triangulum rectilineum C AO aequabitur ubique homo-
  19. 10g0 sectori hyperbolico BAO.
  20. C OR OL E A R F U M TI.
  21. 466. Tungatur OI, eaque prOdUCatUE IN P, CTUNEque AP = OD,
  22. ec OP =HD. NTam, quia OS ipE RD normalis cA, crunt anguli
  23. SOR ejusre alternUS APO _ ODR aequales, atque adeo triangula
  24. rectangula AOF SE ORD Similia, Ob laECFA VETO AO SEOR xqua-
  25. lia erunt etiam hxec triangula aequalia, ac proinde AP =OD et
  26. OP = HD. AP autem CA FANSCNS AECUS AR compolIEI CX arCU AC,
  27. CujuS TInUS OFI aequatuE tangenti AF anruli sectOrIS AOB, _ CX
  28. Temissi CR complementi ejusdemt. RF DC eAt l0g-uS ratiOniS DO
  29. ad AO, id est, l0g- us rationis tangentis AP praedictiarcus seu an-
  30. suli compoliti AOR ex angulis AOG _ GOR ad radium scu (i-
  31. NUM EOTUM AO. AEqui ratiO AP ad AO = rationi OR ad TK, id
  32. est, rationi, quam habet radius OK ad tansentem TI Cemislis com-
  33. plementi anguli AOC, cujus sinus aequatur tangenti anguli sectoris
  34. AOB.
  35. dC1.

Cite

Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo, fol. 268. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/1066518432:0296?run=74