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De Locis Solidis Secunda Divinatio Geometrica, fol. 113

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: 0.89.

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

The machine reads it as

  1. ADDENDA LIBHO TCKSI.
  2. In cribus enim luperius demonstraris PF, FIL, F CE. in continua
  3. rarione harmonica, tres IF, ICF, ITI lune veique in concinua ra-
  4. eione geomerrica; sed media lCr octensa est aequalis ip(i IF, quarum
  5. veraque est dimidium corius H. CF differentia interprimam, ec certii
  6. erium harmoniearum, _ IF aequatur summae IC+ cum CEF, live lum-
  7. inx ejusdem dimidii cum cerria; ac demum III, est differentia in-
  8. Eer LE (quae est summa dicti dimidii cum certis) _ TIF, qua est me-
  9. dis harmoniea data intex exeremas dictas F. P, PCF. Ouore, _C.
  10. SC I OI YV M AL
  11. gEnigue. Si PTOdUCANFUE deXErONLUM ReCIX ABN ad C, B M
  12. ad 1, BC ad 5, AD C ad F, acq; curra ParabOlA BFIC ad H;
  13. et exErA NC ogatur quaecumque recta ch, ipsi NVC Parallela, quie
  14. necessario singulas lineas productas secabie in punctis c, i, 5, F, ec h.
  15. Dico, hujus rectae eh eria segmenea he, hF, hs sempee esse in
  16. quadam continua ratione harmonica.
  17. In similibus enim criangulis C BN, gBC sectis a recta BMi, Osten-
  18. Ta est C H aequalis MNI; quare sc gi aequatue ipsi ic, sed (ob Para-
  19. Bolam BTTCh, _ aequidistantiam rectae in ad diametrUM BD) EreS
  20. iR, 15, iF, sune in quadam continua ratione geometrica; illarumq
  21. erium hc, hF, hg, recta hF est summa differenciarum maxima cum
  22. media, de media cum minima; summa vero ex ih maxima erium, de
  23. ex i8 media, est ipsa hc (quum ic, sic aequalis iph i8) e maxima
  24. demum difterenciarum est tig: quare, per primum Scholium hojus
  25. tres he, hF, ho Cunt in quadam continua racione harmonica: adeo-
  26. que prima hc adcertiam hg, est ur c F prima differentia ad F8 sc-
  27. cundam. Ouod erat demonstrandum.
  28. Ad pac. 86. super fieura, quae ibi, immediate inter
  29. versus 15. 16. addendum est sequens
  30. ILLLM.
  31. D mibasibus DA, DB, sive aequatur luo recto laceri, guxvis sC
  32. ips diameero F D parallela, est media hormonica inter parces ince-
  33. BFaNECS AC, C B datae rectae AB, omnesque ordinata F. D, F C, per
  34. Parabole propriccatem, incer se lunt, ut rectangula ADB, AC B luD
  35. parcibus basis AB; sequitur hinc, quod omnes medix harmonica
  36. E D, F C InCOT DATEOS INEEGTANEeS CaIdeM RECTAM A B LUINE DEO-
  37. porcionales ipsis rectangulis ADB, AC B sub partibus integean-
  38. ribus iplam AB, e incer quas illae lune medix harmonica.
  39. SCa
  40. Fd in hac Parabola, cuius digmeter F. D aquatur vtrigue ex (0.

Cite

De Locis Solidis Secunda Divinatio Geometrica, fol. 113. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/898203430:0305?run=74