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[Vera Circuli Et Hyperbolae Quadratura] Vera Circvli Et Hyperbolæ Quadratura, fol. 30

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. PROP. XII. THTEOREMA.
  2. Tccraperium ABIP, A; PoIrgonum
  3. ABEIOP, C: polrgonum ABCC
  4. IENP, D; _ polYGOnuM ABD L. P, B. di-
  5. coD esse medium harmonicu incer C de B. Cx huiusq. A: C.:
  6. C: B, d componendo A C: C:: C B: B, Sed ex huius5.
  7. A C: C:: 2C: D; _e id eo C H B: B: : 2C: D, _E pErUTAB-
  8. doB, C: 2C:: B: D, X dividendo, disterentia incer B e C
  9. estad2C, ve disterentia inter B e D ad D, e perimurando
  10. differentia incer B C eR ad disterentiam inter B SE D VE, 2C
  11. ad D, hoc est, veC B ad B, de diuidendo, difterentia inter
  12. D_ C est ad disterenciam incer B e D ve C ad B; X proinde
  13. Destmedium harmonicum inter. C de B, quod demonstrare
  14. Oportuie.
  15. Flac propositio eodem modo locum haber in omnibus
  16. polssonis complicatis, repatet ex scholio s huius.
  17. PROP. XIIL. THEOREMA.
  18. Ncex duas quancicates A, B, Ci media a-
  19. arichmerica C, media geometrica D e inc F
  20. dia harmonica F. dico. C, D; F, eNC COn-
  21. tinue proportionales. quoniam A, F, B,
  22. sunemratione harmonicas erie differenria iner A e F 3d
  23. difterentiam inter F _ B vr A ad B; d cemponendo erie dif
  24. ferencia incer A de B ad differeDeia incer F de B, vi A B ad
  25. B. deinde permucando de componendo 2 A: A _ B: : F: B,
  26. sed 2A est duplum ipbius A de A B duplum 1p I:US C; et
  27. ideo A: C:: F: B; de proinde CF = AB, _e AB = DD, iacOG;
  28. C. F = DD: Scigitur C: D:: D. E, quou aCAAAIAre OPOE
  29. TUIE.

Cite

[Vera Circuli Et Hyperbolae Quadratura] Vera Circvli Et Hyperbolæ Quadratura, fol. 30. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/834940469:0038?run=74