Leibniz Legible

Machine transcription of the Leibniz Nachlass

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[Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica, fol. 160

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.

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The machine reads it as

  1. FH E O R E M A S YS P A FIC U N
  2. Lqualitatum quarundam cubicarum adfectarum, in quibus pote-
  3. stanisonea est sub latere.
  4. 60
  5. tus lubtensus à perpendiculo primi, lic tripsus ad angulum acurum sub.
  6. cenlum a perpestunculo secundi: cubus ex dupla bale secundi, Mmuasson
  7. dolib Eriplo quadFaEOtYDOTCNMLRII CALTCICMLDALHIL CIPLALLLCCUIICI a qua
  8. bitur Colidob quadralohs porenula, in cuptam balin primi.
  9. di, contractast proctactamre longitudine ejusrecta, qua porest quadrato
  10. eriplum perpendiculi ejuldem, minus ejuldem balisiFa COnErACLX PTOETa
  11. ctaere cubo; aequabitur eidem Colido lub quadraco hypocenula communisi
  12. inbalin duplanprimi.
  13. IuS F A B, ErIPIUS aHGIHI C A B. PrImL igicur crianguli balIS SIEF A, perpendicolum FB. (WB
  14. in analyricis constiturum est.) Secundibasis C A, perpendiculum CB.
  15. Dicoprimo; cubum ex dupla ipsius C A, minus lolido sub eriplo quadcaco ipsus B R in
  16. duplam ipsus C A, xquari Colido sub quadraco B A in duplam ipsuS F A.
  17. cripla est ipsus OB peripheriae. Si
  18. sccetur peripheria C F bitariam in
  19. K, crune legmenta B C, G K, K
  20. aequalia. ducatur jam recta A R
  21. Frir isicur ex demonstratis a nobis
  22. Theoremare seo ad Sectiones AN
  23. Gulares, ur semidiameter ad rectar
  24. AG, ita recta A C ad compolicam
  25. ex AB, AK. Sc plomdeur diame.
  26. ter A B ad duplam ipsIuS A G, ic3
  27. AC dupla ad duplam compolicani
  28. ex A B, A IE. Igirur A G quadea
  29. cum quateF, aquaBITUT ABGTCBAEC
  30. quadrari dupli a diamerro, de rectangulrtub diamerro AB, _ A R bis.
  31. agoregacum rectangulorum AB in A CbIS, AB In ALbis, aequabicur rectangulo quare
  32. sub AC, AH. _ adhibica in priori a qualicare congrua antiche (, AC quadratum quater. mi-
  33. nus AB quadearo bis, aequabitur AB in A R bis. Ouate adsumpra comimuni alcitudite A R
  34. bis, eric AG quadracum quater, minus A B quadraco bis ad rectangulum quarer sub AC.
  35. AK; id est ad rectangulum sub A G bis in A K bis; vel ex secundx aequaliraris analoeil
  36. mo, ad aggregarum rectanoulorum AB in ACbis, AB in AFbis, ur AB ad AC bis. est au
  37. rem _E A B quadracum ad A B in A C bis, ur A B ad A C bis: eroo (i à similibus similia au.
  38. Ferantur, nempe ab AC quadraro quater minus A B quadrato bis, ablato A B quadrato, et
  39. ab 2gereBacO AB in AC bis, AB in A F bis, ablaco A B in AC bis. R elinqueneur; illic quidé
  40. AC quadratum quacer minus AB quadraro cer; hic vero AB in AF bis, quae inter se crunEuI
  41. AB ad AC bis: quare AG cubusocties, sive cubus duplx ipsius A C, minus AB quadcare
  42. rec in AGBis eguabIu A B guuutaro in A FOs. GuouCat poIoco gemoneranou
  43. Secundo: 2 puncto B educatur reela DI. Hguc lcomencum B l incer B punctum, et
  44. rectam A C incerceprum, aGuale ipsius B C duplae: OcCurTac aurem ip sa B L produca
  45. rectangulo CVl, lacus BI rectoe alieulo, adplum elelareris B C. cric anguu
  46. Dicoisicur Colidum sub a B quac et M A l. inas cubo ipluis A l, 2guar1 1010
  47. CTtueruce duo triansula rectansula aequalis hyporenusae, e angulus ac
  48. Rurlus. Colidum sub guiadrato erip lo hyporenula, in balin simplam (e cun-
  49. CEr cieaas cujus diamerer A B, eique inscribantur urcunque duo rriangula rectan-
  50. sula AFB, AG B, quorum communis hyporenula erit ip (a diamerer: ex sit angu-
  51. Ouoniam eniim peripheria F B
  52. Tcerum: estur AB ad AC bis, ica AIC bis ad duplam compolicam ex AC, AF, ac proinde
  53. circumterenciae circuliin epitele a aalu lecta AO. Quomam isitur in criangule
  54. GBIduarum Cectratum antusecti, live eriens adoe secotum, et lacus GL Poterii
  55. triplum laceris G B. Perpeneccet Marou A6 B.
  56. Cub AB quadrato in AF bis.

Cite

[Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica, fol. 160. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/845634801:0166?run=74