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[Bernhardi Nieuwentiit Analysis Infinitorum, Seu Curvilineorum Proprietates Ex Polygonorum Natura Deductae] Bernhardi Nieuwentiit Analysis Infinitorum, Seu Curvilineorum Proprietates Ex Polygonorum Natura Deductæ, fol. 284

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: 0.88.

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The machine reads it as

  1. 284.
  2. nalysis Infinitorum.
  3. C AP. VIII.
  4. sine quancirares quorlibet astignabiles, sed numero siniex
  5. 3+c+ a + 8 80; quxe (posiro k pro numero quolibet
  6. sinico quancum libet maEnO) sIIE = K9. exit _ q quan
  7. cicas altignabilis; jam si Cumantur sinsularum parces infi
  8. nicetimae, erit earum summa m L m + in L 1
  9. _C. m, Ceu aequalis parri inEniresimae ipsuS kg.
  10. Temm. II. Sine infinicesimae, numero infirirx ac
  11. sibimucum equales, eric earum summa x qualis qugnritaci
  12. Mr
  13. assignabili; sic intinicesima in insinicies sumca est= m
  14. r. Ccu quancicaciastignabili.
  15. Cemm. IIT. SInE ErCSGUTanEIEaTeS, A, B, C, quarum A
  16. est minima, C maxima, B incer ucramque magnirudine
  17. media. Dico A A _ C sint astignabileS, eriam P FOrC
  18. assisnabilem, hoc estnec infinicamnec infiniresimam.
  19. Demonstr. Sineges, sicprimo B intinica, ergo C finira
  20. a astignabilis, erit major ipsa B intinira, quod absur-
  21. dum. Secundo, sc infiniresima, ergo dabitur quanricas asi-
  22. nabilis A minor guanticare infinicesms B, contra lemma 7.
  23. Cemm. IV. Sincinfinicesimx quae libet numero infiniex,
  24. eric earum summa B equalis quancicari astignabili. De-
  25. monstr. E enim omnes supponancur xqualesmaximxe, erit ea-
  26. rum summa C quancitas assignabilis juxta lemm. hujusII.
  27. sin vero supponantur aqualesminimee, erie quoque summa
  28. earum A quanciras assignabilisjaxta lemma II. hujus; unde
  29. cum summa B media sic magnicudine inter A e C, et
  30. harum urraque sic altignabilis, erir e juxta lem. preced.
  31. summa B allionabilis. Sed adrem.
  32. Resumtisiisdem Ermbolis, aC Fig. L. ZZZLIII. SIE VP: B,
  33. DZ: Z. WV A: B, erIC ZWV = y + b, WVV
  34. AIE C, _E Z Y: X,
  35. erir proprer criangulorum FOD e D H F. Similicudinem
  36. equatio prima re:=ra; insuper d ob criangulorum. VZW
  37. _ WV X similicudinem, CA VZ: ZWV:: WVZ: YX seu
  38. B + 1+Z: y + b:: e: x unde Bx L FX F Z∞ 1 y e = BC, PEO
  39. aequatione secunda. Ex quibus sequeneia dedueuneur.
  40. Corol. I.

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[Bernhardi Nieuwentiit Analysis Infinitorum, Seu Curvilineorum Proprietates Ex Polygonorum Natura Deductae] Bernhardi Nieuwentiit Analysis Infinitorum, Seu Curvilineorum Proprietates Ex Polygonorum Natura Deductæ, fol. 284. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/1032977698:0306?run=74