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Leibniz-Handschriften zur Mathematik LH 35, 2, 1, fol. 213r

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: 0.81.

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

The same scan is also registered as fol. 214v; its text is given once, here.

The machine reads it as

  1. de simplici Cattu excerpendo, nempe Z. H = H L3 dc, ejus le
  2. riei infinitae Cummo Facit Z(cu Z. Sed si ex hac iterum, simplici
  3. Caltu terminos excerpamus, nempe: Z F f. 8 _c, ejus sericiinf-
  4. niex Cumma erie Semicireutus, posito gradracum Diametri eAle 1. Cvo-
  5. niam aurem eadem oper à d quadracura syperbolae Rricbmericatrabe.
  6. cur placet cotam harmoniam oculis subjicere:
  7. 364 31 100EIA 169 196 225 256269 74 3SIO
  8. 81524 3548638099 120143 168195224255 288323360399
  9. 36iserss 1005 10 orisoero inssoso
  10. cc.
  11. c.
  12. (cireulo ABCD cujus
  13. agratur SDocencia inscripta
  14. Hyperbola CBEHC, cu
  15. ljus gractratum ABCD
  16. Sicin Figura 5. Asymptoris AF, AE, sibi normalibus, Hyperbolae
  17. curra deseripea OCHI, cujus vertex C, porentia vero Hyperbolae in-
  18. Scripta sive qracratum, quod rectangulo sub ordinatâ quàcungue
  19. EtL, in suam ab scistam AE, semper aeqrale est, sic ABCD: circa hoc
  20. gradratum describacur Circulus, se ponatur Fyperbola ita conti-
  21. nuacA a C VSg; ad FL UE SIE AE dupla iphius AB. Tunc posito AF esleuni-
  22. CaTE, erit AB =, _c ejus quadratum ABCD erit Z, ee Circulus cujus poren
  23. cia in scripea est ABCD, erit Z. f. X, FG _c. Hlyperbolae verolcujus po
  24. cencia inscripra estidem qradrarum Z) porrio CBEHC quae logarictmi
  25. racionis iplius AE. ad AB(sire binarii) repratentat, eric 3. L 40 L72 aC.
  26. JOH.
  27. XAB CLMHBIIEIP BE XHUSABGILMSAI OnEs MmIOd MMSAuT SDEL. 24
  28. rocuei cunsespeab 13 P0nb c2. Ln SJY ~ _ WIHIGLSGLIMSSI MINIEEP
  29. EAB DECY MMOMTD MIBEONET SIBCIEAES SMISIMP MMIOd MTUISAMMuS
  30. DUON LSMNISTDKS SIIDIIOBO E PHIOLBLI ONSLMMIO ge StAEAB
  31. Eso Bos ipouonlus qus uiodiSO3 sausBey uapiou supHI pos
  32. SMUIu
  33. BegC = unuSy sunSyasd noscundes csvonesydnu sivorier
  34. OIIME CMOKSIBL W BnnguOS inSueVs sesurab secp n et Z
  35. DeL inCOQVuMSuEBBS PE VDQV Comabgosin sopio
  36. vrS) eSy n3Q nedISIONeK 94 unX
  37. Odiones agEqus 3g cererpeabruy 39 us eneab sied noy et day
  38. VF E DEY In CLEIMMSUEBSS BEEMSGOSI LWLIMICHISIGU SIVONET NS
  39. =nSES LMIETELMPIOONET DBIOS (∞31GHS op100qu WI 3dWBU) 3X CL2
  40. Druey
  41. CSD)EANIEH LIBIMU iVESVELI (D p3a AV 15
  42. E
  43. =veDSs SAEdeHMI IS eHMSGCAG:C pErnneL. 2per mOqVuind
  44. =TIUMSAI CMMSUEDOSPE VDQV eMSy 113 OSIS: Z SuSCAdXS
  45. WDHOHESGCITMLISIIOTES SIIBEIMU DUMS CTIINIONBLIMW SUONeS vivSyd
  46. nxui n3y. 3∞ SbCi erespeab Mnno3 in Jun) =Dg ~HECIP1O. 3∞ CE17C
  47. SNGHEIMIBE STASCIML IA SNGMUSVIXS
  48. day qV sypiosqe 170
  49. mvd
  50. Merab CEESBdKZ UmpneSienun csusudus unvonesdu
  51. TALS SIVOIEN LMIBIEME DE SesIUM MMEGDQV cMICIISGCMSAIS cmpS
  52. =GEDSIPE VDQV CAMSG LTIS 1I35GO Pa QV aneISqe CeOdIBBN
  53. ne eBsEP erecg me eresdiu sabunssa suones cusuns
  54. E3IELSGIGUIEg rePIO opneaB Siudu ESpgETMLIEE SESpA
  55. =IMS SEAMSS ipVSIISUI SEDOTI 13 MMVHdS OpHSS) ONVON XjOgese
  56. CEMEsPCAb MIAI WSPC: Nyal idnoper om oups, cenS uns
  57. uy L3 D MEKyd) pun CXXGd iperabp, D CmOB Supdin y epuyL
  58. In es E.ZCT umLORUME 13 Syeab Sd syegV SruIMe UpenF
  59. CSPUI L3 ~ CeRXGdy CLINVOS LSIUI Ones sy ab CMISAC CequOS
  60. LNIEVAB COSPBLIILBLV SHLIIZA .LINIOSEELLSGIE NEIXS SrRES
  61. Posurprab Bned Corxoce suipunsord eyes inb csinsou porb cex
  62. -UBAPS SOLIIISI LHIWIOSG LINdDEEMEISHVOI SIUNduTEUSqr
  63. LINLEEKISGSHd ABMIE CIM ∞ : unOd FESONSISESIELESSIV SOVOI
  64. eabie De esxujgo1d say unus absu seresyqud snus vey cs siai
  65. SOBOGISEI LIMPUNOS) 73SICVSIOdUTSIEZ SOS eS CMPVONCMEnqqVE
  66. WesG3S,V Vod iverI 3abonB SUNU iUIE ~ CHevOS Suny LSd
  67. ZBIBIIOSG 3uESyaUs esHII BY pC uniosuan solb 1dO
  68. eAt qradrapla rationis Circuli ad Gractratum. Archimedes quidem. Po.
  69. rgona Circulo inscribens de circumteribens, quoniam major est in-
  70. Scripeis ec minor circum seripeis, modum olédie, exhibendi limites incra
  71. quos circulos cadac, sire extribendi appropingrationes: elle seilicet raci-
  72. em circum ferentiae ad diamerum, majorem quamze adi leu quam 21
  73. ec minorem quam 22 2d7. Hlanc Mechodi alii sunc prolecu, Pco.
  74. lemaeus, Vicca, Mecius, sed maxime Ludolphus Colonienlis, qui octendie
  75. ele circumterenciam uc 3. 14 759265358979323846 dc.
  76. ad diametrum, ad 1. 00000000000000000000
  77. Verum hujusmodi Approxinguaciones, ethi in Geometria practica
  78. vriles, nihil camen exhibent, quod menci Catistaciat, avidae veritatis, nili
  79. rogrestio calium numerorum in infinicum concinuandorii reperiacur.
  80. Mulci quidem perfectum Tecragonilorum protessi Cunc, uc Cardinalis
  81. Cutanus, Oroncius Finaus, solexhus Scalioe Thomas Gephyrander
  82. Thomastlobbes, sed omnes Falso; caleulis enim Archimedis vethodie
  83. Ludolphi, refellebaneur.
  84. Scd quoniam video, multos non latis percepille, quid delidere.
  85. cur: Sciendum est, Tecragonismum sive conversionem cireuli in aqua-
  86. le quadracum, aliamre rectilineam Eguram (quae pendet à ratione
  87. circuli ad gradratum diametri, vel circumferencix ad diametrum)
  88. Posseincellisi qradcuplicem, nempe rel per calculum, vel per constru-
  89. ctionem linearem; utrumq: vel accurate, vel propemodum. Quadracu-
  90. per calculum accuratum voco Analysicam; eam verd quae per
  91. Constructionem accuraTam sC, voco Geometricam: per calculum
  92. proxe verum, habetur appropinquacio; per constructionem prope ve.
  93. tam, Aechanismus. Axproxingrationem loneissimé produxic Ludol.
  94. Phus; Mechanilmos exresios Vieta, Huxenius, aliique dedere.
  95. Constructio Geomerrica accurata haberi porest, qua non cantum
  96. Circulum inceorum, sed de gremlibet sectorem sive arcum metiri li-
  97. Cedc, motu exacto acque ordinato, sed qui curris cranscendencibus
  98. competat; quae per errorem aliogri Mechanicae censentur, cum
  99. nen aque sinc Ccometricae, ac rulsares: licet Algebraicae non sint, nec
  100. ad aegraciones Algebraicas, seu certi pradus, reduei qreane; suas enim
  101. seoprias, et Ei non Algebraicas, camen analycicas habent. Sed ista hic
  102. prodisnicace exponinon poltune. Quadracura Analycica, CeU QVX Per
  103. calculum accuracum Ec, icerum in cres porest dispesei; in Analycicam
  104. Manteendencem, Alscbcaicau, de Arictmericat. Mnalycica trans.
  105. cendens;

Cite

Leibniz-Handschriften zur Mathematik LH 35, 2, 1, fol. 213r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 44). https://leibnizlegible.com/page/00067993:0427?run=44