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Leibniz-Handschriften zur Mathematik LH 35, 15, 1, fol. 22v

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

One image of two folio pages side by side, registered by the library under both labels (also fol. 23r); this page is its left half.

The machine reads it as

  1. fig. 16. pascul. 44) eiaimeter. () RadiutB. Bai Quidratum diametri (2 a) quad. insciptum (R4 2 a) Radis tlticis
  2. idem producitur
  3. summa sinuum
  4. ejus dimudium 47, R42, a = Rq Z, a. 7B = a = B4 a. Ducatur ZB in arcum gB.
  5. peripheria verantem.
  6. Erit portro superficiei colndrice, cujus basis circulus AB. altitudo ipsa ZB.
  7. ponatur ZB. duci in totam peripteriam, manisestum est cylindrum, cujus est ea superficies fieri
  8. ex ductu circuli in buseos in altitudinem cylindri. Radius est a. Esto Peripheria X. erit cirtu
  9. circulgs: aX. et Z Cylinder erit a_, a = gL, a, = ax - a X 19L, - ax -a = ap a
  10. Area cylindri divisa per bacu semibacim, radium basCos AB- a. producto duplicato dabit superficim
  11. r cylindri, totam cujs octava pars est, dicta portu quaesita ergo dividatur per radium, producti,
  12. colum est ax ause
  13. B equo
  14. a 94
  15. eir al
  16. sumatur pars, quarta ax = aX ab hac si aufeatur summa Sinuum versorum
  17. R9128
  18. dupt: Jam quia segmentum circuli majoris non potest commode auferri a minori auferatur a majore
  19. 28 1b B432
  20. rertabit.
  21. ax ax
  22. vel AZ
  23. XG. XD ed sou cegmentum, duplicatum, duplicatum, restabit summa sinuum rectorum DR. DZ. BB
  24. Segmentum daplientum est
  25. ax ax =
  26. ratur ab
  27. na
  28. et a Residuo auferatur differentia inter majorem et minorem. Nam si cauferre debeam _b ab a
  29. idem est ac sianferam ib a C. quod esse suppono majus quam a. et a resituo auferam diffe
  30. rentram inter C et a. a - b = 4 - b, - ( +a Pomo segmento duplicato PB. ablato a
  31. circulo AB. rectabit seminirulus aX + duo Triangula octantis circuli tubra. Ab hoc
  32. residuo auferenda est differentia inter aX et a+ - ad
  33. rectabit
  34. s
  35. F R4128
  36. aX + aX hoc auferatur a ax + 2 Y la octorrtis AB. tam av- 2ap.
  37. R9128
  38. Restabit: 2 Da octantis AB = ax
  39. ax. Ut autem investigemus Flum octantis hubemus
  40. n4 128
  41. rectum 2Z = vel ZY. = Rq a. Xeius quadrato a. aufert Ltum de ZB. a + 1a = 2a 9.
  42. habemus 2a - 2a RqL, hujus Rq. est Recta (QB) Y2a- 2a nai erit
  43. 2a= 2a 2 23 auferatur a quod. radi a. restalit etum fuleri Ergo fulem erit quod
  44. a a erit a-
  45. 2a - 2 a Mq=
  46. 2a+ 2a 21
  47. Et fulcrum eii
  48. a + 2a _42 suppue fulem aequari recter 4 B) ducatur sim oimidiua satr sea in dimido
  49. productu
  50. erit quadruli ZB. dimedium ducatur in QB. productum erit Rg 4a Aa
  51. a-4a
  52. =
  53. ea
  54. a - a
  55. =p
  56. R432
  57. 42.
  58. Jam omnes sinus DI. aequantur radio a. ducto in DA vel 2Q - a9: a fiet (R91 a.) summa simumu
  59. 64
  60. 32 1
  61. a qu auferatur recta ZA vl (vel 22) dacta in arcum, ZB vel 8 fiet q ax, restabit.
  62. R4L a = = na: C ax = - 2a a X - ax. Ergo (quia B1 = a x- aX ) erit a = 2a - a +
  63. X432, ∞ R4128
  64. ecesseest errorem esse in calulo, quia a H 2a
  65. 1g 32
  66. A912B
  67. AG2 932 8
  68. Fortasse datur Meterodus in arithmetica infinitorum, summandi aliquam surdorum progressionem, quoniam
  69. etsi praecise integris expituri non possint, for aliquando tamen id quod dast deest, erit minus quolibet
  70. dato. vig. quoties res reduri st ad eum statum, ut radios quadratae differentiamm aut aliquid
  71. ab illis pendens desit supersitque ed enim tuto negligi potest
  72. R4 a. + R9 b. Rg a + b. + 2ab.
  73. Ag ab. + Rq bC = RqC ab + b + 2Rq abC
  74. aq a e a rbC + Ru d + bC = Rg. a +bC + d + bc + Rq bc +bca +d bc +de
  75. quotres mmilliplicave duarm surdarum in se invice aliquis terminus produci potest,
  76. ex quo possit extrahi radix, suve quadrata sive cubicae. toitres ex diubus
  77. sundis fieri st una.
  78. differentius inz dias radices quadratas semper exprim potest me radiae quaditta ugq Ab
  79. est, ineatur summa quadratorum, eaque duplicetur producto addatu
  80. erit summo Radicno. Jamsi his radices summare velis,
  81. R9 ad + A4 V, Rq prinae duae R9 a +b- (4a R9b + RqC-
  82. Ra 14qa + ab = 2B aqu 14b. 4 14 2ac + b
  83. a - Rq a
  84. ax - Ba
  85. nana
  86. a - R4
  87. 1 = X
  88. isa
  89. in aer se tuo toee
  90. 2 a
  91. a anfenti
  92. F9B R4128
  93. Aota sii velis inire summam quadratorum, sic procedendum ab= bc:
  94. summa quadratum differentiarum inter radices, residuo quadia tradis
  95. eaa
  96. Rg2 AquE Bq2
  97. 24 12
  98. B432
  99. ac p
  100. ad + +0 = =Lttqu - 1qu
  101. Nam Aa ab RquC
  102. Rg ab. - (ebc
  103. 4gabbc + bca
  104. Xa = 2 = A
  105. aa - = A + y
  106. B = A + Y
  107. B- A = . eeam

Cite

Leibniz-Handschriften zur Mathematik LH 35, 15, 1, fol. 22v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068203:0044?run=74