Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

Leibniz-Handschriften zur Mathematik LH 35, 12, 1, fol. 309v

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: 0.79.

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. 310r); this page is its left half.

The machine reads it as

  1. (entro E radio e desccipti sit circumferentia
  2. positione
  3. Circularis YY. Data sit recta quae cunque
  4. in qua sint puncta data A, H, in qam ex C. aga
  5. tur normalis CG, quae sit sg, et AG sit g, EA
  6. Ex agaus in (G, noreetis Cr H Y sit Z et X) sit y
  7. TAX sit x HXB AVS
  8. gu ve XX. KYC HncCXC, 9-XE et
  9. CW = C = y. jam qu CW + AX qu Y1 = e YY
  10. jungatur CH, 1.C . 1G
  11. et fiet, ce +gg - 2Cy + gg + XX = 29X = 1r Rursus
  12. quia XX + gu = vv siit exutraque aequatione
  13. idso posito cc + gg- rr = asat, fiet ex.
  14. vol _F + vn - 29X = 2C (∞D - XX), et sublata surdre it huit chorda GY = AG. jungum ey que rvaetur q et R)
  15. prioribus ambabus equationibus af + vD- 29x = 2cy
  16. v + 4997XXasGP. agXVB. _ 4 ( sit 9 retb= quosic et Etpa i sle. E eeas qu uat. sungatur itHC quae vocetur na
  17. ttiatage gq ier cs2
  18. ao Acl it delpains au ad mgntu
  19. coltar
  20. sutengsi est da voceu
  21. quod si pro vD substituatur recta qualtam potest
  22. qavalite
  23. rectare recta quae a constantem, eam potest, habet
  24. veluti c r quae nempe recta constante sC, (si placet)
  25. recta Cd, pro erponendo eed, habebiitar aequatio
  26. localis secundi grabus pene genecalis; quae si conjurgatur
  27. cum tali ad alium circulum. vel cum aequatione
  28. praecedente aequationem inter X et V exprimente ad rectam
  29. hahebiter habebuntur B et X adeoque etiam cd et X
  30. per intersectione duorum circulorum, vel circuli et rectae
  31. cecdeique At h Et talis quidem aequatio
  32. Interim notandum comparatiodem aequamini localis on data isterdum nos
  33. localis conjungit paralleta ordinatam parallelari
  34. convirgens aequationes solides it tanc jinatius est siltalis constinctio, etsi sit possissilis
  35. sed si velimus aequationem localem ai
  36. ductuam
  37. ad circulum secundum duas convergentes AY ut HX
  38. vil secundum et Z m tantum In aequatione proxime
  39. praecedente secundum v et X, substituaus p ut ad Rectam
  40. localem feceramus) pro X ejus valorem ee + v - 3Z, D: e
  41. sit aeo v L dcellvo -Bge 89C Egej (bb e b v bb Z + Blil verp -8bl. vrZ Z - Beg9g - degqq VB+ 8Cg11 221 - 0
  42. efer
  43. in hac explinatioa Aequatione explicata, debent v et Z inter seervure
  44. legem homogeneorum ee gge 4C, C- 2. sed quia in hua ae quatione vecorit AH se g Alisen, g
  45. Core tet Be beC+ egAt) NI, m
  46. et bb g9+ fiet geem ggg ggke + gg+CC = dAgF cC + AHK gr. Ggtge Ak Kg2C + 29Xci L gL GB
  47. cum partus et absit HG, quam vocabimus K erit C= D+X
  48. ggraem c bb = 29e = gytac - 2ge + ee, eB = KKU-ee
  49. et 4bb-ge = AKKY qCC = aee ergo in aeg. sec. v . Z
  50. libi est (4bb- 8ge + 4 eC) v v prodit +(XC +KX) ess vt - appo
  51. quemadmodum habetur 4bbZ, ita AC ducitur in HV et HC in AY.
  52. decu per decussationem
  53. WV ducitur in dCge eC + 8bb C FDC994
  54. H: gC + bb. = - rX= 19 + 91) - ge r pot cs = ∞ rrg9C ggu gk Hinc
  55. rrep + 9eC -gRee 499q - gk e = - g gocc L gyrrg H9d. P gticC L yKrr
  56. Son ((YY+gG- CC) gK F (YY +KK- c1) 99 + ( YY. 9H) eC)
  57. seu gro ((t C)q A (HKR - cc) gg + g -rrgg M (gK WrKK - gK + 2gK (rgt (99 ))
  58. 2 GGHKH9H
  59. seu zon (g9-cct9 f(G(a +I) gCC = (CCt VTAKK)GK _ = rrKK + 2gggK)
  60. ud si Bv(99 - CC + 2gK) 99 - CYYLGK)KK - rrgK
  61. 1 QVY olee = cc)gg -ggKK CK rrtk (YY+ KK) gK, + A
  62. aei livee es = v2V (C3993 9itV- B00 st ( CGd ctir. Accgt. 4 99 a) 3b. ).
  63. seu 62
  64. re steotud quon
  65. Ubi e est vel summ
  66. ipsarum g et K,
  67. posita X affinuta
  68. sim AG et HS sumtur
  69. partes si G cadat intra X et D
  70. anas potest esse excessus per
  71. agius respectu al aeriys
  72. sit quadraitum suma
  73. vocetur b, erit ec = bb
  74. super el normaliter erigatur radius RCjungatur GR
  75. super ipsis A et GK _ describantur semircirculi RMC
  76. etTB, et ili l accommodetur chonda CQ= ARC, et
  77. rr+ cC-99, et gu 9G + CC. tr = a F) YYHCC- KH = ab H
  78. +qubxx- aqtgx tat 20
  79. p Ut habita est aeq. v 2atwrnete =o
  80. ita tial rad A E+ A ppBY Aast aug -0
  81. 2af -4uc
  82. 299-2
  83. n nat
  84. ∞ KKGg KKgH ZGKGTgt
  85. agKbhgat
  86. Kgg gRCC
  87. snbo rgsenserg gik. Muxx
  88. seu duns rataa
  89. -rgk ccgK
  90. eg = 99+gk

Cite

Leibniz-Handschriften zur Mathematik LH 35, 12, 1, fol. 309v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068194:0618?run=74