Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 96r

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One image of two folio pages side by side, registered by the library under both labels (also fol. 95v); this page is its right half.

The machine reads it as

1. eag - kh
2. + eag + eh a β compendio rp = A q + 59 + Bβ
3. eas N =K
4. rursque efgu que) = h (9. B) rp 4 - rrpp fiet L t ef qu (9. ( - hh Bq = h (9 - ) (54 - B() = 554q - BD B - 2 d8 4B
5. erat Ip =
6. =hh Cq
7. ev V =R
8. adeoque efq4e + efBB + ref gB - hh β9 = hd gq - hq3 - hsqβ + hd B(3 - 5149 - 60B3 - 258 9β
9. tiet 44 tet 40
10. + +Zet) 4 + et = 0 Et habetur 44. BB
11. 0 = f + gy + hdy +KBB comprobemus
12. = h
13. = dd
14. dolutionem prioris aequationis, quae ubi est o= f+ gt hapr KY sentemus in exemplo
15. 758
16. +250
17. sit XX + _ aa d + yB = 0 fiet f a x 9- q b = =aa et K= 1 = L Faciamus v -e +Ey
18. fiet de = de + (C: a) y +(C: a) ly et fiet aa XX P a dc y B ac dy + ccyy = eep ubi G
19. hdy +KDV
20. h
21. tahy
22. jam debet esse f+K = g adeoque aax -adetanee +a CC ace = de Ubi tres sunt variantes, X c, e, et duae incognitae C, e
23. a de +2Cy
24. Pitaque dicelli potest in duas, et -a de = -a de et axx + F aa xX + aa ee + aa cc = 2nace, ex priore fit
25. e= C ex posteriore sit XX +2C = 2 e = C + b unde exx ex posteriore substituto valore ipsiuse
26. fiet; XX + ce + 2bc + bb + ce = 2cc + 2bc sed ita fieret Xx + bb =0 quod absurdum, nam nam b est
27. VY =0 quae aequato
28. =aa a dp -20)c Iaande 2BCC destruentur
29. +BBCCipsi oat gemina est,
30. constans, fiet ergo e = BC + ay, : a et fiet
31. au) Y +2apC
32. Hinc fustra tollimus cc, et C, s enim
33. .tollamus omnes terminos in quibus dx fiet aa XX +aayy - 2aaVc +2a BYC tua cc - 2 a BCC + BBcC, = 0
34. ita simul evanescet dx, et supererit - a dy - dBC - Bdc + adc adeoque fiet ab- aY = BC sed ra fit coest
35. recidemus in idem absurdum
36. devellamus aliter, ut sit au Bdc + 2a (Y C - fit et firt ab 4 a) - βc + ac = 0 seu e = ac + ab
37. Aa sic 2 0 aVV + 2aY Bc +B BBCC, habetur ay = A BC, ubi A pendet ex D. et est onstans
38. sed ta ex UAXX- a de tanee +acce = 2 a ce - a de fit aequatio absuria.
39. umfiat aa cC = 2aβCc + (1 - D) BBCC = 0 seu aa -2a (3 + (- 8) eC =. hantur V, et C, sed B est ostans
40. XX - aa d9 2VC - 5 ( 7 s(Bdc - A - 23 BcC, quod recidit in priora
41. sed sic licebit faciendo -a dy - d βc - Bde + ade seu L( e +C) + D e - etc
42. fiat aa de - aa de =
43. et dβ evanescit, et superest
44. eit c - e = β et fiat e a dβ = (Bh x et a dβ : βB = hdx et ab - = shdx
45. Resumta ergo aequatione XX. aade + ee +cC = 2ce = aade
46. et fit β = ab fhim e a: ab -sMax et βB = a: qu (ab - stid x) = xx F per seq B, et fiet
48. a:, ab- shix = + et Ab - Jhax - + X et et hde = + seu h = + a: x
49. si fecissemus aud (3 = βhax et calou B = shax et (3 = b shar: aa = e A X et β3(3 ed
50. eo dba Nam saequatione aXX (= de + + cc - 2c e A = (ph - BBh,
51. seu axx + a dB ta B3 = -3βh + BCh fiat a d β = AB(h seu seu a β. BB = h. 1x se
52. tade
53. - a: ( + 50 = shax = - a: β + ab = shax et a. B = ab = Shax seu β = a:, ab - stax
54. superest axx + a ββ + BBh = 0 et fint ββ = axx:, a th = a . qus ab - shax)
55. (ab - Jhax) ex = hx dx
56. qu ab a cet ha) = ax ax (ib - st dx) dh
57. Estraias
58. aXX et dh. Rshdr = abdx = hax a H) sed ita sh vocando Z diitur ad dtZ nam hax = dZ
59. ab = shax itaque opus foret loco aeq. _ adB = BBhax assumi
60. ad
61. aliquid ex (3, voc quode voc abimus H, et fiet q aa dB = rchax, adeoque seribe c
62. 2f(..-
63. et dhdx = ddzue posita dx constante
64. aequatio resolvenda sic scribetur _xBB = Ghax - ahdx, et
65. aa dB = rh dx posito r = B. Et fit aa fd B. H1) = Thax et faβ. e =
66. rursus XX + BB = - rch adeoque 1 ( Xax + 23d β3 = - ndh = hd, ubi H pendet ex B et h ex X
67. A idem jatem ent generatius adhuc, si nh = W, fiet a al B = 1 dx et 2XdX + 2β.X = - Y dx. seu
68. xx + (3, + Y = 0 et nx dx + 2Bd3+ d p et ( = ( + - X X) it d β = - a A I - 24 ax
69. Y_- ap - XX)
70. si assumatur aa d B = Ahdx et 2xdx + 2BdB = - rdh - hd F
71. sit du = d dB adeoque et dh = Ah dx et divellendo in duas 2Xdx = - r dh dx (seu 2X = n dh)
72. et 26d B = - h dn dB seu 2B = - hd et 2 d B = dh lX = 2 nh Lx. Ergo ZH = log h
73. = y dxC
74. et +Xdr = logh dh seu BNX LXX S loghdh
75. Rresumatur a d 3 = r hdx 2x dx + 2βdβ = - rEdh = L_ hdr. et divellendo fiat
76. et 2B eth dx iaa + hdH =0 fiet
77. et
78. destruendo h fiet 2BdX + aa dec: H = 0 seu log r = - 2sβdx et H = B PF
79. 2X dx + H dh = 0
80. et 2BdB + s dH
81. a d B = b et 2Xdx + 12(Bdx dh
82. et qu-d =
83. 2X dxdx: b25βax
84. et -dh = 2x dx; B2s x
85. EXaxAX
86. et log(I: h) = ad
87. = 2X Ax: lsde fint ad B: p.s = 2dx
88. a d β =
89. dh = h 2Xdxdx: ad 3
90. F. SPdx
91. dd β = 2 du 2βdx bFe
92. et dd B = 2dx 2dx ad B D 2da seu dd ( = 2dx
93. del
94. seu 2X = sad (3: b2S Bdr
95. sin I = 2loq dB et B log X = - 2 (log. d 5.
96. f 5 d L B: dB
97. et a dβ: b. 2 sad B. C = hdx. Ergo h = (a + β : b. 2(.). : de B: 2 dB β
98. Ergo X =
99. seu h X aad (3 = rhdx 2xdx = - rdh 2β dB = - hdF. Ex 3 per 2 fit onhcx ina = h dN
100. Ergo fit dH ua d M: A = = 2(3 dX et g log(1: 17) = 25 βdx et log r = - 2s dx i - (25Bd
101. Ergo ex 1 fit aad B = b. 2 h dx eto 27. dx = = b 2t dh et 2B +B -h. B dx b 2s da quae
102. aadd β = dx, bs dh h=Bdx Bs
103. seu hdx = aa dB b2S. coincidit ortae ex 1.
104. dh = t
105. aa c (3: 2∞d X = _ 2X dX : aa d)
106. Y. 2XdXdX: aad B = dh: h. Ergo t Bh - s. Eaala Af.t B3)
107. io ponsem +. rtlarae tae hi nes aa pre Bueim 1 et ta poneo
108. ad quaesitam pullo fractu
109. Valorem- m.B
110. P. C
111. - )
112. Se = constans

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Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 96r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068199:0191?run=74