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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 89r, page id 00068196:0175
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Aequatio
Si in aeq. paginae primae 4, destruamus
 s, faciendo. P 20. 30 = 10. 40, in aeg. 4 aberunt
quia ad sespjus vepama
y et gydy. ita 40-  20
data dende multiplicetr per 51, et at eg. 5 destruttatur demini ubi 50
Mitim loco 51 adhiberi bi ita omnes in cognitae habert potam simstram parem
61 = d41 + dex 4 - d31 22 - 31 d22 = 10 41 + 12. 90-21,. 31 = 22. 40 = . 1a 41 + 11. 40 - (410 0 ) 40. 31 - 21. 30
11. 304 + 1230, 40 (= 41. 30.3 = 22. 30. 30 = 10. 31, A1 F 11. 31. 40- 18 31. 31. 40 (,21. 30.31
Hine commodissime habetur 22, et fiel 11. 30. 30. g1 = 10. 31. 4. 40 - 10. 30 31. 41 : 303 = 22
compendio 22 = 30. 130 _ + 10. 31. 21. 40,:303 et d32 f d(5B. 120) 41 + (D. 1120 d41 + ( d (18. 431) qd + 18. 313) d40
Et fiet 48 12. 36 d 41 + 38 d1 2. 41 - 30. 1130 31, p. 31 31 4u d31 = 30 210. 12 H1 + 30. 1 8. 4u - 1 1.30. 131 - 1. 25. 21
Cams aequationis ope habetur 21 quo vaslore substituta in valore posteriorenasius 61. habetur 61
 303.31.  47 8) 41 - 30113al4 S 4 (o. 31. 31) 4 40 - 10. 31. 31 31. d40
per 40 et 41, uti jam habentur 22 et 2I. His jam valoribus substitutis in  Temmnis yus ex etgax
Habebuntim aqu in qua 404.. qu +. 41 f. de40 +. 441 =o et rursus. 40 t. . 41+.. d r. d21 = 0
 t in valore sdo ipsus 61 ponatur H(1 - 1021) 40 = 2. 4D  At d sccundo
sed video per d21 descendi ad d41 quia
valorem 3tio aequando fit 10. 31. 41 A 7. 31. 40 (= 30. 31. 21) = 11. 30. 41 F 12. 30. 40(2V. ∞1= 30. 38. 22
et  conpendiose fiat 22 = 8.40 +9. 91 et d22= 18,40 +8d40 + dg. 41+9d41,i quem valorm
sstatuendo in aquatione nimqualeris ipsiuis si cum ultimo fiet dat 3do
fiet 10. 12. 41 + 7. 12.40- 12) 4070 = +12. 3od41 + 50. d12. 41 . 3ol31. 840  g - 20d 31. 94
-30 3148.90. 30. 31 9440 = 30 31 d9. 41 - 20. 319d41
His jam ex ydos agi pt porro hanc ex pra ex valore 3 explicato 2, Aet
Unde compendid fiet 21 = 6. 40 +7. + 1L 4140 +5141
fiet 61 = 5041 + Z40 f21. Hic ob yen fit 10. 41+2 40 - 21 = 407 1 41 + 2 apo t di 4g0 a 190 20 -9 dv. H
3
B +30. 4840 f50. 8140  43049. 41 130. 9d41
A- d3121 - 31 d2
tot  d rrto fit L. M+ Z, g0 - 2 =  44,  d5.   3. qu a ta r. 4 901 540 - o , 2. 1g0 2t - 30 d21 .
ila lrabemus tres segai sud 40, 41, 21, quas compendiosies esserr licet quaula sunt 40, 440, 4, 4
21, d21, sublato 2) habebimus duas ubi q et 41 descendunt ad dd go, da 41, ubi siquid judico, non
potest tolli 4I, nisc descendatur ad d d140, nam tollo potsst dd4I, restunt d441, d 41, differentiando
habetur ihuc senel dd41, et d40. ubi nusu unde tolli poss potest etiam da, restat 41, cum  40, 440, dqu
Ergo idme sendi dsferentiando descendetur ad d. 40, et tolletur 41
d2L ex aeq. 16, d21 + 4sset 4. X() 21 + XX2(2 - - 2. 4 1XX  + 41 - 2 s21 + 41 - si Aad per ta set +. EF sat = L XF L a1X + a - 2( it + 41, et differtulando fer.
x
s
vyarex
A 8- V Bo sia d log  f ag L hg bts v et a V- vB  s   =  do b + dtotr b + de dso. lul epupuirbid qu nus sen foe tile prio sim letepes ater