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# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 30
# Folio 147v, page id 00068124:0298
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Exih
solvenda jam esset aequatio W0W -2WX+XX = aa b. a = um
quod jieret si extrahendo valorem hinc inveniri posset valor ipsius X cculo
finitos et per formulam finitam, atque inde ostendi quando per moadcipiat
quando incipiat impossibilitas. Sed hoc difficile foret. venit ergo
in meutem via sequens, per duas radices aequales
aa b: a +5X + ag qua quadretur, et prodibit
Xch
4 I- 2X: h
x
haec ut comparabilis reddatur isti
X. H
ab: a
L mm
2
+ aaXX + 2a aWX + aatW =S
fiat -m m = 2aafx b: a + 2a9b: 42: h  + aaex + aed
xtr
et fiet f = a et g = W + e et ( W) +2wet ee = (aa WW) + àd
unde si fiat seu ad =2wet ee. et proinde erit
aamm = 28X b: a + 2a (0+0) b: a +2aa ex + 2 auve
+ aaeC
biHn rosen 20e =qee 9: ) 2aX + 2 a C0 + C)
sium ioro - XX F 2WX: a
Hinc
aa b: a  + aX +ao + C) = 0
seu aab: ch = = ax = a (10+ C) =  - mm = 2eX -2C (0 + C), a:, 2(X. + 1 + C)
Rursus
seu 2,XX +qoWo (+ CC) + quX Ygex + (QeW = nn  rex + rerottr ed
seu = mm = XX + W0W0 + 210X + dC (10 +X). sed hinc non indeo exdum,
illud potuis videam an non curva ipsa it loco logarithaicae
illud potius videamus, a
possit assumi, sic ut habe duas radices aequales habenti compacetur
unde fit
+SX + WW
=mm
conferendicum aa b. a + 25x b. a vag bia  + st xx + 2FGX + gg
iti
+2
eit L= q et g=r: 2 et f2a ergo qura et fit. 2W + s = 2g = Y
ergo W = _. s - Y, : 2 et m =  eat  ((at +  sst =  - 2) (- = YY))
ubi potest poni 5=0
inveniendu
et hinc facilis erit modus talis curvae tangentes
XX. XX - 2WX + WW + yy ∞mm =0 fial
ut in pambola
posilo gy = 2ax, fieret XX - 2W0X + wW =0. conserenda cum XX - 2ex + e
a 2aXa um
fit A e = W - a et (101) + aa - 2ua = (11) - mm. sed W - et a
=  = - xx L WX = WW -2aX. et fiet tande
XX F WW + aa + 2WX ( =2aX - 2aW = 0 seu X + W - a =0, quod est verum
sed in nostro casu nimium indetur assumi, nempe non una radio aequalis, sed multae
suffecerit interim minimo lnique  formulae reperto, idto +xx-x +aa b: a : B
haberi quadruturam hyperbolae. An l el P esset ro +  Hqus sayius) - 21os sagiu) + gu = um
in loganithuica, ideo firt 2H (Ag. 7) sdgeu LGeg: y + 2ydy = 0. Ergone ( fit 2H say: y - 2tW + 2yy = 0
sed Sagius = X: t et fiet, 2+X - 2tW + 29y =0 sed W = X + agyit ut
id est W = X + qyit, quod jam tum simus