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10. Et

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par conféquent (§. XXVII. n. 5. & §. XXX. n. 1.) K = a; puisque K eft l'angle dont le cofinus

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Si dans le §. XXIX. on fuppofe = 1, on aura

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lorfque x=2 a, c'eft-à-dire, lorfque z 90°.

WIN

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Les mêmes choses étant pofées que dans le §. XXIX.

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d z

Or on a donné ci-dessus les valeurs de f(e+cof. 2)2

& def.

dz
(g + cof. 2)3

(s. XXIX, XXX & XXXI.) quelle que foit la valeur de p; & dans le §. XXXII. on a donné les valeurs particulieres de ces deux intégrales, dans le cas où = 1. Ainfi on aura facilement les valeurs des trois intégrales précédentes, dans le cas de p = à un nombre quelconque, & dans celui de 1, En général fi = 1, on aura

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15

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x x

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lorfque z=90°.

8a a

( 1 + col.z)3

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90°.

dz fin. z ( 1 + col. z ) 3

lorfque z=90°.

x

= 1 lorfque

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étant prise de maniere qu'elle foit = o =olorfque x = a. Mais on peut encore trouver autrement cette inté

grale, en remarquant que s

dz (col. 34 + col. z2)
z4

( 1 + col. x) *

s d z cof. z2

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( 1 + cof. z )3

?

dfin. cof. q2

(I + col. Z)3

=Sdz (3

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8 d z col.z

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( 1 + col.z)3

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cof.z)

3 dz

( 1 + col.z)3

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l'intégrale des deux premiers termes est 3 z - fin. l'intégrale des trois derniers eft aifée à trouver par les précédens no. 4 & 12. & par le §. XXXII. n°. 4. 16. f_d? fin. 33 cof. ?

( 1 + col, z ) 3
(x

l'intégrale de

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dz fin. col. 3

( 1 + cof, z ) 3.

dx

fera égal à l'intégrale de

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