Obra Completa - Universidade de Coimbra

s em n n'esta formula, o que dá
Pnn = Pxx COS s (ti, x) + pyy COS 2 (ti, y) + pzz COS 2 (w, z) \
7
+ 2pyt cos (n, y) cos («, Z) + Ipzx cos {«, 2) cos («, ®)> ... (2).
+ 2pXy cos (w, x) cos {n, y) \
O. Pondo successivamente em vez de «esas direcções x',
y', 2' de tres novos eixos rectangulares ou oblíquos, obtêm-se
as formulas
Px'x' = Pxx COS 2 (x, X r ) +Pyy COS 2 (y, X 1 ) + pzz COS 2 (2, x\
+ 2pyz cos (y, x') cos (z, x) + c Ipzx cos (2, x') cos (x, x')\
+ 2pxy cos [x, x') 4- cos (y, x'),
Py',/ = Pxx COS 2 (x, y') + pyy cos 2 [y, y') + pzz cos 2 {z, y')
+ 2pyt cos (y, y') cos {z, y') + 2pyx cos (y, y') cos (ar, y'\
+ 2Pxy cos (x, y') cos y, y'),
Pt'z' = Pxx COS 2 (o?, z')+ Pyy cos' 2 (y, z') + pzt cos 2 (2, z')
+ Ipyz cos (y, Z^cos (2, 2') + 2pzx cos (z, z') cos (a;, z)
+ Ipxz cos [x, 2') cos Iy, Z r ],
Py'Z' = Pxx COS (x, y') cos [x, z') + pyy cos [y, y) cos (y, z')
+P ZZ cos (2, y') COS (2, 2')
+ Pyz [cos (y, y') cos (2. 2') + cos (y, z') cos (2, 2')] \ (3\
+ Pzx [cos (2, y') cos (x, z') + cos (2, 2') cos (x, y 1
+ Pxy [cos (ar, y') cos (y, 2') + cos (x, 2') cos (y, y')\,
Pz'X 1 = Pxx COS (x, z') COS (x, x') + Pyy cos (ij, z') cos [y, X 1 )
+ Pzz COS (2, 2')cOS(z, x)
+Pyz [cos (y, 2') cos (z, x r ) + cos (y, x') cos (z, x')]
+ Pzx [cos (z, Z 1 )cos(x, a:')+ cos (2, 2') cos z')]
+ pxy [cos [x, z) cos (y, x) + cos(x, x") cos (?/, 2')],
Pxhj! = Pxx COS (x, x') cos (x, y') + pyy cos (y, x') cos (y, y')
+Pzz cos (2, x!) cos (2, y")
+pyz [cos (y, a;') cos (2, y') + cos {y, y') cos (2, .2')]
+Pzx [cos (2, í/) cos (a:; y') + cos (2, «/) cos (a;, ?/)]
+ pxy [cos [x, x') cos [y, y') + cos (x, y') cos (y, a/)].