Elements of analytical geometry and the differential and integral calculus (1856)
Robinson, Horatio N. (Horatio Nelson), 1806-1867 · Cincinnati : J. Ernst · leaf 136
to the axes. Through the origin draw two lines respectively parallel to thegiven lines. An expression for the angle between these twolines is the quantity sought. Let AP be parallel to one of the given lines, and^§ parallelto the other. The angle PAQ is the angle sought. STRAIGHT LINES IN SPACE.… … From Prop. VI, we have Expanding, and D^==(x^+y^+z^)-^ix^+y^+z)^ 2xx—2yy—2zz. But from Prop. Y, we learn that And x^+y^+z^=rK Whence 2xX\-2yy-\-2zz=r^^r^ —1>^. This equation applied to (1) reduces it to rr xx-\-yy-\-zzCOS. V—— ^^X— rrBut r and r may be any values taken at pleasure, their…
Geometry, Analytic · Calculus
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