Elements of analytical geometry and the differential and integral calculus (1856)
Robinson, Horatio N. (Horatio Nelson), 1806-1867 · Cincinnati : J. Ernst · leaf 146
\-a.y=zbz+^. Take any point F in the given line, andlet fall FB, the perpendicular, upon the plane ; i?§ is its pro-jection on the plane, and FQF is obviously the least angle madebetween the line and the plane, and it is the angle sought. Let xz=az-\~a\ and y=62-J-/5, be the equation of the… … COS. F=: (Prop. VIII.) But the COS. V is the same as the sin.P§JS, or sin. V, as thetwo angles are complements to each other. 338 ANALYTICAL GEOMETRY. Making this change, and substituting the values of a and b,we have for the required result. CoRROLLARY. When F=0, sin.F=0, and this hypothesisgives…
Geometry, Analytic · Calculus
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