Elements of analytical geometry and the differential and integral calculus (1856)
Robinson, Horatio N. (Horatio Nelson), 1806-1867 · Cincinnati : J. Ernst · leaf 81
E, TA, ON, proportional tothe squares of 01, OT, 00, or in proportion to the squares oftheir equals QE, EA, &c.Let OQ=IEz=x. OE=TA=zx\ QE~y. EA=y\Then by the construction X : ^=y2 : y^.But this is the property of the parabola, therefore the curvemade by a projectile is a parabola. PROPOSITION… … (0 From(l)Or The co-ordinates of the point F beingc, b, as in the last proposition, whenceb^=2pc. (2) b^sm,m=p^cos.^m. :=:p^(l—sm.^m)=p^—p^8in.-m. sm.m= —±- =— =——,—
Geometry, Analytic · Calculus
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