A General Course of Pure Mathematics From Indices to Solid Analytical Geometry
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To quickly assess the difficulty of the text, read a short excerpt:
155-6, (x-aY y y = mx+ -/a^w^ + P^ touches -^ + f^ = 1.
y = m{x-o)+ Vo.^m^ + P' touches ^^ + |^ = 1, i.e. y'^ = 4^2^x in limit ; g2 i y= WiC-?;za + am(l + ^^"^ = mx — ma+am (l + - — 5 +...), by the Binomial Series, ^ 2 am- ■' p \ jfi ^ ... 1 = mx H -!—. + terms involving -5- , nt 2 am^ a^ = ma; H — in limit.
m As an exercise, the equation of the tangent or polar, m= 2p{x+x;), should be obtained by this method of limits.
Before going hack to the general equation we will obtain some further geome...trical properties of the parahola and ellipse.
THE PARABOLA 165 The Parabola.
It lias already been shown that y = mx + - touches y^ = 4_px at (V 2_P), and that i.V=ii,A7^ = ^.
If this tangent meets the axis ai T,y = 0, and AT = x = ^■ .-. TA = AN.
.-. TS= AN+AS = AF+ KA = KX = SP.
Fig. 65.
Draw Pf? perpendicular to the tangent at P. PG is called the nwmal.
Since SP = ST and TPG is a right angle, .•. S is centre of circle TPG, and ,?(? = /SP = 2W = » f 1 + i ) since TS = AN + AS, and and is constant for all normals.
What to read after A General Course of Pure Mathematics From Indices to Solid Analytical Geometry?
You can find similar books in the "Read Also" column, or choose other free books by A L Arthur Lyon Sir Bowley to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
155-6, (x-aY y y = mx+ -/a^w^ + P^ touches -^ + f^ = 1.
y = m{x-o)+ Vo.^m^ + P' touches ^^ + |^ = 1, i.e. y'^ = 4^2^x in limit ; g2 i y= WiC-?;za + am(l + ^^"^ = mx — ma+am (l + - — 5 +...), by the Binomial Series, ^ 2 am- ■' p \ jfi ^ ... 1 = mx H -!—. + terms involving -5- , nt 2 am^ a^ = ma; H — in limit.
m As an exercise, the equation of the tangent or polar, m= 2p{x+x;), should be obtained by this method of limits.
Before going hack to the general equation we will obtain some further geome...trical properties of the parahola and ellipse.
THE PARABOLA 165 The Parabola.
It lias already been shown that y = mx + - touches y^ = 4_px at (V 2_P), and that i.V=ii,A7^ = ^.
If this tangent meets the axis ai T,y = 0, and AT = x = ^■ .-. TA = AN.
.-. TS= AN+AS = AF+ KA = KX = SP.
Fig. 65.
Draw Pf? perpendicular to the tangent at P. PG is called the nwmal.
Since SP = ST and TPG is a right angle, .•. S is centre of circle TPG, and ,?(? = /SP = 2W = » f 1 + i ) since TS = AN + AS, and and is constant for all normals.
What to read after A General Course of Pure Mathematics From Indices to Solid Analytical Geometry?
You can find similar books in the "Read Also" column, or choose other free books by A L Arthur Lyon Sir Bowley to read onlineMoreLess
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