A Treatise On Analytic Geometry Especially As Applied to the Properties of Coni
A Treatise On Analytic Geometry Especially As Applied to the Properties of Coni
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To quickly assess the difficulty of the text, read a short excerpt:
From Art. 92 we shall have cos a = A B cos ^ > and . Hence (Trig, 838) '(A'' 2 + E ri 2 A'B' cos w) sin a = !/ (^4 /2 + /2 - 2 ^S 7 cos w) ' B A cos w Therefore (Trig, 845, HI and iv . , _, _*' x _ (AB / + ^ x ^) cos c^ ~ Whence (Trig, 839) . D'. B)sino (AB / + ^ x ) cos w ' a formula which evidently becomes that of Art. 96, Cor. 1, if a 90.
Corollary 1 The condition that the two lines shall be parallel, is AB' A'B = : from the identity of which with the condition of Art. 96, Cor. 2, we learn t...hat the condition of parallelism is independent of the value of w. The same follows from the fact that the condition itself is not a function of w.
Corollary 2. The condition that the lines shall be perpendicular to each other, is AA' + B& (AB' + A'B) cos w = 0.
98. Equation to a right line parallel to a given one. Let the given line be y = mx -\- b. The required equation will be of the form y m'x -\- b'.
102 ANALYTIC GEOMETRY.
But in this, the condition of parallelism (Art. 96, Cor. 2 ; Art. 97, Cor.
What to read after A Treatise On Analytic Geometry Especially As Applied to the Properties of Coni?
You can find similar books in the "Read Also" column, or choose other free books by Howison, George Holmes, 1834-1917 to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
From Art. 92 we shall have cos a = A B cos ^ > and . Hence (Trig, 838) '(A'' 2 + E ri 2 A'B' cos w) sin a = !/ (^4 /2 + /2 - 2 ^S 7 cos w) ' B A cos w Therefore (Trig, 845, HI and iv . , _, _*' x _ (AB / + ^ x ^) cos c^ ~ Whence (Trig, 839) . D'. B)sino (AB / + ^ x ) cos w ' a formula which evidently becomes that of Art. 96, Cor. 1, if a 90.
Corollary 1 The condition that the two lines shall be parallel, is AB' A'B = : from the identity of which with the condition of Art. 96, Cor. 2, we learn t...hat the condition of parallelism is independent of the value of w. The same follows from the fact that the condition itself is not a function of w.
Corollary 2. The condition that the lines shall be perpendicular to each other, is AA' + B& (AB' + A'B) cos w = 0.
98. Equation to a right line parallel to a given one. Let the given line be y = mx -\- b. The required equation will be of the form y m'x -\- b'.
102 ANALYTIC GEOMETRY.
But in this, the condition of parallelism (Art. 96, Cor. 2 ; Art. 97, Cor.
What to read after A Treatise On Analytic Geometry Especially As Applied to the Properties of Coni?
You can find similar books in the "Read Also" column, or choose other free books by Howison, George Holmes, 1834-1917 to read onlineMoreLess
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