The Elements of Analytical Geometry: Comprehending the Doctrine of the Conic Sections, and the General Theory of Curves and Surfaces of the Second Order
E. H. Butler, 1848 - 288 من الصفحات
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abscissa assumed asymptotes axes axis base becomes bisects called centre chords circle condition conjugate consequently constant construction containing coordinates curve denote described determine diameter difference distance divided draw drawn ellipse equa equal equation expression extremities focus follows former formulas Geom geometrical given given point gives greater half hence hyperbola inclination inscribed intersection join known length less locus manner meet negative oblique obtain obviously ordinate origin parabola parallel passing perpendicular plane point of contact positive principal diameters PROBLEM produced proposed question radius rectangle rectangular reduces referred remaining represent result right angle shows sides similar square straight line substituting suppose surface taken tangent tion transformed triangle vertical whence
الصفحة 67 - In a triangle, having given the ratio of the two sides, together with both the segments of the base, made by a perpendicular from the vertical angle, to determine the sides of the triangle.
الصفحة 160 - In article (100), it was found that the principal parameter is equal to 4m, the coefficient of x, in the equation of the curve, when referred to rectangular conjugates. By analogy, the coefficient 4r, when any system of conjugates are employed, is called the parameter of that diameter, which is taken for the axis of x, so that generally the parameter of any diameter is equal to four times the distance of its vertex from the focus. By equation (5) the parameter is always equal to the double ordinate,...
الصفحة 30 - To find the side of a regular octagon inscribed in a circle whose radius is known.
الصفحة 200 - Given the base and the sum of the sides of a triangle to find the locus of the centre of the circle touching the base, and the prolongation of the other two sides.
الصفحة 62 - Given the hypothenuse (10) of a right angled triangle, and the difference of two lines drawn from its extremities to the centre of the inscribed circle (2), to determine the base and perpendicular. Ans. 8.08004 and 5.87447 PROBLEM XIX.
الصفحة 104 - To draw a tangent to a circle from a given point without it. Let (a...
الصفحة 37 - In an isosceles triangle, the square of a line drawn from the vertex to any point in the base, together with the rectangle of the segments of the base, is equal to the square of one of the equal sides of the triangle.
الصفحة 201 - Given the base, an angle adjacent to the base, and the difference of the sides of a triangle, to construct it.
الصفحة 120 - From these expressions for y and z, it appears that for the same value of x, there are two values of y numerically equal, but having contrary signs ; hence the chord AB bisects all the chords drawn parallel to CD.
الصفحة 142 - A, which intimates that the hyperbola, like the ellipse, intersects the axis of x in two points, B, A, equidistant from O, the one to the right, and the other to the left, and that A expresses this distance. If, in the same equation, we suppose x = 0, we have for the corresponding value of y the expression y = V JA2 — c2^.