A General Geometry and Calculus |
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A²y² Algebra angle axis of abscissas axis of ordinates Ay² B² cos² B²x² becomes centre circle cissoid Cissoid of Diocles coefficients conic section conjugate axis Construct curve cuts the axis cycloid determine diameter directrix draw e² sin² ellipse equa five equations fixed line fixed point focal distance focus formula generatrix Geometry give given point hyperbola imaginary infinite intersection latus rectum line passing located loci locus is symmetrical negative oblique axes origin parabola perpendicular plane polar axis polar co-ordinates polar equation pole position prime radius primitive axis Prob Produce the equation quantity radius vector ratio rectangular axes referred to rectangular represented right line second degree signs sin ai SOLUTION.-Let SUG'S symmetrical with respect tangent tion transformation transverse axis triangle variables versin vertex whence Witch of Agnesi
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Page 27 - In this equation n is the tangent of the angle which the line makes with the axis of abscissas, and B is the intercept on this axis from the origin.
Page 62 - Conic, is the locus of a point which moves so that its distance from a fixed point is in a constant ratio to its distance from a fixed straight line.
Page 71 - Hypocycloid ; but to this there is one exception, in which the radius of one of the circles is double that of the other : in this case, the locus is a straight line, as may be easily shewn from the figure.
Page 10 - A surface may be considered as generated by the motion of a line, and thus afford another illustration of continuous number. Thus let the parallelogram AF be conceived as generated by the right line AB moving parallel to itself from AB to E F.
Page 17 - ... to the right if the abscissa is -)-, and to the left if it is— . Through the point thus...
Page 15 - ... LOXODROMIC ANGLE, in Navigation, is the constant angle which a rhumb line or loxodromic curve makes with the meridians which it crosses. In Analytical Geometry, in the rectilineal system, the co-ordinate plane is divided into four angles by the two rectilineal axes which bave been numbered as follows : 1st Angle.
Page 62 - A point moves so that the sum of the squares of its distances from the three angles of a triangle is constant. Prove that it moves along the circumference of a circle.
Page 14 - The ordinate of any point is its distance from the axis of abscissas, measured on a line parallel to the axis of ordinales.
Page 26 - Locus is an equation which expresses the relation between the coordinates of every point of the locus.
Page 30 - ... are the tangents of the angles which the lines make with the axis of JT. If a and a' are both arbitrary constants, the equation is indeterminate, and may be satisfied in an infinite number of ways.