An Analytical System of Conic Sections: Designed for the Use of Students ...J. & J. J. Deighton, 1834 - 207 páginas |
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Outras edições - Ver todos
An Analytical System of Conic Sections: Designed for the Use of Students Henry Parr Hamilton Visualização completa - 1834 |
An Analytical System of Conic Sections: Designed for the Use of Students Henry Parr Hamilton Prévia não disponível - 2015 |
Termos e frases comuns
a² a² a² b2 a² e² a² sin² a² y² a²b² a²yy abscissa angles to AX axes of co-ordinates axis AX b2 a² b² cos² b²x² bisect centre circle CONIC SECTIONS conjugate diameters conjugate hyperbola curve cut the axis denote diameter be drawn directrix draw e²x² equal equation required fall the perpendicular find the equation find the intersection find the locus focus given in position given point Hence joining the points latus rectum Let CP let fall major axis meeting the ellipse middle points ordinate pairs of tangents parabola parallel to MN parallelogram perpendicular PM point of intersection points of contact polar equation proved rectangle contained right angles semi-minor axis ß² substitution subtangent supplemental chords tangents be drawn theory of equations values vertex x²²
Passagens mais conhecidas
Página 97 - ... a diameter, in a constant ratio, the author proves the following propositions relating to this curve : — 1. The rectangle of the abscissae is to the square of the ordinate, as the square of the semiaxis major to the difference of the squares of the semiaxis major and the excentricity. 2. The distance of any point in the curve from the focus, is to its distance from the directrix, as the excentricity is to the semiaxis major. 3. The sum of the distances of any point in the curve from the two...
Página 117 - AB, and equal to the altitude of the triangle, (i. 11, 3.) Through C, draw CDE parallel to AB, and meeting the circumference in D and E. (i. 31.) Join DA, DB ; also EA, EB ; then EAB or DAB is the triangle required.
Página 165 - Fig. 83,84. conjugate diameters is equal to the sum of the squares of the axes ; but in an hyperbola the difference of the squares of any two conjugate diameters is equal to the difference of the squares of the axes.
Página 22 - We have thus the well-known theorem that the perpendiculars let fall from the angles of a triangle on the opposite sides meet in a point.
Página xvi - To find the locus of a point, the difference of whose distances from two fixed points is always equal to a given quantity 2 a.
Página 90 - In any equation in its simplest form the coefficient of the second term is equal to the sum of the roots with their signs changed ; the coefficient of the third term is equal to the sum of the products of every two...
Página 174 - AB describe a segment of a circle containing an angle equal to the given angle, (in.
Página iv - A conic section is the locus of a point whose distances from a fixed point and a fixed line are in a constant ratio. 4. Show that every conic is represented by an equation of the second degree in x and y. Hint. Take Y Y' to coincide with the fixed line, and draw XX
Página 57 - If from the several points of a straight line given in position, pairs of tangents be drawn to a parabola, the straight lines joining the corresponding points of contact will all pass through the same point.
Página 33 - IF a straight line touch a circle, the straight line drawn from the centre to the point of contact is perpendicular to the line touching the circle.