Problems in Illustration of the Principles of Plane Coordinate GeometryJ. Deighton, 1851 - 429 páginas |
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Otras ediciones - Ver todo
Problems in illustration of the principles of plane coordinate geometry. By ... Vista completa - 1851 |
Términos y frases comunes
a² b2 abscissa Algebraic Geometry Annales de Mathématiques asymptotes ax² axes of coordinates axis major bisecting centre chord conic section conjugate diameters conjugate hyperbola constant cos² cose curve cutting denoting diagonals directrix distance diverses propositions drawn equal equation x² find the equation find the locus focus Gergonne given point given straight line hyperbola inclined inscribed intercepted la Hire latus-rectum Let the equation Lhuilier line joining major axis middle point ordinates parabola parallel pass perpendicular point of intersection points of contact polar equation pole produced indefinitely prop propositions de Géométrie prove Puissant quadrilateral radius Recueil de diverses required equation required locus respectively right angles Sectiones Conica semi-axis semi-diameters shews sides sin² taken as axes tangent touch triangle troisième édition vertex x₁ x² y² Y₁ Y₂
Pasajes populares
Página 105 - Porisma est propositio in qua proponitur demonstrare rem aliquam vel plures datas esse, cui vel quibus, ut et cuilibet ex rebus innumeris non quidem datis, sed quae ad ea quae data sunt eandem habent relationem, convenire ostendendum est affectionem quandam communem in propositione descriptam.
Página 106 - Find the locus of a point such that the sum of the squares of its distances from two fixed points shall be equivalent to the square of the distance between the fixed points.
Página 227 - ... 6. Two concentric ellipses which have their axes in the same directions intersect, and four common tangents are drawn so as to ' form a rhombus, and the points of intersection of the ellipses are joined so as to form a rectangle ; prove that the product of the areas of the rhombus and rectangle is equal to half the continued product of the four axes. 7. If <j>f(x) - <j>F(x) for all values of x from a to b, and if c be a quantity not less than a nor greater than b such that f(c) = F(c) and...
Página 164 - To find the locus of the centre of a circle which passes through a given point and touches a given straight line.
Página 161 - Find the locus of the centre of a circle inscribed in a sector of a given circle, one of the bounding radii of the sector remaining fixed.
Página 106 - A Porism is a proposition in which it is proposed to demonstrate that some one thing, or more things than one, are given, to which, as also to each of innumerable other things, not given indeed, but which have the same relation to those which are given, it is to be shewn that there belongs some common affection described in the proposition.
Página 325 - AP is the arc of a conic section of which the vertex is A; PG the normal, and PK a perpendicular to the chord AP, meet the axis in G and K respectively.