The Solutions of the Geometrical Problems: Consisting Chiefly of Examples in Plane Co-ordinate Geometry, Proposed at St. John's College, Cambridge, from Dec. 1830 to Dec. 1846. With an Appendix, Containing Several General Properties of Curves of the Second Order, and the Determination of the Magnitude and Position of the Axes of the Conic Section Represented by the General Equation of the Second DegreeJ. & J. J. Deighton, 1847 - 263 páginas |
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Página 10
... contain equal angles . 3 . The sum of the perpendiculars from any point in the base of an isosceles triangle is equal to a line of fixed length . 4. To find a point in the side or side produced of any parallelogram , such that the angle ...
... contain equal angles . 3 . The sum of the perpendiculars from any point in the base of an isosceles triangle is equal to a line of fixed length . 4. To find a point in the side or side produced of any parallelogram , such that the angle ...
Página 16
... contained by three plane angles , any two of them are greater than the third . 3. If a straight line be divided into any two parts ; to find a point without the line at which the segments shall contain equal angles . 4. Given the base ...
... contained by three plane angles , any two of them are greater than the third . 3. If a straight line be divided into any two parts ; to find a point without the line at which the segments shall contain equal angles . 4. Given the base ...
Página 17
... contain a right angle , and one of them is inclined to the axis of a at a given angle . 11. If from a point without a given circle , two straight lines be drawn touching the circle ; find the equation to the line joining the points of ...
... contain a right angle , and one of them is inclined to the axis of a at a given angle . 11. If from a point without a given circle , two straight lines be drawn touching the circle ; find the equation to the line joining the points of ...
Página 28
... contained by three plane angles , any two are together greater than the third . Define the inclination of a plane to a plane , and shew that it is equal to the inclination of their normals . 4. If there be two concentric circles , and ...
... contained by three plane angles , any two are together greater than the third . Define the inclination of a plane to a plane , and shew that it is equal to the inclination of their normals . 4. If there be two concentric circles , and ...
Página 29
... contained by three plane right angles , the square of the face subtending the right angle is equal to the squares of the three faces which contain it . SOLUTIONS TO ( No. V. ) 1 . SEE Potts GEOMETRICAL PROBLEMS . NO . V. DEC . 1834 . 29.
... contained by three plane right angles , the square of the face subtending the right angle is equal to the squares of the three faces which contain it . SOLUTIONS TO ( No. V. ) 1 . SEE Potts GEOMETRICAL PROBLEMS . NO . V. DEC . 1834 . 29.
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Términos y frases comunes
2c sin² a₁ a²² ABCD angular points asymptotes axes axis axis-major ay² b₁ bisected C₁ chord of contact co-ordinates conic section conjugate conjugate hyperbola constant cos² cosw curve diagonals diameter draw ellipse equal Euclid find the locus fixed point given points given straight lines hence hk g hyperbola inclined inscribed joining the points latus rectum Let A fig line joining m₁ meet middle point n₂ pair of tangents parabola parallel parallelogram pass through three perpendicular plane points of contact points of intersection polar equation polygon position quadrilateral figure radius remaining sides respectively right angles shew Similarly sin w sin² ST JOHN'S COLLEGE t₁ t₂ tangents be drawn tangents drawn three sides touch vertex y₁
Pasajes populares
Página 54 - If two triangles which have two sides of the one proportional to two sides of the other, be joined at one angle, so as to have their homologous sides parallel to one another ; the remaining sides shall be in a straight line. Let ABC, DCE be two triangles which have the two sides BA, AC proportional to the two CD, DE, viz.
Página 117 - Similar triangles are to one another in the duplicate ratio of their homologous sides.
Página 117 - IF from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle,. shall be equal to the square of the line which touches it.
Página 96 - The rectangle contained by the diagonals of a quadrilateral ,figure inscribed in a circle, is equal to both the rectangles contained by i'ts opposite sides.
Página 16 - MAGNITUDES which have the same ratio to the same magnitude are equal to one another ; and those to which the same magnitude has the same ratio are equal to one another.
Página 28 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one part may be equal to the square on the other part*.
Página 28 - THEOREM. lf the first has to the second the same ratio which the third has to the fourth, but the third to the fourth, a greater ratio than the fifth has to the sixth ; the first shall also have to the second a greater ratio than the fifth, has to the sixth.
Página 10 - ... not in the same plane with the first two ; the first two and the other two shall contain equal angles.
Página 87 - The locus of the middle points of a system of parallel chords in a parabola is called a diameter.