Solid Geometry, Volumes 6-9 |
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Page 238
... BOOK IX . CONIC SECTIONS . 397 402 405 THE PARABOLA • EXERCISES . THE ELLIPSE EXERCISES THE HYPERBOLA TABLE OF FORMULAS INDEX • 409 424 425 • € 443 445 • 460 463 GENERAL AXIOMS . 1. Magnitudes which are equal to the vi CONTENTS .
... BOOK IX . CONIC SECTIONS . 397 402 405 THE PARABOLA • EXERCISES . THE ELLIPSE EXERCISES THE HYPERBOLA TABLE OF FORMULAS INDEX • 409 424 425 • € 443 445 • 460 463 GENERAL AXIOMS . 1. Magnitudes which are equal to the vi CONTENTS .
Page 408
... to a plane not cutting the tetrahedron is equal to one fourth the sum of the perpendiculars from the vertices of the tetrahedron to the plane . BOOK IX . ICONIC SECTIONS . THE PARABOLA . 850. 408 BOOK VIII . SOLID GEOMETRY .
... to a plane not cutting the tetrahedron is equal to one fourth the sum of the perpendiculars from the vertices of the tetrahedron to the plane . BOOK IX . ICONIC SECTIONS . THE PARABOLA . 850. 408 BOOK VIII . SOLID GEOMETRY .
Page 409
... parabola is a curve which is the locus of a point that moves in a plane so that its distance from a fixed point in the plane is always equal to its distance from a fixed line in the plane ... parabola by 409 CONIC SECTIONS THE PARABOLA •
... parabola is a curve which is the locus of a point that moves in a plane so that its distance from a fixed point in the plane is always equal to its distance from a fixed line in the plane ... parabola by 409 CONIC SECTIONS THE PARABOLA •
Page 410
George Albert Wentworth. PROPOSITION I. PROBLEM . 853. To construct a parabola by points , having given its focus and ... parabola whose focus is F and directrix CDE . Q. E. F. : = Ax . 1 $ 850 854. DEF . The point A is called the vertex ...
George Albert Wentworth. PROPOSITION I. PROBLEM . 853. To construct a parabola by points , having given its focus and ... parabola whose focus is F and directrix CDE . Q. E. F. : = Ax . 1 $ 850 854. DEF . The point A is called the vertex ...
Page 411
... parabola is not a closed curve . For any point on the axis of the curve to the right of F is evidently nearer to the focus than to the directrix . Hence , the parabola QAP cannot cross the axis to the right of F. 861. COR . 4. The latus ...
... parabola is not a closed curve . For any point on the axis of the curve to the right of F is evidently nearer to the focus than to the directrix . Hence , the parabola QAP cannot cross the axis to the right of F. 861. COR . 4. The latus ...
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Common terms and phrases
ABCDE altitude angles are equal auxiliary circle bisects called centre chord circumference circumscribed coincide convex cube curve diameter dihedral angles directrix distance draw drawn ellipse equidistant equivalent face angles feet Find the volume focal radii foci frustum given plane given point Hence homologous hyperbola inches inscribed intersection lateral area lateral edges lateral faces latus rectum limit locus lune parabola parallel planes parallelogram pass a plane perimeter perpendicular plane MN plane parallel plane passing polyhedral angle polyhedron prismatoid Proof PROPOSITION prove radius rectangular parallelopiped regular polygon regular pyramid respectively right circular cone right circular cylinder right prism right section S-ABC segment similar slant height sphere spherical angle spherical polygon spherical triangle square straight line symmetrical tangent tetrahedron THEOREM total surface triangular prism trihedral upper base vertex vertices
Popular passages
Page 274 - If two planes are perpendicular to each other, a straight line drawn in one of them perpendicular to their intersection is perpendicular to the other plane.
Page 258 - ... of two oblique lines meeting the plane at unequal distances from the foot of the perpendicular the more remote is the greater.
Page 360 - A sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre.
Page 249 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. To prove that Proof. A Let the triangles ABC and ADE have the common angle A. A ABC -AB X AC Now and A ADE AD X AE Draw BE.
Page 244 - PERIPHERY of a circle is its entire bounding line ; or it is a curved line, all points of which are equally distant from a point within called the centre.
Page 260 - COR. 1. If one of two parallel lines is perpendicular to a plane, the other is also perpendicular to the plane.
Page 376 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (gr). If A'B'C' is the polar triangle of ABC...
Page 243 - The straight line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of it 46 INTERCEPTS BY PARALLEL LINES.
Page 366 - A plane perpendicular to a radius at its extremity is tangent to the sphere. Let...
Page 395 - The area of a lune is to the area of the surface of the sphere as the angle of the lune is to four right angles.