Plane and Solid GeometryMacmillan, 1902 - 370 σελίδες |
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Αποτελέσματα 6 - 10 από τα 46.
Σελίδα 330
... sphere is the distance of a point in the circumference from the nearer pole . 689. SCHOLIUM . A quadrant in Spherical Geometry is the fourth part of the circumference of a great circle . 690. COR . The polar distance of a great circle ...
... sphere is the distance of a point in the circumference from the nearer pole . 689. SCHOLIUM . A quadrant in Spherical Geometry is the fourth part of the circumference of a great circle . 690. COR . The polar distance of a great circle ...
Σελίδα 331
... sphere , a point at a quad- rant's distance from two other points , not the extremi- ties of a diameter , is the pole of a great circle passing through these two points . P 0 --- B 1 ... spheres are tangent if their surfaces THE SPHERE 331.
... sphere , a point at a quad- rant's distance from two other points , not the extremi- ties of a diameter , is the pole of a great circle passing through these two points . P 0 --- B 1 ... spheres are tangent if their surfaces THE SPHERE 331.
Σελίδα 332
... sphere . 697. DEF . A sphere is circumscribed about a polyedron if all the vertices of the polyedron lie in the surface of the sphere . PROPOSITION IV . THEOREM 698. A plane perpendicular to a radius of a sphere at its extremity is ...
... sphere . 697. DEF . A sphere is circumscribed about a polyedron if all the vertices of the polyedron lie in the surface of the sphere . PROPOSITION IV . THEOREM 698. A plane perpendicular to a radius of a sphere at its extremity is ...
Σελίδα 333
... sphere at its extremity is a tangent to the sphere . 00. COR . 2. Any line or plane tangent to a sphere is per- dicular to the radius drawn to the point of contact . PROPOSITION V. THEOREM 701. A sphere may be circumscribed about any ...
... sphere at its extremity is a tangent to the sphere . 00. COR . 2. Any line or plane tangent to a sphere is per- dicular to the radius drawn to the point of contact . PROPOSITION V. THEOREM 701. A sphere may be circumscribed about any ...
Σελίδα 334
... sphere described from O as a center with a radius equal to AO will be circumscribed about the tetraedron . 702. COR . Four points not in the same plane determine a sphere . PROPOSITION VI . THEOREM 703. A sphere may be inscribed in any ...
... sphere described from O as a center with a radius equal to AO will be circumscribed about the tetraedron . 702. COR . Four points not in the same plane determine a sphere . PROPOSITION VI . THEOREM 703. A sphere may be inscribed in any ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD altitude angles are equal bisect bisector chord circumference circumscribed cone construct a triangle cylinder diagonals diagram for Prop diameter diedral angles divide draw drawn equiangular equiangular polygon equilateral triangle equivalent exterior angle face angles Find the area Find the radius Find the volume frustum given circle given line given point given triangle Hence HINT homologous homologous sides hypotenuse inches inscribed intersecting isosceles triangle joining the midpoints lateral area lateral edges line joining mean proportional median opposite sides parallel lines parallelogram parallelopiped perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION prove Proof quadrilateral radii ratio rectangle regular polygon respectively equal rhombus right angles right triangle SCHOLIUM segment similar triangles sphere spherical polygon spherical triangle square straight line surface tangent THEOREM trapezoid triangle ABC triangle are equal triedral vertex
Δημοφιλή αποσπάσματα
Σελίδα 45 - If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first triangle greater than the included angle of the second, then the third side of the first is greater than the third side of the second.
Σελίδα 119 - In any proportion, the product of the means is equal to the product of the extremes.
Σελίδα 180 - 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. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.
Σελίδα 31 - The median to the base of an isosceles triangle is perpendicular to the base.
Σελίδα 305 - A cylinder is a solid bounded by a cylindrical surface and two parallel planes; the bases of a cylinder are the parallel planes; and the lateral surface is the cylindrical surface.
Σελίδα 337 - A spherical polygon is a portion of the surface of a sphere bounded by three or more arcs of great circles. The bounding arcs are the sides of the polygon ; the...
Σελίδα 250 - A straight line perpendicular to one of two parallel planes is perpendicular to the other also.
Σελίδα 297 - A truncated triangular prism is equivalent to the sum of three pyramids whose common base is the base of the prism, and whose vertices are the three vertices of the inclined section.
Σελίδα 105 - I. When the given point, A, is in the circumference. HINT. — What is the angle formed by a radius and a tangent at its extremity ? II. When the given point, A, is without the circle. \ Construction. Join A, and 0 the center of the given circle. On OA as a diameter, construct a circumference, intersecting the given circumference in B and C.
Σελίδα 276 - An oblique prism is equivalent to a right prism whose base is a right section of the oblique prism, and whose altitude is equal to a lateral edge of the oblique prism. Hyp. GM is a right section of oblique prism AD', and OM ' a right prism whose altitude is equal to a lateral edge of AD'. To prove AD' =s= GM'. Proof. The lateral edges of GM