The Essentials of GeometryD.C. Heath & Company, 1899 - 395 σελίδες |
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Σελίδα 1
... face , or simply a surface ; it is also called the surface of the solid . 3. If two geometrical surfaces intersect each other , that which is common to both is called a geometrical line , or simply a line . Thus , if surfaces AB and CD ...
... face , or simply a surface ; it is also called the surface of the solid . 3. If two geometrical surfaces intersect each other , that which is common to both is called a geometrical line , or simply a line . Thus , if surfaces AB and CD ...
Σελίδα 254
... face between them ; as , ABEC and CBED . Two diedral angles are said to be vertical when the faces of one are the extensions of the faces of the other . E D C 429. A plane angle of a diedral angle is the angle be- tween two straight ...
... face between them ; as , ABEC and CBED . Two diedral angles are said to be vertical when the faces of one are the extensions of the faces of the other . E D C 429. A plane angle of a diedral angle is the angle be- tween two straight ...
Σελίδα 255
... faces in lines perpendicular to the edge ( § 398 ) ; hence , a plane perpendicular to the edge of a diedral angle intersects the faces in lines which include the plane angle of the diedral angle ( § 429 ) . 432. Two diedral angles are ...
... faces in lines perpendicular to the edge ( § 398 ) ; hence , a plane perpendicular to the edge of a diedral angle intersects the faces in lines which include the plane angle of the diedral angle ( § 429 ) . 432. Two diedral angles are ...
Σελίδα 259
... faces . B M F Given P any point in bisecting plane BE of diedral ABDC , and lines PM and PN 1 to AD and CD , respec- tively . To Prove PM = PN . Proof . Let the plane determined by PM and PN inter- sect planes AD , BE , and CD in lines ...
... faces . B M F Given P any point in bisecting plane BE of diedral ABDC , and lines PM and PN 1 to AD and CD , respec- tively . To Prove PM = PN . Proof . Let the plane determined by PM and PN inter- sect planes AD , BE , and CD in lines ...
Σελίδα 260
... faces , lies in the bisecting plane of the diedral angle . Given point P within diedral ABDC , equally distant from AD and CD , and plane BE determined by BD and P. ( Fig . of Prop . XXIV . ) To Prove that BE bisects diedral ABDC ...
... faces , lies in the bisecting plane of the diedral angle . Given point P within diedral ABDC , equally distant from AD and CD , and plane BE determined by BD and P. ( Fig . of Prop . XXIV . ) To Prove that BE bisects diedral ABDC ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
AB² ABCD AC² adjacent angles altitude apothem approach the limit area ABC axis base and altitude BC² bisector bisects centre chord circle circumference circumscribed coincide cone of revolution Converse of Prop diagonals diameter diedral angle distance Draw line equally distant equilateral equivalent exterior angle faces Find the area frustum Given line given point Hence homologous homologous sides hypotenuse intersecting isosceles triangle lateral area lateral edges line drawn line joining middle point number of sides parallel parallelogram parallelopiped perimeter perpendicular plane MN polyedral polyedron prism pyramid quadrilateral radii radius rectangle regular inscribed regular polygon rhombus right angles right triangle segment side BC similar slant height spherical polygon spherical triangle square tangent tetraedron THEOREM trapezoid triangle ABC triangular prism triedral vertex vertices volume Whence
Δημοφιλή αποσπάσματα
Σελίδα 371 - A zone is a portion of the surface of a sphere included between two parallel planes.
Σελίδα 49 - ... the three sides of one are equal, respectively, to the three sides of the other. 2. Two right triangles are congruent if...
Σελίδα 261 - The projection of a point on a plane is the foot of the perpendicular drawn from the point to the plane.
Σελίδα 336 - A spherical polygon is a portion of the surface of a sphere bounded by three or more arcs of great circles. The...
Σελίδα 73 - A chord is a straight line joining the extremities of an arc ; as AB.
Σελίδα 328 - A sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre.
Σελίδα 205 - S' denote the areas of two © whose radii are R and R', and diameters D and D', respectively. Then, | = "* § = ££ = £• <§337> That is, the areas of two circles are to each other as the squares of their radii, or as the squares of their diameters.
Σελίδα 170 - 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.
Σελίδα 224 - The perpendiculars from the vertices of a triangle to the opposite sides are the bisectors of the angles of the triangle formed by joining the feet of the perpendiculars.
Σελίδα 325 - A right circular cone may be generated by the revolution of a right triangle about one of its legs as an axis.