Plane and Solid Geometry |
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Page 3
... distance from A to B. A line whose ends are not marked represents a line of indefinite length , as CD . HB D FIG . 5 . 22. The direction of the line AB means the direction from A toward B ; of BA , from B toward A. D B FIG . 6 . 23. To ...
... distance from A to B. A line whose ends are not marked represents a line of indefinite length , as CD . HB D FIG . 5 . 22. The direction of the line AB means the direction from A toward B ; of BA , from B toward A. D B FIG . 6 . 23. To ...
Page 8
... distance between two points . ( For Axiom 11 , see page 17 on parallel lines . ) POSTULATES 1. A straight line can be drawn between any two points . 2. A straight line can be produced indefinitely . BOOK I LINES AND RECTILINEAR FIGURES ...
... distance between two points . ( For Axiom 11 , see page 17 on parallel lines . ) POSTULATES 1. A straight line can be drawn between any two points . 2. A straight line can be produced indefinitely . BOOK I LINES AND RECTILINEAR FIGURES ...
Page 15
... distances be laid off from the vertex , and the ends be joined to any point in the bisector of the angle , these lines are equal . Ex . 39. If in the triangle ABC , 2 A = 2 B , and the points D and E be taken in AC and BC so as to make ...
... distances be laid off from the vertex , and the ends be joined to any point in the bisector of the angle , these lines are equal . Ex . 39. If in the triangle ABC , 2 A = 2 B , and the points D and E be taken in AC and BC so as to make ...
Page 36
... distance from B to C , describe two arcs intersect- ing at D. Join AD . AD bisects / CAB . HINT . - Q.E.F What is the usual means of proving the equality of angles ? Ex . 141. Divide an angle into four equal parts . Ex . 142. To bisect ...
... distance from B to C , describe two arcs intersect- ing at D. Join AD . AD bisects / CAB . HINT . - Q.E.F What is the usual means of proving the equality of angles ? Ex . 141. Divide an angle into four equal parts . Ex . 142. To bisect ...
Page 41
... distance of a point from a line is the length of the perpendicular from the point to the line . PROPOSITION XXVI . THEOREM 121. All points in the bisector of an angle are equi- distant from the sides of the angle . P B 0 D C Hyp . / DAB ...
... distance of a point from a line is the length of the perpendicular from the point to the line . PROPOSITION XXVI . THEOREM 121. All points in the bisector of an angle are equi- distant from the sides of the angle . P B 0 D C Hyp . / DAB ...
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Common terms and phrases
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 a point Find the area Find the radius Find the volume frustum given circle given line given point given triangle Hence HINT homologous 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 point equidistant polyedral angle polyedron PROPOSITION prove Proof quadrilateral radii ratio rectangle regular polygon respectively equal rhombus right angles right triangle SCHOLIUM segments sphere spherical polygon spherical triangle square straight angle straight line surface tangent THEOREM trapezoid triangle ABC triangle are equal triedral vertex
Popular passages
Page 148 - If two chords intersect within a circle, the product of the segments of one is equal to the product of the segments of the other.
Page 150 - If, from a point without a circle, a tangent and a secant be drawn, the tangent is the mean proportional between the secant and its external segment.
Page 180 - Two triangles having 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.
Page 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.
Page 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...
Page 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.
Page 312 - The lateral areas, or the total areas, of similar cylinders of revolution are to each other as the squares of their altitudes, or as the squares of their radii ; and their volumes are to each other as the cubes of their altitudes, or as the cubes of their radii. Let S, S' denote the lateral areas, T, T...
Page 149 - If, from a point without a circle, two secants are drawn, the product of one secant and its external segment is equal to the product of the other and its external segment.
Page 328 - Every section of a sphere made by a plane is a circle.
Page 257 - If two intersecting planes are each perpendicular to a third plane, their intersection is perpendicular to that plane.