Plane and Solid Geometry |
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Page 10
... proposition , ZAOC is 80 ° , find the other angles . Ex . 27. If , in the same figure , ZAOB be bisected , and the bisector be produced through O , prove that COD is also bisected . Ex . 28. If three lines , AB , CD , and EF , meet in a ...
... proposition , ZAOC is 80 ° , find the other angles . Ex . 27. If , in the same figure , ZAOB be bisected , and the bisector be produced through O , prove that COD is also bisected . Ex . 28. If three lines , AB , CD , and EF , meet in a ...
Page 13
... propositions , the fol- lowing abbreviation is suggested for the above proposition : a . s . a . = a.s.a. Similar abbreviations will be suggested for other propositions . 71. DEF . Polygons are mutually equiangular if their angles are ...
... propositions , the fol- lowing abbreviation is suggested for the above proposition : a . s . a . = a.s.a. Similar abbreviations will be suggested for other propositions . 71. DEF . Polygons are mutually equiangular if their angles are ...
Page 19
... PROPOSITION VI . THEOREM 83. Two lines are parallel if a transversal to these lines makes the corresponding angles equal . E- H B F Hyp . CD and EF are intersected by AB in H and I respec- tively , and To prove ZAHD = △ HIF . CD || EF ...
... PROPOSITION VI . THEOREM 83. Two lines are parallel if a transversal to these lines makes the corresponding angles equal . E- H B F Hyp . CD and EF are intersected by AB in H and I respec- tively , and To prove ZAHD = △ HIF . CD || EF ...
Page 27
Arthur Schultze, Frank Louis Sevenoak. PROPOSITION XIII . THEOREM 100. An exterior angle of a triangle is equal to the sum of the two remote interior angles . B ... PROPOSITION XIV . THEOREM 101. The base angles of an PARALLEL LINES 27.
Arthur Schultze, Frank Louis Sevenoak. PROPOSITION XIII . THEOREM 100. An exterior angle of a triangle is equal to the sum of the two remote interior angles . B ... PROPOSITION XIV . THEOREM 101. The base angles of an PARALLEL LINES 27.
Page 36
... PROPOSITION XX . PROBLEM 114. To bisect a given angle . 1 B Given . 2. САВ . Required . To bisect CAB . Construction . From A as a center , with any radius , as AB , describe an arc cutting the sides of the A at B and C. From B and C as ...
... PROPOSITION XX . PROBLEM 114. To bisect a given angle . 1 B Given . 2. САВ . Required . To bisect CAB . Construction . From A as a center , with any radius , as AB , describe an arc cutting the sides of the A at B and C. From B and C as ...
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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.