The Elements of Geometry |
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Page ix
... . line . ] But AC ICE , and ... AC 1 CD . PROP . XXVI . BOOK I. The sum of the angles of any triangle is equal to two right angles . B E N A Let ABC be any A. D .39.37 * GEOMETRY . NOTE . The attention of teachers INTRODUCTION . ix.
... . line . ] But AC ICE , and ... AC 1 CD . PROP . XXVI . BOOK I. The sum of the angles of any triangle is equal to two right angles . B E N A Let ABC be any A. D .39.37 * GEOMETRY . NOTE . The attention of teachers INTRODUCTION . ix.
Page 22
Webster Wells. TRIANGLES . DEFINITIONS . 57. A triangle is a portion of a plane bounded by three straight lines ; as ABC . The bounding lines , AB , BC , and CA , are called the sides of the triangle , and their points of intersection ...
Webster Wells. TRIANGLES . DEFINITIONS . 57. A triangle is a portion of a plane bounded by three straight lines ; as ABC . The bounding lines , AB , BC , and CA , are called the sides of the triangle , and their points of intersection ...
Page 23
... triangle . The altitude of a triangle is the per- pendicular drawn from the vertex to the base , produced if necessary . B D Thus , in the triangle ABC , BC is the base , BAC the vertical angle , and AD the altitude . 61. Since a ...
... triangle . The altitude of a triangle is the per- pendicular drawn from the vertex to the base , produced if necessary . B D Thus , in the triangle ABC , BC is the base , BAC the vertical angle , and AD the altitude . 61. Since a ...
Page 24
... triangles ABC and DEF , let AB = DE , AC : To prove = DF , and A = 2 D. Δ ΑΒΓ = Δ DEF . Superpose the triangle ABC upon DEF in such a way that A shall coincide with its equal D ; the side AB falling upon DE , and the side AC upon DF ...
... triangles ABC and DEF , let AB = DE , AC : To prove = DF , and A = 2 D. Δ ΑΒΓ = Δ DEF . Superpose the triangle ABC upon DEF in such a way that A shall coincide with its equal D ; the side AB falling upon DE , and the side AC upon DF ...
Page 25
... triangles ABC and DEF , let / AB DE , LAZ D , and B = E. To prove = = Δ ΑΒΓ : = A DEF . Superpose the triangle ABC upon DEF in such a way that the side AB shall coincide with its equal DE ; the point A falling at D , and the point B at ...
... triangles ABC and DEF , let / AB DE , LAZ D , and B = E. To prove = = Δ ΑΒΓ : = A DEF . Superpose the triangle ABC upon DEF in such a way that the side AB shall coincide with its equal DE ; the point A falling at D , and the point B at ...
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Common terms and phrases
ABC and DEF ABCD adjacent angles altitude angles are equal approach the limit arc BC area ABC bisector bisects centre chord circle circumference circumscribed cone of revolution construct the triangle Converse of Prop cylinder denote diagonals diameter diedral Draw AC equal respectively equally distant equilateral triangle equivalent exterior angle Find the area frustum given point given straight line Hence homologous hypotenuse intersection isosceles triangle lateral area lateral edges Let ABC measured by arc middle point number of sides parallelogram parallelopiped perimeter perpendicular to MN plane MN polyedral polyedrons prism produced PROPOSITION prove pyramid quadrilateral radii radius rectangle regular polygon rhombus right angles right triangle secant secant line segment similar slant height sphere spherical polygon spherical triangle square surface tangent tetraedron THEOREM trapezoid triangle ABC triangles are equal triangular prism triedral vertex vertices volume Whence
Popular passages
Page 38 - If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first 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 65 - 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.
Page 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. 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 120 - The first and fourth terms of a proportion are called the extremes, and the second and third terms the means.
Page 24 - Two triangles are congruent if (a) two sides and the included angle of one are equal, respectively, to two sides and the included angle of the other...
Page 123 - In any proportion the terms are in proportion by composition and division ; that is, the sum of the first two terms is to their difference as the sum of the last two terms to their difference.
Page 322 - A spherical polygon is a portion of the surface of a sphere bounded by three or more arcs of great circles. The...
Page 248 - The projection of a point on a plane is the foot of the perpendicular from the point to the plane.