Elements of Geometry and Trigonometry from the Works of A. M. Legendre: Revised and Adapted to the Course of Mathematical Instruction in the United StatesA.S. Barnes, 1857 - 432 páginas |
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Página 17
... vertices of two angles not adjacent . 27. A base of a plane figure is one of its sides on which it may be supposed to stand . DEFINITIONS OF TERMS . 1. An axiom is a self - evident truth . 2. A demonstration is a train of logical ...
... vertices of two angles not adjacent . 27. A base of a plane figure is one of its sides on which it may be supposed to stand . DEFINITIONS OF TERMS . 1. An axiom is a self - evident truth . 2. A demonstration is a train of logical ...
Página 58
... vertices of its three angles in the circumference . And generally , a polygon is said to be inscribed in a circle , when the vertices of all its angles are in the circumfer- ence . The circumference of the circle is then said to ...
... vertices of its three angles in the circumference . And generally , a polygon is said to be inscribed in a circle , when the vertices of all its angles are in the circumfer- ence . The circumference of the circle is then said to ...
Página 103
... vertices B and C in a line paral- lel to the base : and therefore , we have ( B. II . , P. 4 , C. ) AD : DB :: AE EC . • Cor . 1. Hence , by composition , we have ( B. II . , P. 6 ) , AD + DB : AD :: AE + EC : AE , or AB : AD :: AC : AE ...
... vertices B and C in a line paral- lel to the base : and therefore , we have ( B. II . , P. 4 , C. ) AD : DB :: AE EC . • Cor . 1. Hence , by composition , we have ( B. II . , P. 6 ) , AD + DB : AD :: AE + EC : AE , or AB : AD :: AC : AE ...
Página 104
... same altitude ( P. 6 , c . ) ; and consequently , their vertices B and lie in a parallel to the base DE ( B. I. , P. 23 ) : hence , DE is parallel to BC . PROPOSITION XVII . THEOREM . The line which bisects the 104 GEOMETRY .
... same altitude ( P. 6 , c . ) ; and consequently , their vertices B and lie in a parallel to the base DE ( B. I. , P. 23 ) : hence , DE is parallel to BC . PROPOSITION XVII . THEOREM . The line which bisects the 104 GEOMETRY .
Página 115
... vertices of the other angles . The polygons being similar , the homologous angles , ABC , FGH , are equal , and the sides AB , BC , proportional to FG , GH , that is , AB : FG :: BC : GH ( D. 1 ) . Wherefore , the triangles ABC , FGH ...
... vertices of the other angles . The polygons being similar , the homologous angles , ABC , FGH , are equal , and the sides AB , BC , proportional to FG , GH , that is , AB : FG :: BC : GH ( D. 1 ) . Wherefore , the triangles ABC , FGH ...
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Términos y frases comunes
altitude angle ACB angle BAD bisect centre chord circ circumference circumscribed common comp cone consequently convex surface cos² cosine Cotang cubes cylinder diagonal diameter distance divided draw drawn edges equations equivalent feet figure find the area frustum given angle given line given point gles greater hence homologous homologous sides hypothenuse included angle inscribed circle intersect less Let ABC let fall logarithm magnitudes measured by half middle point number of sides opposite parallelogram parallelopipedon pendicular perimeter perpendicular plane MN polyedral angle polyedron PROBLEM PROPOSITION pyramid quadrant radii radius ratio rectangle regular polygon right angles right-angled triangle Scholium secant segment side BC similar similar triangles sin² sine slant height solidity sphere spherical polygon spherical triangle square described straight line Tang tangent THEOREM three angles triangle ABC triangular prism triedral angles vertex vertices
Pasajes populares
Página 227 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Página 34 - If two right-angled triangles have the hypothenuse and a side of the one, equal to the hypothenuse and a side of the other, each to each, the triangles are equal. Let...
Página 271 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees...
Página 278 - In any triangle, the sum of the two sides containing either angle, is to their difference, as the tangent of half the sum of the two other angles, to the tangent of half their difference.
Página 107 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Página 1 - O's, points or dots are introduced instead of the 0's through the rest of the line, to catch the eye, and to indicate that from thence the annexed first two figures of the Logarithm in the second column stand in the next lower line. N'.
Página 43 - BtSL hence the sum of all the interior and exterior angles, is equal to twice as many right angles as the polygon has sides.
Página 119 - The angle formed by a tangent and a chord is measured by half the intercepted arc.
Página 30 - B : hence the two triangles have two sides and the included angle of the one equal to two sides and the included angle of the other, each to each : hence, the two triangles are equal (Th.
Página 97 - The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides.