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 20
... drawn . 12. A straight line is the shortest distance between two points . 13. Through the same point , only one straight line can be drawn which shall be parallel to a given line . 14. Magnitudes , which being applied the one to the ...
... drawn . 12. A straight line is the shortest distance between two points . 13. Through the same point , only one straight line can be drawn which shall be parallel to a given line . 14. Magnitudes , which being applied the one to the ...
Página 30
... drawn from the vertex of an isosceles triangle to the middle point of the base , divides the angle at the vertex into ... draw CD . Now , in the two triangles BDC , BAC , we have BD = AC , by construction ; the angle B equal to the angle ...
... drawn from the vertex of an isosceles triangle to the middle point of the base , divides the angle at the vertex into ... draw CD . Now , in the two triangles BDC , BAC , we have BD = AC , by construction ; the angle B equal to the angle ...
Página 31
... drawn to that line . Let A be the point , and DE the given line . Let us suppose that we can draw D F -E B two perpendiculars , AB , AC . Pro- long either of them , as AB , till BF is equal to AB , and draw FC . Then the two triangles ...
... drawn to that line . Let A be the point , and DE the given line . Let us suppose that we can draw D F -E B two perpendiculars , AB , AC . Pro- long either of them , as AB , till BF is equal to AB , and draw FC . Then the two triangles ...
Página 32
... drawn from the same point to the same straight line . Cor . At a given point C , in the line AB , it is also impossible ... draw FC , FD . First . The triangle BCF , is equal to the triangle CAB , for they have the right angle CBF = CBA ...
... drawn from the same point to the same straight line . Cor . At a given point C , in the line AB , it is also impossible ... draw FC , FD . First . The triangle BCF , is equal to the triangle CAB , for they have the right angle CBF = CBA ...
Página 33
... drawn ; for , if there could be more , we should have at least two equal oblique lines on the same side of the ... draw DA and DB . Then , since AC = CB , the two oblique lines AD , DB , are equal ( P. 15 ) . So , likewise , are ...
... drawn ; for , if there could be more , we should have at least two equal oblique lines on the same side of the ... draw DA and DB . Then , since AC = CB , the two oblique lines AD , DB , are equal ( P. 15 ) . So , likewise , are ...
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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.