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 & Company, 1854 - 432 páginas |
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Página 23
... intersect each other , the opposite or vertical angles , which they form , are equal . Let AB and DE be two straight lines , intersecting each other at C ; then will the angle ECB be equal to the angle ACD , and the angle ACE to the ...
... intersect each other , the opposite or vertical angles , which they form , are equal . Let AB and DE be two straight lines , intersecting each other at C ; then will the angle ECB be equal to the angle ACD , and the angle ACE to the ...
Página 32
... intersect the given line at points equally distant from the foot of the perpendicular , will be equal . 3d . Of two oblique lines which intersect the given line at points unequally distant from the perpendicular , the one which cuts off ...
... intersect the given line at points equally distant from the foot of the perpendicular , will be equal . 3d . Of two oblique lines which intersect the given line at points unequally distant from the perpendicular , the one which cuts off ...
Página 46
... intersecting at E ; then will AE = EC , and DE : EB . Comparing the triangles AED , BEC , we find the side AD = CB ( p . 28 ) , the angle ADB = CBE , and the angle DAE = ECB ( p . 20 , c . 2 ) ; hence , these triangles are equal ( P. 6 ) ...
... intersecting at E ; then will AE = EC , and DE : EB . Comparing the triangles AED , BEC , we find the side AD = CB ( p . 28 ) , the angle ADB = CBE , and the angle DAE = ECB ( p . 20 , c . 2 ) ; hence , these triangles are equal ( P. 6 ) ...
Página 62
... intersect in some point O. For , they intersect each other unless they are parallel ( B. I. , D. 16 ) . Now , if they are parallel , the line AB which is perpendicular to DE 62 GEOMETRY .
... intersect in some point O. For , they intersect each other unless they are parallel ( B. I. , D. 16 ) . Now , if they are parallel , the line AB which is perpendicular to DE 62 GEOMETRY .
Página 63
... intersect in some point 0 . Moreover , since the point O lies in the perpendicular DE , it is equally distant from the two points , A and B ( B. I. , P. 16 ) ; and since the same point O lies in the perpendicu lar FG , it is also ...
... intersect in some point 0 . Moreover , since the point O lies in the perpendicular DE , it is equally distant from the two points , A and B ( B. I. , P. 16 ) ; and since the same point O lies in the perpendicu lar FG , it is also ...
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Términos y frases comunes
adjacent angles altitude angle ACB angle BAD base ABCD bisect centre chord circ circumference circumscribed common comp cone consequently convex surface cosine Cotang 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 oblique lines 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 sine slant height solidity sphere spherical polygon spherical triangle square described straight line Tang tangent THEOREM triangle ABC triangular prism triedral angles vertex vertices
Pasajes populares
Página 27 - If two triangles have two sides of the one equal to two sides of the...
Página 227 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Página 256 - The logarithm of . the quotient of two numbers, is equal to the logarithm of the dividend diminished by the logarithm of the divisor.
Página 97 - The square described on the hypothenuse of a right-angled triangle is equivalent to the sum of the squares described on the other two sides.
Página 26 - The sum of any two sides of a triangle is greater than the third side.
Página 271 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees...
Página 93 - The area of a parallelogram is equal to the product of its base and altitude.
Página 358 - CUBIC MEASURE 1728 cubic inches = 1 cubic foot 27 cubic feet = 1 cubic yard...
Página 323 - A'B'C', and applying the law of cosines, we have cos a' = cos b' cos c' + sin b' sin c' cos A'. Remembering the relations a' = 180° -A, b' = 180° - B, etc. (this expression becomes cos A = — cos B cos C + sin B sin C cos a.
Página 64 - Two equal chords are equally distant from the centre ; and of two unequal chords, the less is at the greater distance from the centre.