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 25
... consequently , are equal ( a . 14 ) . Cor . Whenever , in two triangles , these three things are equal , viz . the angle E = B , the angle FC , and the included side EF equal to the included side BC , it may be inferred that the ...
... consequently , are equal ( a . 14 ) . Cor . Whenever , in two triangles , these three things are equal , viz . the angle E = B , the angle FC , and the included side EF equal to the included side BC , it may be inferred that the ...
Página 27
... consequently , CG is equal to EF ( P. 5 , c ) . There may be three cases in this proposition . 1st . When the point G falls without the triangle BAC . 2d . When it falls on the side BC ; and 3d . When it falls within the triangle . Case ...
... consequently , CG is equal to EF ( P. 5 , c ) . There may be three cases in this proposition . 1st . When the point G falls without the triangle BAC . 2d . When it falls on the side BC ; and 3d . When it falls within the triangle . Case ...
Página 28
... the side EF = BC , and the side DF = AC ; then will the angle D = A , the angle E = B , and the angle F = C , and consequently the triangle EDF will be equal to the triangle BAC . For , since the sides ED , DF , are 23 GEOMETRY .
... the side EF = BC , and the side DF = AC ; then will the angle D = A , the angle E = B , and the angle F = C , and consequently the triangle EDF will be equal to the triangle BAC . For , since the sides ED , DF , are 23 GEOMETRY .
Página 29
... consequently , the equal sides opposite the equal angles : thus , the equal angles D and A , lie opposite the equal sides EF and BC . PROPOSITION XI . THEOREM . In an isosceles triangle , the angles opposite the equal sides are equal ...
... consequently , the equal sides opposite the equal angles : thus , the equal angles D and A , lie opposite the equal sides EF and BC . PROPOSITION XI . THEOREM . In an isosceles triangle , the angles opposite the equal sides are equal ...
Página 33
... consequently , the oblique line which cuts off the greater distance , is the longer . Cor . 1. The perpendicular measures the shortest distance of a point from a line . Cor . 2. From the same point to the same straight line , only two ...
... consequently , the oblique line which cuts off the greater distance , is the longer . Cor . 1. The perpendicular measures the shortest distance of a point from a line . Cor . 2. From the same point to the same straight line , only two ...
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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.