Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United States |
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Page 49
... ; they are , therefore , equal in all respects : hence , the angles AEB , BEC , are equal , and therefore , the two diagonals bisect each other at right angles . EXERCISES . 1. Show that the lines which bisect ( BOOK I. 49.
... ; they are , therefore , equal in all respects : hence , the angles AEB , BEC , are equal , and therefore , the two diagonals bisect each other at right angles . EXERCISES . 1. Show that the lines which bisect ( BOOK I. 49.
Page 50
... show that BD + AE is greater than BE + AD . ( P. VII . ) B- 3. One of the two interior angles on the same side ... Show Show that the line which bisects the exterior vertical angle of an isos- celes triangle is parallel to the base of ...
... show that BD + AE is greater than BE + AD . ( P. VII . ) B- 3. One of the two interior angles on the same side ... Show Show that the line which bisects the exterior vertical angle of an isos- celes triangle is parallel to the base of ...
Page 51
... Show that any two adjacent angles of a parallelo- gram are supplements of each other . 15. Show that if two parallelograms have one angle in each equal , their remaining angles are equal each to each . 16. Show that if two sides of a ...
... Show that any two adjacent angles of a parallelo- gram are supplements of each other . 15. Show that if two parallelograms have one angle in each equal , their remaining angles are equal each to each . 16. Show that if two sides of a ...
Page 140
... Show that the sum of the squares of two lines , drawn from any point in the circumference of a circle to two points ... Show that if a line bisects the exterior vertical angle of a triangle , the dis- long , from the diameter of the ...
... Show that the sum of the squares of two lines , drawn from any point in the circumference of a circle to two points ... Show that if a line bisects the exterior vertical angle of a triangle , the dis- long , from the diameter of the ...
Page 141
... Show that the area of an equilateral triangle is equal to one fourth the square of one side multiplied by V3 ; or to the square of one side multiplied by .433 . 16. From a point , O , in an equilateral triangle , ABC , the dis- tances ...
... Show that the area of an equilateral triangle is equal to one fourth the square of one side multiplied by V3 ; or to the square of one side multiplied by .433 . 16. From a point , O , in an equilateral triangle , ABC , the dis- tances ...
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Common terms and phrases
ABCD AC² adjacent angles altitude apothem Applying logarithms bisects centre chord circle circumference circumscribed cone consequently convex surface cosec cosine Cotang cylinder denote diagonals diameter difference distance divided draw drawn edges equilateral feet find the area formula frustum given angle given line given point greater hence homologous hypothenuse included angle inscribed intersection isosceles less Let ABC log sin lower base lune mantissa number of sides parallel parallelogram parallelopipedon perimeter perpendicular plane angles plane MN polyedral angle polyedron principle demonstrated prism PROBLEM.-In PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium secant segment semi-circumference similar sine slant height solution sphere spherical angle spherical polygon spherical triangle square straight line subtracting supplement Tang tangent THEOREM THEOREM.-Show tri-rectangular triangle ABC triangular prism triedral angle upper base vertex vertices volume whence
Popular passages
Page 28 - If two triangles have two sides of the one equal to two sides of the...
Page 90 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...
Page 18 - Things which are equal to the same thing, are equal to each other. 2. If equals are added to equals, the sums are equal. 3. If equals are subtracted from equals, the remainders are equal. 4. If equals are added to unequals, the sums are unequal.
Page 4 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 253 - For, the point A being the pole of the arc EF, the distance AE is a 'quadrant ; the point C being the pole of the arc DE, the distance CE is likewise a quadrant : hence the point E is...
Page 61 - A Circle is a plane figure bounded by a curved line every point of which is equally distant from a point within called the center.
Page 94 - 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.
Page 126 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.
Page 46 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 125 - THEOREM. Similar triangles are to each other as the squares of their homologous sides.