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 26
... , AC BC AB ; < that is , the difference between any two sides of a triangle is less than the third side . Scholium . In order that any three given lines may rep- resent the sides of a triangle , the sum of 26 GEOMETRY .
... , AC BC AB ; < that is , the difference between any two sides of a triangle is less than the third side . Scholium . In order that any three given lines may rep- resent the sides of a triangle , the sum of 26 GEOMETRY .
Page 27
... difference of any two must be less than the third . PROPOSITION VIII . THEOREM . if from any point within a triangle two straight lines are drawn to the extremities of any side , their sum is less than that of the two remaining sides of ...
... difference of any two must be less than the third . PROPOSITION VIII . THEOREM . if from any point within a triangle two straight lines are drawn to the extremities of any side , their sum is less than that of the two remaining sides of ...
Page 51
... difference between that angle and a right angle ; thus , EOB is the complement of AOE . NOTE 2. - The supplement of an angle is the difference between that E angle and two right angles ; thus , EOC is the supplement of AOE . 13. An ...
... difference between that angle and a right angle ; thus , EOB is the complement of AOE . NOTE 2. - The supplement of an angle is the difference between that E angle and two right angles ; thus , EOC is the supplement of AOE . 13. An ...
Page 53
... difference of the antecedent and consequent is compared with either antecedent or consequent . 9. Four quantities are reciprocally proportional , when the first is to the second as the fourth is to the third . Two varying quantities are ...
... difference of the antecedent and consequent is compared with either antecedent or consequent . 9. Four quantities are reciprocally proportional , when the first is to the second as the fourth is to the third . Two varying quantities are ...
Page 71
... difference of HQ and HP ( A. 3 ) ; which was to be proved . 2o . Let the secant AB and tangent DE be parallel ; then the intercepted arcs MH and PH are equal . For , draw the radius CH to the point of contact H ; it will be ...
... difference of HQ and HP ( A. 3 ) ; which was to be proved . 2o . Let the secant AB and tangent DE be parallel ; then the intercepted arcs MH and PH are equal . For , draw the radius CH to the point of contact H ; it will be ...
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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.