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 27
... extremities of any side , their , sum is less than that of the two remaining sides of the triangle . Let O be any point within the triangle BAC , and let the lines OB , OC , be drawn to the extremities of any side , as BC : then the sum ...
... extremities of any side , their , sum is less than that of the two remaining sides of the triangle . Let O be any point within the triangle BAC , and let the lines OB , OC , be drawn to the extremities of any side , as BC : then the sum ...
Page 35
... extremities of the line : 2 ° . Any point , without the perpendicular , is unequally dis- tant from the extremities . Let AB be a given straight line , C its middle point , and EF the perpendicular . Then any point of EF is equally ...
... extremities of the line : 2 ° . Any point , without the perpendicular , is unequally dis- tant from the extremities . Let AB be a given straight line , C its middle point , and EF the perpendicular . Then any point of EF is equally ...
Page 61
... extremities of an arc . Any chord belongs to two arcs : the smaller one is meant , unless the contrary is expressed . 6. A SEGMENT is a part of a circle included between an arc and its chord . 7. A SECTOR is a part of a circle included ...
... extremities of an arc . Any chord belongs to two arcs : the smaller one is meant , unless the contrary is expressed . 6. A SEGMENT is a part of a circle included between an arc and its chord . 7. A SECTOR is a part of a circle included ...
Page 63
... extremity , as A : then will AB be greater than AD . Draw the radius CD . In the tri- angle ACD , we have AD less than the sum of AC and CD ( B. I. , P. VII . ) . But this sum is equal to AB ( D. 3 ) : hence , AB is greater than AD ...
... extremity , as A : then will AB be greater than AD . Draw the radius CD . In the tri- angle ACD , we have AD less than the sum of AC and CD ( B. I. , P. VII . ) . But this sum is equal to AB ( D. 3 ) : hence , AB is greater than AD ...
Page 70
... extremity , it is tangent to the circle at that point ; conversely , if a straight line is tangent to a circle at any point , it is perpendicular to the radius drawn to that point . 1o . Let BD be perpendicular to the radius CA , at A ...
... extremity , it is tangent to the circle at that point ; conversely , if a straight line is tangent to a circle at any point , it is perpendicular to the radius drawn to that point . 1o . Let BD be perpendicular to the radius CA , at A ...
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Common terms and phrases
ABē ABCD ACē adjacent angles altitude angles is equal apothem base and altitude bisects centre chord circle circumference circumscribed cone consequently convex surface corresponding Cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant equilateral feet find the area formula frustum given angle given line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides parallel parallelogram parallelopipedon perimeter perpendicular plane angles plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium secant segment side BC similar sine slant height solution sphere spherical angle spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence