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 13
... position , but not magni- tude . 3. A LINE is that which has length , but neither breadth nor thickness . Lines are divided into two classes , straight and curved . 4. A. STRAIGHT LINE is one which does not change its direction at any ...
... position , but not magni- tude . 3. A LINE is that which has length , but neither breadth nor thickness . Lines are divided into two classes , straight and curved . 4. A. STRAIGHT LINE is one which does not change its direction at any ...
Page 21
... position just demonstrated , the sum of any two adjacent angles is equal to two right angles . · PROPOSITION II . THEOREM . If two straight lines intersect each other , the opposite or vertical angles will be equal . Let AB and DE ...
... position just demonstrated , the sum of any two adjacent angles is equal to two right angles . · PROPOSITION II . THEOREM . If two straight lines intersect each other , the opposite or vertical angles will be equal . Let AB and DE ...
Page 30
... position , that the side E F BC would be greater than EF ; and if the angle A were less than D , the side BC would be less than EF . But BC is equal to EF , by hypothesis ; therefore , the angle A can neither be greater nor less than D ...
... position , that the side E F BC would be greater than EF ; and if the angle A were less than D , the side BC would be less than EF . But BC is equal to EF , by hypothesis ; therefore , the angle A can neither be greater nor less than D ...
Page 63
... position AH . Draw the radii CA , CD , and CH . Now , the sides AC , CH , of the triangle ACH , are equal to the sides AC , CD , of the triangle ACD , and the angle ACH is greater than ACD : hence , the side A , BOOK III . 63.
... position AH . Draw the radii CA , CD , and CH . Now , the sides AC , CH , of the triangle ACH , are equal to the sides AC , CD , of the triangle ACD , and the angle ACH is greater than ACD : hence , the side A , BOOK III . 63.
Page 65
... position of a straight line ( A. 11 ) : hence , any straight line which passes through two of these points , will pass through the third , and be perpendicular to the chord . PROPOSITION VII . THEOREM . Through any three points , not in ...
... position of a straight line ( A. 11 ) : hence , any straight line which passes through two of these points , will pass through the third , and be perpendicular to the chord . PROPOSITION VII . THEOREM . Through any three points , not in ...
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Common terms and phrases
AB² AC² altitude angle ACB apothem axis base and altitude base multiplied BC² bisect centre chord circumference coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diameter distance divided draw drawn edges equal bases equal in volume equal to AC equal to half equally distant Formula frustum given angle given line greater hence homologous hypothenuse included angle intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides opposite parallelogram perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION XI proved pyramid quadrant radii radius rectangle regular polygons right-angled triangle Scholium segment semi-circumference side BC similar sine slant height sphere spherical angle spherical excess spherical polygon spherical triangle straight line tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence