Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
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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 . at 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 . at Let AB and DE ...
Page 30
... position , that the side AA B 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 ...
... position , that the side AA B 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 ...
Page 63
... position AH . Draw the radii CA , CD , and CH . Now , the sides AC , CH , of the triangle 4CH , are equal to the sides AC , CD , of the triangle ACD , and the angle ACH is greater than ACD : hence , the side AH , BOOK III . 63.
... position AH . Draw the radii CA , CD , and CH . Now , the sides AC , CH , of the triangle 4CH , are equal to the sides AC , CD , of the triangle ACD , and the angle ACH is greater than ACD : hence , the side AH , 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
ABĀ² ABCD altitude apothem Applying logarithms centre chord circle circumference cone consequently convex surface cosec Cosine Cotang cylinder demonstrated in Book denote diameter distance divided draw edges Equation feet find the area Find the logarithmic following RULE frustum given angle greater hence homologous hypothenuse included angle inscribed intersection less Let ABC linear units log cot log sin lower base lune mantissa multiplied number of sides opposite parallel parallelogram parallelopipedon perpendicular plane MN polar triangle polyedral angle polyedron principle demonstrated prism proportional PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium segment similar six right slant height solution sphere spherical angle spherical excess spherical polygon spherical triangle square straight line subtracting Tang tangent THEOREM triangle ABC triangular prism upper base vertex volume whence write the following