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 65
... position AH . Draw the radii CA , CD , 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 AH , BOOK ...
... position AH . Draw the radii CA , CD , 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 AH , BOOK ...
Page 67
... position of a straight line ( A. 11 ) : hence , any straight line which passes through two of these points , passes through the third , and is per- pendicular 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 , passes through the third , and is per- pendicular to the chord . PROPOSITION VII . THEOREM . Through any three points , not in ...
Page 74
... have any one of six positions with respect to each other , depending upon the distance between their centres : 1 ° . When the distance between their centres is greater than the sum of their radii , they are external 74 GEOMETRY .
... have any one of six positions with respect to each other , depending upon the distance between their centres : 1 ° . When the distance between their centres is greater than the sum of their radii , they are external 74 GEOMETRY .
Page 77
... : then are they proportional to the arcs AB and FH . DIOB For , let the less angle FOH , be placed upon the greater angle ACB , so that it shall take the position ACD . Then , if the proposition is not true , let us suppose BOOK III . 77.
... : then are they proportional to the arcs AB and FH . DIOB For , let the less angle FOH , be placed upon the greater angle ACB , so that it shall take the position ACD . Then , if the proposition is not true , let us suppose BOOK III . 77.
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Common terms and phrases
AB² ABCD AC² 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