Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United States |
From inside the book
Results 1-5 of 80
Page 61
... centre . The bounding line is called the cir- cumference . Ө 2. A RADIUS is a straight line drawn from the centre to any point of the circumference . 3. A DIAMETER is a straight line drawn through the centre and terminating in the ...
... centre . The bounding line is called the cir- cumference . Ө 2. A RADIUS is a straight line drawn from the centre to any point of the circumference . 3. A DIAMETER is a straight line drawn through the centre and terminating in the ...
Page 63
... centre ; which is impossible ( D. 1 ) : hence , AB divides the circle , and also its circum- ference , into two equal parts ; which was to be proved . PROPOSITION II . THEOREM . A diameter is greater than any other chord . Let AD be a ...
... centre ; which is impossible ( D. 1 ) : hence , AB divides the circle , and also its circum- ference , into two equal parts ; which was to be proved . PROPOSITION II . THEOREM . A diameter is greater than any other chord . Let AD be a ...
Page 65
... centre O shall fall upon the centre C , and the point E upon A ; then , because the arc EGP is greater than AMD , the point P will fall at some point H , beyond D , and the chord EP will take the position AH . Draw the radii CA , CD ...
... centre O shall fall upon the centre C , and the point E upon A ; then , because the arc EGP is greater than AMD , the point P will fall at some point H , beyond D , and the chord EP will take the position AH . Draw the radii CA , CD ...
Page 67
... centre of the circle . Scholium . The centre C , the middle point D of the chord AB , and the middle point G of the subtended arc , are points of the radius perpendicular to the chord . But two points determine the position of a ...
... centre of the circle . Scholium . The centre C , the middle point D of the chord AB , and the middle point G of the subtended arc , are points of the radius perpendicular to the chord . But two points determine the position of a ...
Page 68
... centres ; and of two unequal chords , the less is at the greater distance from the centre . 1o . In the equal circles ACH and KLG , let the chords AC and KL be equal ; then are they equally distant from the centres . S For , let the ...
... centres ; and of two unequal chords , the less is at the greater distance from the centre . 1o . In the equal circles ACH and KLG , let the chords AC and KL be equal ; then are they equally distant from the centres . S For , let the ...
Other editions - View all
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