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 73
Page 59
... centre . The bounding line is called the cir- cumference . D 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 . D 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 60
... circumference touches all of the sides of the polygon . о © о POSTULATE . A circumference can be described from any point as a centre , and with any radius . PROPOSITION I. THEOREM . Any diameter divides the circle , 60 GEOMETRY .
... circumference touches all of the sides of the polygon . о © о POSTULATE . A circumference can be described from any point as a centre , and with any radius . PROPOSITION I. THEOREM . Any diameter divides the circle , 60 GEOMETRY .
Page 61
... centre ; which is impossible ( D. 1 ) : hence , AB divides the circle , and also its circumference , 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 circumference , 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 63
... 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 , and CH . Now , the sides AC ...
... 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 , and CH . Now , the sides AC ...
Page 65
... centre of the circle . Scholium . The centre C , C , the middle point D of the chord AB , and the middle point 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 , C , the middle point D of the chord AB , and the middle point of the subtended arc , are points of the radius perpendicular to the chord . But two points determine the position of a ...
Other editions - View all
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