Elements of Geometry and Trigonometry |
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Page 59
... 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 circumference . All radii of the same circle are equal . are also equal ...
... 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 circumference . All radii of the same circle are equal . are also equal ...
Page 60
... its circumference touches all of the sides of the polygon . ооо хо POSTULATE . A circumference can be described from any point as a centre . and with any radius . PROPOSITION L. THEOREM . Any diameter divides the circle , 60 GEOMETRY .
... its circumference touches all of the sides of the polygon . ооо хо POSTULATE . A circumference can be described from any point as a centre . and with any radius . PROPOSITION L. THEOREM . Any diameter divides the circle , 60 GEOMETRY .
Page 61
... radius CD . In the tri- angle ACD , we have AD less than the sum of AC and CD ( B. I. , P. VII . ) . But this sum is equal to AB ( D. 3 ) hence , AB is greater than AD ; which was to be proved . A PROPOSITION III . THEOREM . A straight ...
... radius CD . In the tri- angle ACD , we have AD less than the sum of AC and CD ( B. I. , P. VII . ) . But this sum is equal to AB ( D. 3 ) hence , AB is greater than AD ; which was to be proved . A PROPOSITION III . THEOREM . A straight ...
Page 64
... radius which is perpendicular to the chord AB : then will this radius bisect the chord AB , and also the arc AGB . For , draw the radii CA and CB . Then , the right - angled triangles CDA and CDB will have the hypothenuse CA equal to CB ...
... radius which is perpendicular to the chord AB : then will this radius bisect the chord AB , and also the arc AGB . For , draw the radii CA and CB . Then , the right - angled triangles CDA and CDB will have the hypothenuse CA equal to CB ...
Page 65
... radius perpendicular to the chord . But two points determine the 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 ...
... radius perpendicular to the chord . But two points determine the 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 ...
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Common terms and phrases
ABCD AC² adjacent angles altitude angle ACB apothem Applying logarithms base and altitude bisect centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin logarithm lower base mantissa mean proportional measured by half middle point number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROBLEM PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment side BC similar sine slant height sphere spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence