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 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 . All diameters ...
... 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 . All diameters ...
Page 60
... when its circumference touches all of the sides of the polygon . Ө 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 .
... when its circumference touches all of the sides of the polygon . Ө 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
... 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 ...
... 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 ...
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
AB² 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 straight line greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin lower base mantissa mean proportional measured by half number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment semi-circumference side BC similar sine six right slant height sphere spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence