Elements of Geometry and Trigonometry |
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Page 41
... diameter . From the definition of a circle , it follows that all the radii are equal ; that all the diameters are equal also , and each double of the radius . 3. A portion of the circumference , such as FHG , is called an arc . The ...
... diameter . From the definition of a circle , it follows that all the radii are equal ; that all the diameters are equal also , and each double of the radius . 3. A portion of the circumference , such as FHG , is called an arc . The ...
Page 42
... diameter divides the circle and its circumference into two equal parts . Let AEDF be a circle , and AB a diameter . Now , if the figure AEB be applied to AFB , their common base AB retaining its position , the curve line AEB must fall ...
... diameter divides the circle and its circumference into two equal parts . Let AEDF be a circle , and AB a diameter . Now , if the figure AEB be applied to AFB , their common base AB retaining its position , the curve line AEB must fall ...
Page 43
... diameter . Let AD be any chord . Draw the radii CA , CD , to its extremities . We shall then have AD AC + CD ( Book I. Prop . VII . * ) ; A or AD AB . Cor . ( Hence the greatest line which can be inscribed in a circle is its diameter ...
... diameter . Let AD be any chord . Draw the radii CA , CD , to its extremities . We shall then have AD AC + CD ( Book I. Prop . VII . * ) ; A or AD AB . Cor . ( Hence the greatest line which can be inscribed in a circle is its diameter ...
Page 44
... diameters AB , EF , are equal , the semi- circle AMDB may be applied K N BE F exactly to the semicircle ENGF , and the curve line AMDB will coincide entirely with the curve line ENGF . But the part AMD is equal to the part ENG , by ...
... diameters AB , EF , are equal , the semi- circle AMDB may be applied K N BE F exactly to the semicircle ENGF , and the curve line AMDB will coincide entirely with the curve line ENGF . But the part AMD is equal to the part ENG , by ...
Page 54
... diameter AE , and the radii CB , CD . E D The angle BCE , being exterior to the triangle ABC , is equal to the sum of the two interior angles CAB , ABC ( Book I. Prop . XXV . Cor . 6. ) : but the triangle BAC being isosceles , the angle ...
... diameter AE , and the radii CB , CD . E D The angle BCE , being exterior to the triangle ABC , is equal to the sum of the two interior angles CAB , ABC ( Book I. Prop . XXV . Cor . 6. ) : but the triangle BAC being isosceles , the angle ...
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Common terms and phrases
adjacent altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone convex surface cosine cotangent cylinder diagonal diameter dicular distance divided draw drawn equal angles equally distant equations equivalent feet figure find the area formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC logarithm measured by half number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE PROBLEM proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABCDE Scholium secant segment similar sine slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex