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 . CA , CD , to its extremities . Draw the radii We shall then have AD AC + CD ( Book I. Prop . VII . * ) ; or AD AB . Cor . Hence the greatest line which can be inscribed in a circle is its diameter ...
... diameter . Let AD be any chord . CA , CD , to its extremities . Draw the radii We shall then have AD AC + CD ( Book I. Prop . VII . * ) ; 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 M N 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 M N 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 . 19 The angle BCE , being exterior to the triangle ABC , is equal to the sum of the two interior angles CAB , ABC ( Book I. B Prop . XXV . Cor . 6. ) : but the triangle BAC being isosceles , the ...
... diameter AE , and the radii CB , CD . 19 The angle BCE , being exterior to the triangle ABC , is equal to the sum of the two interior angles CAB , ABC ( Book I. B Prop . XXV . Cor . 6. ) : but the triangle BAC being isosceles , the ...
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Common terms and phrases
adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book centre chord circ circumference circumscribed common cone convex surface Cosine Cotang cylinder diagonal diameter dicular distance draw drawn equal angles equally distant equiangular equivalent figure formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed polygon intersection less Let ABC let fall logarithm measured by half number of sides oblique lines opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE prism proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant secant line segment side BC similar sine solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex