Elements of Geometry and Trigonometry |
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Page 54
... hence evident that the arcs of the circle , which serve as a measure of the different angles , are proportional to ... hence the angle BCE is double of BAC . Since BCE lies at the centre , it is measured by the arc BE ; hence BAC will be ...
... hence evident that the arcs of the circle , which serve as a measure of the different angles , are proportional to ... hence the angle BCE is double of BAC . Since BCE lies at the centre , it is measured by the arc BE ; hence BAC will be ...
Page 113
... hence also MB = OM ; hence the triangle BMO is isosceles . Again , the angle AMB being exterior to the isosceles trian- gle BMO , is double of the interior angle O ( Book I. Prop . XXV . Cor . 6. ) : but the angle AMB MAB ; hence the ...
... hence also MB = OM ; hence the triangle BMO is isosceles . Again , the angle AMB being exterior to the isosceles trian- gle BMO , is double of the interior angle O ( Book I. Prop . XXV . Cor . 6. ) : but the angle AMB MAB ; hence the ...
Page 196
... Hence those two triangles , having all their sides re- D spectively equal in both , must either be absolutely equal , or at least symmetrically so ; in either of which cases , their corres- B ponding angles must be equal , and lie ...
... Hence those two triangles , having all their sides re- D spectively equal in both , must either be absolutely equal , or at least symmetrically so ; in either of which cases , their corres- B ponding angles must be equal , and lie ...
Contents
BOOK | 7 |
Problems relating to the First and Third Books 57 | 57 |
BOOK IV | 68 |
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Common terms and phrases
adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone consequently convex surface cosine Cotang cylinder diagonal diameter dicular distance divided draw drawn 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 number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE PROBLEM Prop proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant segment similar sine slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line TABLE OF LOGARITHMIC tang tangent THEOREM triangle ABC triangular prism vertex