Elements of Geometry and Trigonometry |
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Page 139
... formed about the point O , is greater than the sum of the angles formed about the point S. But the sum of the angles about the point O is equal to four right angles ( Book I. Prop . IV . Sch . ) ; therefore the sum of the plane angles ...
... formed about the point O , is greater than the sum of the angles formed about the point S. But the sum of the angles about the point O is equal to four right angles ( Book I. Prop . IV . Sch . ) ; therefore the sum of the plane angles ...
Page 194
... formed will have all its parts equal to those of the given triangle . Let ABC be the given triangle , CED , DFC ... formed at O by the three plane angles AOB , AOC , BOC ; likewise another solid angle may be conceived as formed by the ...
... formed will have all its parts equal to those of the given triangle . Let ABC be the given triangle , CED , DFC ... formed at O by the three plane angles AOB , AOC , BOC ; likewise another solid angle may be conceived as formed by the ...
Page 205
... formed of them , having solid angles contained by three of those triangles , by four , or by five : hence arise three regular bodies , the tetraedron , the octaedron , the icosaedron . No other can be formed with equilateral triangles ...
... formed of them , having solid angles contained by three of those triangles , by four , or by five : hence arise three regular bodies , the tetraedron , the octaedron , the icosaedron . No other can be formed with equilateral triangles ...
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