Elements of Geometry and Trigonometry |
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Page 13
... half of the angle A. The square of the line AB is designated by AB2 ; its cube by AB3 . What is meant by the square and cube of a line , will be explained in its proper place . The sign indicates a root to be extracted ; thus √2 means ...
... half of the angle A. The square of the line AB is designated by AB2 ; its cube by AB3 . What is meant by the square and cube of a line , will be explained in its proper place . The sign indicates a root to be extracted ; thus √2 means ...
Page 23
... half of ABF , is shorter than AC , the half of ACF ; hence , the per- pendicular is shorter than any oblique line . Secondly . Let us suppose BC - BE ; then will the triangle CAB be equal to the the triangle BAE ; for BC = BE , the side ...
... half of ABF , is shorter than AC , the half of ACF ; hence , the per- pendicular is shorter than any oblique line . Secondly . Let us suppose BC - BE ; then will the triangle CAB be equal to the the triangle BAE ; for BC = BE , the side ...
Page 47
... half of AB , is equal to the side DG , the half of DE : hence the triangles are equal , and CF is equal to CG ( Book I. Prop . XVII . ) ; hence , the two equal chords AB , DE , are equally distant from the centre . F K H Secondly Let ...
... half of AB , is equal to the side DG , the half of DE : hence the triangles are equal , and CF is equal to CG ( Book I. Prop . XVII . ) ; hence , the two equal chords AB , DE , are equally distant from the centre . F K H Secondly Let ...
Page 54
... half of BE . For a like reason , the angle CAD will be measured by the half of ED ; hence BAC + CAD , or BAD will be measured by half of BE + ED , or of BED . Suppose , in the second place , that the centre C lies without the angle BAD ...
... half of BE . For a like reason , the angle CAD will be measured by the half of ED ; hence BAC + CAD , or BAD will be measured by half of BE + ED , or of BED . Suppose , in the second place , that the centre C lies without the angle BAD ...
Page 55
... half of the same arc BOC . B Cor . 2. Every angle BAD , inscribed in a semicircle is a right angle ; because it is mea- sured by half the semicircumference BOD , that is , by the fourth part of the whole cir- cumference . Cor . 3. Every ...
... half of the same arc BOC . B Cor . 2. Every angle BAD , inscribed in a semicircle is a right angle ; because it is mea- sured by half the semicircumference BOD , that is , by the fourth part of the whole cir- cumference . Cor . 3. Every ...
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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