Elements of Geometry and Trigonometry |
From inside the book
Results 6-10 of 32
Page 46
... three common points , there would be two circumferences passing through the same three points ; which has been shown by the proposition to be impossible . PROPOSITION VIII . THEOREM . Two equal chords are equally 46 GEOMETRY .
... three common points , there would be two circumferences passing through the same three points ; which has been shown by the proposition to be impossible . PROPOSITION VIII . THEOREM . Two equal chords are equally 46 GEOMETRY .
Page 47
... chords , the less is at the greater distance from the centre First . Suppose the chord AB = DE . Bisect these chords by the per- pendiculars CF , CG , and draw the radii CA , CD . D M In the right angled triangles CAF , DCG , the ...
... chords , the less is at the greater distance from the centre First . Suppose the chord AB = DE . Bisect these chords by the per- pendiculars CF , CG , and draw the radii CA , CD . D M In the right angled triangles CAF , DCG , the ...
Page 48
... chord MP . It will , at the same time be perpendicular to NQ ( Book J.Prop.XX.Cor.1 . ) ; therefore , the point H will be at once the middle of the arc MHP , and of the arc NHQ ( Prop . VI . ) ; therefore , we shall have the arc MH - HP ...
... chord MP . It will , at the same time be perpendicular to NQ ( Book J.Prop.XX.Cor.1 . ) ; therefore , the point H will be at once the middle of the arc MHP , and of the arc NHQ ( Prop . VI . ) ; therefore , we shall have the arc MH - HP ...
Page 49
... chord which joins the points of intersection , and will divide it into two equal parts . For , let the line AB join the points of intersection . It will be a common chord to the two circles . Now if a perpendicular D be erected from the ...
... chord which joins the points of intersection , and will divide it into two equal parts . For , let the line AB join the points of intersection . It will be a common chord to the two circles . Now if a perpendicular D be erected from the ...
Page 55
... chords , which intersect each other , is measured by half the sum of the arcs included between its sides . ដ Let AB , CD , be two chords intersecting each BOOK III . 55.
... chords , which intersect each other , is measured by half the sum of the arcs included between its sides . ដ Let AB , CD , be two chords intersecting each BOOK III . 55.
Other editions - View all
Common terms and phrases
adjacent 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 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 number of sides opposite parallel 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
Popular passages
Page 241 - In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference.
Page 19 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Page 232 - ... the logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator.
Page 168 - The radius of a sphere is a straight line drawn from the centre to any point of the surface ; the diameter or axis is a line passing through this centre, and terminated on both sides by the surface.
Page 18 - America, but know that we are alive, that two and two make four, and that the sum of any two sides of a triangle is greater than the third side.
Page 169 - The convex surface of a cylinder is equal to the circumference of its base multiplied by its altitude, Fig.
Page 20 - In an isosceles triangle the angles opposite the equal sides are equal.
Page 86 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.
Page 225 - B) = cos A cos B — sin A sin B, (6a) cos (A — B) = cos A cos B + sin A sin B...
Page 168 - CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.