Elements of Geometry and Trigonometry |
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Page 12
... coincide throughout their whole extent : they are equal in all their parts when each part of one is equal to the corresponding part of the other , when taken either in the same or in the reverse order . ELEMENTS OF GEOMETRY . BOOK I ...
... coincide throughout their whole extent : they are equal in all their parts when each part of one is equal to the corresponding part of the other , when taken either in the same or in the reverse order . ELEMENTS OF GEOMETRY . BOOK I ...
Page 23
... coincide throughout their whole extent , and form one and the same line . Let A and B be two points common to two lines : then will the lines coincide throughout . E A B C -D Between A and B they must coincide ( A. 11 ) . Suppose , now ...
... coincide throughout their whole extent , and form one and the same line . Let A and B be two points common to two lines : then will the lines coincide throughout . E A B C -D Between A and B they must coincide ( A. 11 ) . Suppose , now ...
Page 25
... coincide with the vertex F ; consequently , the side BC will coincide with the side EF ( A. 11 ) . The two triangles , therefore , coincide throughout , and are consequently equal in all their parts ( I. , D. 14 ) ; which was to be ...
... coincide with the vertex F ; consequently , the side BC will coincide with the side EF ( A. 11 ) . The two triangles , therefore , coincide throughout , and are consequently equal in all their parts ( I. , D. 14 ) ; which was to be ...
Page 26
... coincide with the vertex F ; and because the angle C is equal to the angle F , the side CA will take the direction FD . Now , the vertex A being at the same time on the lines ED and FD , it must be at their intersection D ( P. III . , C ...
... coincide with the vertex F ; and because the angle C is equal to the angle F , the side CA will take the direction FD . Now , the vertex A being at the same time on the lines ED and FD , it must be at their intersection D ( P. III . , C ...
Page 61
... coincide ; otherwise there would be some points in either one or the other of the curves unequally distant from the centre ; which is impossible ( D. 1 ) : hence , AB divides the circle , and also its circumference , into two equal ...
... coincide ; otherwise there would be some points in either one or the other of the curves unequally distant from the centre ; which is impossible ( D. 1 ) : hence , AB divides the circle , and also its circumference , into two equal ...
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Common terms and phrases
ABCD ACĀ² adjacent angles altitude angle ACB apothem Applying logarithms base and altitude bisect centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin logarithm lower base mantissa mean proportional measured by half middle point number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROBLEM PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment side BC similar sine slant height sphere spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence