Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United States |
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Page 12
... when they are equal in measure , When they may be so placed as to coincide through- out their whole extent , they are equal in all their parts . ELEMENTS OF GEOMETRY . BOOK I. ELEMENTARY PRINCIPLES . DEFINITIONS 12 GEOMETRY .
... when they are equal in measure , When they may be so placed as to coincide through- out their whole extent , they are equal in all their parts . ELEMENTS OF GEOMETRY . BOOK I. ELEMENTARY PRINCIPLES . DEFINITIONS 12 GEOMETRY .
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 D ( P. III . , C. ) and are and FD , it must be at their ...
... 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 D ( P. III . , C. ) and are and FD , it must be at their ...
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
AB² AC² altitude angle ACB apothem axis base and altitude base multiplied BC² bisect centre chord circumference coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diameter distance divided draw drawn edges equal bases equal in volume equal to AC equal to half equally distant Formula frustum given angle given line greater hence homologous hypothenuse included angle intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides opposite parallelogram perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION XI proved pyramid quadrant radii radius rectangle regular polygons right-angled triangle Scholium segment semi-circumference side BC similar sine slant height sphere spherical angle spherical excess spherical polygon spherical triangle straight line tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence