Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
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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 Now , the vertex A being at the same time direction FD . on the lines ED D ( P. III . , C. ) 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 Now , the vertex A being at the same time direction FD . on the lines ED D ( P. III . , C. ) 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
ABĀ² ABCD altitude apothem Applying logarithms centre chord circle circumference cone consequently convex surface cosec Cosine Cotang cylinder demonstrated in Book denote diameter distance divided draw edges Equation feet find the area Find the logarithmic following RULE frustum given angle greater hence homologous hypothenuse included angle inscribed intersection less Let ABC linear units log cot log sin lower base lune mantissa multiplied number of sides opposite parallel parallelogram parallelopipedon perpendicular plane MN polar triangle polyedral angle polyedron principle demonstrated prism proportional PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium segment similar six right slant height solution sphere spherical angle spherical excess spherical polygon spherical triangle square straight line subtracting Tang tangent THEOREM triangle ABC triangular prism upper base vertex volume whence write the following