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
... unit an equal number of times . 15. Magnitudes are equal in all their parts , when they may be so placed as to coincide throughout their whole extent . ELEMENTS OF OF GEOMETRY . BOOK I. BLEMENTARY PRINCIPLES . 12 GEOMETRY .
... unit an equal number of times . 15. Magnitudes are equal in all their parts , when they may be so placed as to coincide throughout their whole extent . ELEMENTS OF OF GEOMETRY . BOOK I. BLEMENTARY PRINCIPLES . 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 . Between A and B they must E A- B C -D coincide ( A. 11 ) . Suppose ...
... 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 . Between A and B they must E A- B C -D coincide ( A. 11 ) . Suppose ...
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. ) ; which was to be proved ...
... 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. ) ; which was to be proved ...
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
AB² AC² 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 straight line greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin lower base mantissa mean proportional measured by half number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment semi-circumference side BC similar sine six right slant height sphere spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence