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 iv
... placed at the end of the several books , and comprise additional theorems , problems , and numerical exercises upon the principles of the Book or Books preceding . They will , it is hoped , be found of service in accustoming students ...
... placed at the end of the several books , and comprise additional theorems , problems , and numerical exercises upon the principles of the Book or Books preceding . They will , it is hoped , be found of service in accustoming students ...
Page 12
... placed as to 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 ...
... placed as to 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 ...
Page 65
... placed upon the sector EOG , so that the angle ACD shall coincide with the angle EOG , the sectors will coincide throughout ; and , consequently , the arcs AMD and ENG will coincide : hence , they are equal ; which was to be proved ...
... placed upon the sector EOG , so that the angle ACD shall coincide with the angle EOG , the sectors will coincide throughout ; and , consequently , the arcs AMD and ENG will coincide : hence , they are equal ; which was to be proved ...
Page 68
... at the greater distance from the centre . 1o . In the equal circles ACH and KLG , let the chords AC and KL be equal ; then are they equally distant from the centres . S For , let the circle KLG be placed upon 68 GEOMETRY .
... at the greater distance from the centre . 1o . In the equal circles ACH and KLG , let the chords AC and KL be equal ; then are they equally distant from the centres . S For , let the circle KLG be placed upon 68 GEOMETRY .
Page 69
... placed upon ACH , so that the centre R shall fall upon the centre O , and the point K upon the point A : then will the chord KL coincide with AC ( P. IV . ) ; and con- sequently , they are equally distant from the centre ; which was to ...
... placed upon ACH , so that the centre R shall fall upon the centre O , and the point K upon the point A : then will the chord KL coincide with AC ( P. IV . ) ; and con- sequently , they are equally distant from the centre ; which was to ...
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Common terms and phrases
AB² ABCD AC² adjacent angles altitude angles is equal apothem base and altitude bisects centre chord circle circumference circumscribed cone consequently convex surface corresponding Cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant equilateral feet find the area formula frustum given angle given line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides parallel parallelogram parallelopipedon perimeter perpendicular plane angles plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium secant segment side BC similar sine slant height solution sphere spherical angle spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence