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 iii
... taken to represent any one of the class to which it belongs . By this arrangement . the difficulty experienced by beginners in comprehending abstract truths is lessened , without in any manner impairing the gener- ality of the truths ...
... taken to represent any one of the class to which it belongs . By this arrangement . the difficulty experienced by beginners in comprehending abstract truths is lessened , without in any manner impairing the gener- ality of the truths ...
Page 9
... taken as a stand- ard . The assumed standard is called the unit of measure . 2. In GEOMETRY , there are four species of quantity , viz .: LINES , SURFACES , VOLUMES , and ANGLES . These are called GEOMETRICAL MAGNITUDES . Since the unit ...
... taken as a stand- ard . The assumed standard is called the unit of measure . 2. In GEOMETRY , there are four species of quantity , viz .: LINES , SURFACES , VOLUMES , and ANGLES . These are called GEOMETRICAL MAGNITUDES . Since the unit ...
Page 10
... taken . When a compound quantity is to be operated upon as a single quantity , its parts are connected by a vinculum ... taken . Thus , 3 ( A + B ) , indicates that the sum of A and B is to be taken three times . The Sign of Equality ...
... taken . When a compound quantity is to be operated upon as a single quantity , its parts are connected by a vinculum ... taken . Thus , 3 ( A + B ) , indicates that the sum of A and B is to be taken three times . The Sign of Equality ...
Page 12
... 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. ELEMENTARY PRINCIPLES . DEFINITIONS 12 GEOMETRY .
... 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. ELEMENTARY PRINCIPLES . DEFINITIONS 12 GEOMETRY .
Page 15
... Two polygons are mutually equilateral , when their sides , taken in the same order , are equal , each to each : that is , following their perimeters in the same direction , the first side of the one is equal to the first side BOOK I. 15.
... Two polygons are mutually equilateral , when their sides , taken in the same order , are equal , each to each : that is , following their perimeters in the same direction , the first side of the one is equal to the first side BOOK I. 15.
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Common terms and phrases
ABē ABCD ACē 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