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
... means of the diagrams employed in their demonstration . This departure from the method of Euclid is much to be regretted . The propositions of Geometry are general truths , and ought to be stated in general terms , without reference to ...
... means of the diagrams employed in their demonstration . This departure from the method of Euclid is much to be regretted . The propositions of Geometry are general truths , and ought to be stated in general terms , without reference to ...
Page 9
... means of the straight line and curve . The operations to be performed upon the quantities , and the rela tions between them , are indicated by signs , as in Analysis . The following are the principal signs employed : The Sign GEOMETRY ...
... means of the straight line and curve . The operations to be performed upon the quantities , and the rela tions between them , are indicated by signs , as in Analysis . The following are the principal signs employed : The Sign GEOMETRY ...
Page 11
... mean 1st , 2d , etc. 5. The general truths of Geometry are deduced by a course of logical reasoning , the premises being definitions and principles previously established . The course of reasoning employed in establishing any truth or ...
... mean 1st , 2d , etc. 5. The general truths of Geometry are deduced by a course of logical reasoning , the premises being definitions and principles previously established . The course of reasoning employed in establishing any truth or ...
Page 53
... means , and the fourth term , a fourth proportional to the three others . When the second term is equal to the third ... mean proportional between A and C , and C is a third proportional to A and B. 5. Quantities are in proportion by ...
... means , and the fourth term , a fourth proportional to the three others . When the second term is equal to the third ... mean proportional between A and C , and C is a third proportional to A and B. 5. Quantities are in proportion by ...
Page 54
... mean is equal to the product of the extremes . PROPOSITION II . THEOREM . If the product of two factors is equal to the product of two other factors , either pair of factors may be made the extremes and the other pair the means of a ...
... mean is equal to the product of the extremes . PROPOSITION II . THEOREM . If the product of two factors is equal to the product of two other factors , either pair of factors may be made the extremes and the other pair the means of a ...
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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