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. deduced by a 5. The general truths of Geometry are 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. deduced by a 5. The general truths of Geometry are course of logical reasoning , the premises being definitions and principles previously established . The course of reasoning employed in establishing any truth or ...
Page 51
... means , and the fourth term , a fourth proportional to the other three . When the second term is equal to the third , it ... 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 other three . When the second term is equal to the third , it ... mean proportional between A and C , and C is a third proportional to A and B. 5. Quantities are in proportion by ...
Page 52
... mean is equal to the product of the extremes . PROPOSITION II . THEOREM . If the product of two quantities is equal to the product of two other quantities , two of them may be made the means , and the other two the extremes of a ...
... mean is equal to the product of the extremes . PROPOSITION II . THEOREM . If the product of two quantities is equal to the product of two other quantities , two of them may be made the means , and the other two the extremes of a ...
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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