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 18
... drawn joining two given points . 12. The shortest distance from one point to another is measured on the straight line which joins them . 13. Through the same point , only one straight line can be drawn parallel to a given straight line ...
... drawn joining two given points . 12. The shortest distance from one point to another is measured on the straight line which joins them . 13. Through the same point , only one straight line can be drawn parallel to a given straight line ...
Page 19
... drawn joining any two points . 2. A straight line may be prolonged to any length . 3. If two straight lines are ... drawn to a given straight line , either from a point without , or from a point on the line . 7. A straight line may be ...
... drawn joining any two points . 2. A straight line may be prolonged to any length . 3. If two straight lines are ... drawn to a given straight line , either from a point without , or from a point on the line . 7. A straight line may be ...
Page 20
... drawn perpen- dicular to AB ( Post . 6 ) ; then , by definition ( D. 12 ) , the angles ECA E and ECB are both right angles , and consequently , their sum is equal to two right angles . The angle DCA is equal to the sum of the angles ECA ...
... drawn perpen- dicular to AB ( Post . 6 ) ; then , by definition ( D. 12 ) , the angles ECA E and ECB are both right angles , and consequently , their sum is equal to two right angles . The angle DCA is equal to the sum of the angles ECA ...
Page 22
... mutually perpen dicular to each other . Cor . 3. The sum of all the angles ACB , BCD , DCE , ECF , FCA , that can be formed about a point , is equal to four right angles . ж For , if two lines are drawn through the point 22 GEOMETRY .
... mutually perpen dicular to each other . Cor . 3. The sum of all the angles ACB , BCD , DCE , ECF , FCA , that can be formed about a point , is equal to four right angles . ж For , if two lines are drawn through the point 22 GEOMETRY .
Page 27
... drawn to the extremities of any side , their , sum is less than that of the two remaining sides of the triangle . Let O be any point within the triangle BAC , and let the lines OB , OC , be drawn to the extremities of any side , as BC ...
... drawn to the extremities of any side , their , sum is less than that of the two remaining sides of the triangle . Let O be any point within the triangle BAC , and let the lines OB , OC , be drawn to the extremities of any side , as BC ...
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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