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 between two points . 12. The shortest distance between any two points is mea- sured on the straight line which joins them . 13. Through the same point , only one line can be drawn parallel to a given line . POSTULATES . 1. A ...
... drawn between two points . 12. The shortest distance between any two points is mea- sured on the straight line which joins them . 13. Through the same point , only one line can be drawn parallel to a given line . POSTULATES . 1. A ...
Page 19
... drawn , making with a given line an angle equal to a given angle . 8. A line may be drawn through a given point , parallel to a given line . NOTE . In making references , the following abbreviations are employed , viz . ‹ A. for Axiom ...
... drawn , making with a given line an angle equal to a given angle . 8. A line may be drawn through a given point , parallel to a given line . NOTE . In making references , the following abbreviations are employed , viz . ‹ A. for Axiom ...
Page 20
... drawn per- pendicular to AB ( Post . 6 ) ; then , by definition ( D. 12 ) , the angles Ε D B ECA and ECB will both be right angles , and conse quently , their sum will be equal to two right angles . The angle DCA is equal to the sum ECA ...
... drawn per- pendicular to AB ( Post . 6 ) ; then , by definition ( D. 12 ) , the angles Ε D B ECA and ECB will both be right angles , and conse quently , their sum will be equal to two right angles . The angle DCA is equal to the sum ECA ...
Page 22
... are mutually perpendicular 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 , B For , if two lines be drawn through the point 22 GEOMETRY .
... are mutually perpendicular 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 , B For , if two lines be drawn through the point 22 GEOMETRY .
Page 23
... drawn through the point , mutually perpendicular to each other , the sum of the angles which they form will be equal to four right angles , and it will also be equal to the sum of the given angles ( A. 9 ) . Hence , the sum of the given ...
... drawn through the point , mutually perpendicular to each other , the sum of the angles which they form will be equal to four right angles , and it will also be equal to the sum of the given angles ( A. 9 ) . Hence , the sum of the given ...
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Common terms and phrases
AB² AC² altitude angle ACB apothem axis base and altitude base multiplied BC² bisect centre chord circumference coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diameter distance divided draw drawn edges equal bases equal in volume equal to AC equal to half equally distant Formula frustum given angle given line greater hence homologous hypothenuse included angle intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides opposite parallelogram perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION XI proved pyramid quadrant radii radius rectangle regular polygons right-angled triangle Scholium segment semi-circumference side BC similar sine slant height sphere spherical angle spherical excess spherical polygon spherical triangle straight line tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence