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 . may be prolonged to any length . lines are unequal , the length of the less may be ... 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 . may be prolonged to any length . lines are unequal , the length of the less may be ... 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 per- pendicular to AB ( Post . 6 ) ; then , by definition ( D. 12 ) , the angles A- E 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 ...
... drawn per- pendicular to AB ( Post . 6 ) ; then , by definition ( D. 12 ) , the angles A- E 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 ...
Page 22
... 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 . F B 租-D For , if two lines be drawn through the point 22 GEOMETRY .
... 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 . F B 租-D 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 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