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 14
... perpendicular to the second . 13. An OBLIQUE ANGLE is formed by one straight line meeting another so as to make the adjacent angles unequal . B D Oblique angles are subdivided into two classes , acute ngles , and obtuse angles . 14. An ...
... perpendicular to the second . 13. An OBLIQUE ANGLE is formed by one straight line meeting another so as to make the adjacent angles unequal . B D Oblique angles are subdivided into two classes , acute ngles , and obtuse angles . 14. An ...
Page 19
... perpendicular may be drawn to a given line , either from a point without , or from a point on the line . 7. A line may be drawn , making with a given line an angle equal to a given angle . 8. A line may be drawn through a given point ...
... perpendicular may be drawn to a given line , either from a point without , or from a point on the line . 7. A line may be drawn , making with a given line an angle equal to a given angle . 8. A line may be drawn through a given point ...
Page 22
... perpendicular to another AB , then will the second line AB be perpendicular to the first DE For , the angles DCA and DCB are right angles , by definition ( D. 12 ) ; and from what has just been proved , the angles ACE and ВСЕ are also ...
... perpendicular to another AB , then will the second line AB be perpendicular to the first DE For , the angles DCA and DCB are right angles , by definition ( D. 12 ) ; and from what has just been proved , the angles ACE and ВСЕ are also ...
Page 23
... 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 angles is equal to four right ...
... 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 angles is equal to four right ...
Page 33
... perpendicular can be drawn to a given straight line . Let A be a given point , and AB no a perpendicular to DE : then other perpendicular to DE be drawn from A. D B F For , suppose a second perpendicular AC to be drawn . Prolong AB till ...
... perpendicular can be drawn to a given straight line . Let A be a given point , and AB no a perpendicular to DE : then other perpendicular to DE be drawn from A. D B F For , suppose a second perpendicular AC to be drawn . Prolong AB till ...
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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