Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
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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 . D B Oblique angles are subdivided into two classes , acute angles , 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 . D B Oblique angles are subdivided into two classes , acute angles , 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 . and DCB are right angles , by For , the angles DCA definition ( D. 12 ) ; and from what has just been proved , the angles ACE and BCE are also ...
... perpendicular to another AB , then will the second line AB be perpendicular to the first DE . and DCB are right angles , by For , the angles DCA definition ( D. 12 ) ; and from what has just been proved , the angles ACE and BCE 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 a perpendicular to DE : then then can no other perpendicular to to DE be drawn from A. For , suppose a second perpendicular AC to be drawn . Prolong ...
... perpendicular can be drawn to a given straight line . Let A be a given point , and AB a perpendicular to DE : then then can no other perpendicular to to DE be drawn from A. For , suppose a second perpendicular AC to be drawn . Prolong ...
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Common terms and phrases
ABĀ² ABCD altitude apothem Applying logarithms centre chord circle circumference cone consequently convex surface cosec Cosine Cotang cylinder demonstrated in Book denote diameter distance divided draw edges Equation feet find the area Find the logarithmic following RULE frustum given angle greater hence homologous hypothenuse included angle inscribed intersection less Let ABC linear units log cot log sin lower base lune mantissa multiplied number of sides opposite parallel parallelogram parallelopipedon perpendicular plane MN polar triangle polyedral angle polyedron principle demonstrated prism proportional PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium segment similar six right slant height solution sphere spherical angle spherical excess spherical polygon spherical triangle square straight line subtracting Tang tangent THEOREM triangle ABC triangular prism upper base vertex volume whence write the following