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 . 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 . Oblique angles are subdivided into two classes , acute angles , and obtuse angles . 14. An ...
Page 19
... perpendicular 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 , making with a given straight line an angle equal to a given angle . 8. A straight line ...
... perpendicular 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 , making with a given straight line an angle equal to a given angle . 8. A straight line ...
Page 33
... perpendicular can be drawn to a given straight line . Let A be a given point , and AB a perpendicular to DE : then can no other perpendicular to DE be drawn from A. 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 a perpendicular to DE : then can no other perpendicular to DE be drawn from A. For , suppose a second perpendicular AC to be drawn . Prolong AB till ...
Page 34
... perpendicular is let fall on the line , and oblique lines are drawn to dif- ferent points of it : 1o . The perpendicular is shorter than any oblique line . 2 ° . Any two oblique lines that meet the given line at points equally distant ...
... perpendicular is let fall on the line , and oblique lines are drawn to dif- ferent points of it : 1o . The perpendicular is shorter than any oblique line . 2 ° . Any two oblique lines that meet the given line at points equally distant ...
Page 35
... perpendicular ; which is im- possible . PROPOSITION XVI . THEOREM . If a perpendicular is drawn to a given straight line at its middle point : 1o . Any point of the perpendicular is equally distant from the extremities of the line : 2 ...
... perpendicular ; which is im- possible . PROPOSITION XVI . THEOREM . If a perpendicular is drawn to a given straight line at its middle point : 1o . Any point of the perpendicular is equally distant from the extremities of the line : 2 ...
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