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
... given line . POSTULATES . 1. A straight line can be drawn between any two points . 2. A straight line may be prolonged to any length . 3. If two lines are unequal , the length of the less may be laid off on the greater 43 4. A line may ...
... given line . POSTULATES . 1. A straight line can be drawn between any two points . 2. A straight line may be prolonged to any length . 3. If two lines are unequal , the length of the less may be laid off on the greater 43 4. A line may ...
Page 19
... 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 , parallel to a given line . NOTE ...
... 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 , parallel to a given line . NOTE ...
Page 23
... given angles ( A. 9 ) . Hence , the sum of the given angles is equal to four right angles . PROPOSITION III . THEOREM . If two straight lines have two points in common , they will coincide throughout their whole extent , and form one ...
... given angles ( A. 9 ) . Hence , the sum of the given angles is equal to four right angles . PROPOSITION III . THEOREM . If two straight lines have two points in common , they will coincide throughout their whole extent , and form one ...
Page 26
... 5 ) , AC BC < AB ; - that is , the difference between any two sides of a triangle is less than the third side . Scholium . In order that any three given lines may re- present the sides of a triangle , the sum of 26 GEOMETRY .
... 5 ) , AC BC < AB ; - that is , the difference between any two sides of a triangle is less than the third side . Scholium . In order that any three given lines may re- present the sides of a triangle , the sum of 26 GEOMETRY .
Page 33
... given point only one 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 ...
... given point only one 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 ...
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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