Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
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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 . 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 . 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` ; as BC , for 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` ; as BC , for 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 a perpendicular to DE : then then can no other perpendicular to to DE be drawn from A. For , suppose a second perpendicular AC to ...
... given point only one 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 ...
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Common terms and phrases
AB² 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