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 points . 12. The shortest distance from one point to another is measured on the straight line which joins them . 13. Through the same point , only one straight line can be drawn parallel to a given straight line . 1. A straight ...
... given points . 12. The shortest distance from one point to another is measured on the straight line which joins them . 13. Through the same point , only one straight line can be drawn parallel to a given straight line . 1. A straight ...
Page 19
... given straight line an angle equal to a given angle . 8. A straight line may be drawn through a given point , parallel to a given line . NOTE .. In making references , the following abbreviations are employed , viz .: A. for Axiom ; B ...
... given straight line an angle equal to a given angle . 8. A straight line may be drawn through a given point , parallel to a given line . NOTE .. In making references , the following abbreviations are employed , viz .: A. for Axiom ; B ...
Page 20
... , CAD , DAE , EAF , formed about a given point on the same side of a straight line BF , is equal to two right an- gles . For , their sum is equal to D C E B- -F the sum of the angles EAB and EAF ; which 20 GEOMETRY . Propositions,
... , CAD , DAE , EAF , formed about a given point on the same side of a straight line BF , is equal to two right an- gles . For , their sum is equal to D C E B- -F the sum of the angles EAB and EAF ; which 20 GEOMETRY . Propositions,
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 twc 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 twc 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 .
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Common terms and phrases
AB² AC² adjacent angles altitude angle ACB apothem Applying logarithms base and altitude bisect centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec Cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given straight line greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin lower base mantissa mean proportional measured by half number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment semi-circumference side BC similar sine six right slant height sphere spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence