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
... 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 line 2 . A straight line 3. 18 ...
... 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 line 2 . A straight line 3. 18 ...
Page 19
... 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 ... a straight line meet another BOOK I. 19.
... 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 ... a straight line meet another BOOK I. 19.
Page 20
... a right angle , the other must also be a right angle . Cor . 2. The sum of the an- gles BAC , 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 ...
... a right angle , the other must also be a right angle . Cor . 2. The sum of the an- gles BAC , 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 ...
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 ... a straight line meet BOOK I. 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 ... a straight line meet BOOK I. 23.
Page 26
... A being at the same time direction FD . on the lines ED D ( P. III . , C ... straight line AC ( A. 12 ) : hence , the sum of AB and BC is greater than AC ... given lines may re- present the sides of a triangle , the sum of 26 GEOMETRY .
... A being at the same time direction FD . on the lines ED D ( P. III . , C ... straight line AC ( A. 12 ) : hence , the sum of AB and BC is greater than AC ... 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