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 19
... angle may be bisected . 6. A 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 may be bisected . 6. A 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 ...
Page 20
... angles ; which was to be proved . Cor . 1. If one of the angles DCA , DCB , 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 ...
... angles ; which was to be proved . Cor . 1. If one of the angles DCA , DCB , 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 ...
Page 26
... angle C is equal to the angle F , the side CA will take the Now , the vertex A being at the same time direction FD ... given lines may re- present the sides of a triangle , the sum of 26 GEOMETRY .
... angle C is equal to the angle F , the side CA will take the Now , the vertex A being at the same time direction FD ... 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 t a given straight line . Let A be a given point , and AB a ... angle : hence , FCB must also be a right angle , and consequently , the line ACF must be a straight line ( P. IV . ) . But ...
... given point only one perpendicular can be drawn t a given straight line . Let A be a given point , and AB a ... angle : hence , FCB must also be a right angle , and consequently , the line ACF must be a straight line ( P. IV . ) . But ...
Page 44
... angles ( P. I. , C. 2 ) ; consequently , the sum of the three angles of the triangle , is equal to two right angles ( A. 1 ) ; which was to be proved . Cor . 1. Two angles of a triangle being given , the third will be found by ...
... angles ( P. I. , C. 2 ) ; consequently , the sum of the three angles of the triangle , is equal to two right angles ( A. 1 ) ; which was to be proved . Cor . 1. Two angles of a triangle being given , the third will be found by ...
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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