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 20
... 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 of a straight line BF , is ...
... 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 of a straight line BF , is ...
Page 22
... proved . Cor . 1. If one of the angles about C all of the others will be right angles also . each of its adjacent angles will be a right angle ; and from the proposition just demonstrated , its opposite angle will also be a right angle ...
... proved . Cor . 1. If one of the angles about C all of the others will be right angles also . each of its adjacent angles will be a right angle ; and from the proposition just demonstrated , its opposite angle will also be a right angle ...
Page 23
... proved , and then continuing the reasoning until the assumed hypothesis is shown to be false . Its contradictory is thus proved to be true . This method of demonstration is often used in Geometry . PROPOSITION IV . THEOREM . If a ...
... proved , and then continuing the reasoning until the assumed hypothesis is shown to be false . Its contradictory is thus proved to be true . This method of demonstration is often used in Geometry . PROPOSITION IV . THEOREM . If a ...
Page 24
... proved . PROPOSITION V. THEOREM . If two triangles have two sides and the included angle of the one equal to two sides and the included angle of the other , each to each , the triangles will be equal in all their parts . In the ...
... proved . PROPOSITION V. THEOREM . If two triangles have two sides and the included angle of the one equal to two sides and the included angle of the other , each to each , the triangles will be equal in all their parts . In the ...
Page 25
... proved . PROPOSITION VI . THEOREM . If two triangles have two angles and the included side of the one equal to two angles and the included side of the other , each to each , the triangles will be equal in all their parts . triangles In ...
... proved . PROPOSITION VI . THEOREM . If two triangles have two angles and the included side of the one equal to two angles and the included side of the other , each to each , the triangles will be equal in all their parts . triangles In ...
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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