Elements of Geometry and Trigonometry |
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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 uti 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 uti 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 . In the ...
... 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 . In the ...
Page 26
... proved . and are PROPOSITION VII . THEOREM . The sum of any two sides of a triangle is greater than the third side . Let ABC be a triangle : then will the sum of any two sides , as AB , BC , be greater than the third side AC . For , the ...
... proved . and are PROPOSITION VII . THEOREM . The sum of any two sides of a triangle is greater than the third side . Let ABC be a triangle : then will the sum of any two sides , as AB , BC , be greater than the third side AC . For , the ...
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Common terms and phrases
ABCD ACĀ² 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 line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin logarithm lower base mantissa mean proportional measured by half middle point number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROBLEM PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment side BC similar sine slant height sphere spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence