Elements of Geometry and Trigonometry |
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Page 21
... proposition just demonstrated , is equal to two right angles . DEFINITIONS . If two straight lines intersect each other , they form four angles about the point of intersection , which have received different names , with respect to each ...
... proposition just demonstrated , is equal to two right angles . DEFINITIONS . If two straight lines intersect each other , they form four angles about the point of intersection , which have received different names , with respect to each ...
Page 22
... proposition is 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 ...
... proposition is 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 ...
Page 23
... PROPOSITION III . THEOREM . If two straight lines have two points in common , they will coincide throughout their whole extent , and form one and the same line . Let A and B be two points common to two lines : then will the lines ...
... PROPOSITION III . THEOREM . If two straight lines have two points in common , they will coincide throughout their whole extent , and form one and the same line . Let A and B be two points common to two lines : then will the lines ...
Page 24
... 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 triangles ABC and ...
... 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 triangles ABC and ...
Page 27
... PROPOSITION VIII . THEOREM . If from any point within a triangle two straight lines be drawn to the extremities of any side , their sum will be less than that of the two remaining sides of the triangle . A Let be any point within the ...
... PROPOSITION VIII . THEOREM . If from any point within a triangle two straight lines be drawn to the extremities of any side , their sum will be less than that of the two remaining sides of the triangle . A Let be any point within 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