Elements of Geometry and Trigonometry |
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Page 22
... Hence , the 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 ...
... Hence , the 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 ...
Page 23
... Hence , the sum of the given angles is equal to four right angles . 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 ...
... Hence , the sum of the given angles is equal to four right angles . 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 ...
Page 29
... Hence , in each case , BC is greater than EF ; which was to be proved . Conversely : If in two triangles ABC and DEF , the side AB is equal to the side DE , the side AC to DF , and BU greater than EF , then will the angle BAC be greater ...
... Hence , in each case , BC is greater than EF ; which was to be proved . Conversely : If in two triangles ABC and DEF , the side AB is equal to the side DE , the side AC to DF , and BU greater than EF , then will the angle BAC be greater ...
Page 31
... hence , the triangles BAD , and DAC , have the three sides of the one equal to those of the other , each to each ; therefore , by the last Proposition , the angle B is equal to the angle C ; which was to be proved . B- D Cor . 1. An ...
... hence , the triangles BAD , and DAC , have the three sides of the one equal to those of the other , each to each ; therefore , by the last Proposition , the angle B is equal to the angle C ; which was to be proved . B- D Cor . 1. An ...
Page 32
... hence , the hypothesis that AB and AC are unequal , is false . They must , therefore , be equal ; which was to be proved . Cor . An equiangular triangle is equilateral . PROPOSITION XIII . THEOREM . In any triangle , the greater side is ...
... hence , the hypothesis that AB and AC are unequal , is false . They must , therefore , be equal ; which was to be proved . Cor . An equiangular triangle is equilateral . PROPOSITION XIII . THEOREM . In any triangle , the greater side is ...
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Common terms and phrases
ABCD ACē 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