Elements of Geometry and Trigonometry |
From inside the book
Results 6-10 of 77
Page 20
... greater than A , while the sides ED , DF , were equal to BA , AC , each to each , it would fol- low , by the last proposition , that the side EF must be greater than BC ; and if the angle D were less than A , it would follow , that the ...
... greater than A , while the sides ED , DF , were equal to BA , AC , each to each , it would fol- low , by the last proposition , that the side EF must be greater than BC ; and if the angle D were less than A , it would follow , that the ...
Page 21
... greater . Then , take BD equal to AC , and draw CD . Now , in the two triangles BDC , BAC , we have BD - AC , by ... greater side of every triangle is opposite to the greater an- gle ; and conversely , the greater angle is opposite to ...
... greater . Then , take BD equal to AC , and draw CD . Now , in the two triangles BDC , BAC , we have BD - AC , by ... greater side of every triangle is opposite to the greater an- gle ; and conversely , the greater angle is opposite to ...
Page 24
... greater . On BC take BG = EF , and draw AG . Then , in the two triangles BAG , DEF , the angles B and E are equal , being right angles , the side BA - ED by hypothesis , and the side BG = EF by construction : consequently , AG = DF ...
... greater . On BC take BG = EF , and draw AG . Then , in the two triangles BAG , DEF , the angles B and E are equal , being right angles , the side BA - ED by hypothesis , and the side BG = EF by construction : consequently , AG = DF ...
Page 31
... greater than two right angles . But to avoid all ambiguity , we shall henceforth limit our reasoning to polygons with salient angles , which might otherwise be named convex polygons . Every convex polygon is such that a straight line ...
... greater than two right angles . But to avoid all ambiguity , we shall henceforth limit our reasoning to polygons with salient angles , which might otherwise be named convex polygons . Every convex polygon is such that a straight line ...
Page 36
... greater or less than Q , the same ratio that M has to N ; that is , let M : N :: P : Q ' ; then Mx N = Px Q ' ( Prop . I. ) : hence , Q ' = Mx N P ; but Q = MxN P ; conse- quently Q = Q ' , and the four quantities are proportional ...
... greater or less than Q , the same ratio that M has to N ; that is , let M : N :: P : Q ' ; then Mx N = Px Q ' ( Prop . I. ) : hence , Q ' = Mx N P ; but Q = MxN P ; conse- quently Q = Q ' , and the four quantities are proportional ...
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Common terms and phrases
adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book centre chord circ circumference circumscribed common cone convex surface Cosine Cotang cylinder diagonal diameter dicular distance draw drawn equal angles equally distant equiangular equivalent figure formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed polygon intersection less Let ABC let fall logarithm measured by half number of sides oblique lines opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE prism proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant secant line segment side BC similar sine solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex