Elements of Geometry and Trigonometry |
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Page 53
... similar , it may be shown that the fourth term of the proportion cannot be less than AD ; hence it is AD itself ; therefore we have Angle ACB angle ACD :: arc AB : arc AD . Cor . Since the angle at the centre of a circle , and the arc ...
... similar , it may be shown that the fourth term of the proportion cannot be less than AD ; hence it is AD itself ; therefore we have Angle ACB angle ACD :: arc AB : arc AD . Cor . Since the angle at the centre of a circle , and the arc ...
Page 68
... similar figures , are called homologous sides or angles . A 3. In two different circles , similar arcs , sectors , or segments , are those which correspond to equal angles at the centre . Thus , if the angles A and O are equal , the arc ...
... similar figures , are called homologous sides or angles . A 3. In two different circles , similar arcs , sectors , or segments , are those which correspond to equal angles at the centre . Thus , if the angles A and O are equal , the arc ...
Page 73
... similar manner , by measuring its sides with the same linear unit ; a second product is thus obtained , and the ratio of the two pro- ducts is the same as that of the rectangles , agreeably to the proposition just demonstrated . For ...
... similar manner , by measuring its sides with the same linear unit ; a second product is thus obtained , and the ratio of the two pro- ducts is the same as that of the rectangles , agreeably to the proposition just demonstrated . For ...
Page 84
... similar when they have their angles equal , each to each , and their homolo- gous sides proportional ( Def . 1. ) ; consequently the equiangu- lar triangles BAC , CED , are two similar figures . Cor . For the similarity of two triangles ...
... similar when they have their angles equal , each to each , and their homolo- gous sides proportional ( Def . 1. ) ; consequently the equiangu- lar triangles BAC , CED , are two similar figures . Cor . For the similarity of two triangles ...
Page 85
... similar . In the two triangles BAC , DEF , suppose we have BC : EF :: AB DE :: AC : DF ; then will the triangles ABC , DEF have their an- gles equal , namely , A = D , B = E , C = F . B C E At the point E , make the angle FEG B , and at ...
... similar . In the two triangles BAC , DEF , suppose we have BC : EF :: AB DE :: AC : DF ; then will the triangles ABC , DEF have their an- gles equal , namely , A = D , B = E , C = F . B C E At the point E , make the angle FEG B , and at ...
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Common terms and phrases
adjacent altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone convex surface cosine cotangent cylinder diagonal diameter dicular distance divided draw drawn equal angles equally distant equations equivalent feet figure find the area formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC logarithm measured by half number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE PROBLEM proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABCDE Scholium secant segment similar sine slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex