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 are ...
... 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 are ...
Page 68
... similar figures , are called homologous sides or angles . 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 . 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 équiangu- 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 équiangu- 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 A E At the point E , make the angle FEG = B , and ...
... 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 A E At the point E , make the angle FEG = B , and ...
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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