Elements of Geometry and Trigonometry |
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Page 45
... likewise , that the perpendicular raised from the middle of a chord passes through the centre of the circle , and through the middle of the arc subtended by that chord . For , this perpendicular is the same as the one let fall from the ...
... likewise , that the perpendicular raised from the middle of a chord passes through the centre of the circle , and through the middle of the arc subtended by that chord . For , this perpendicular is the same as the one let fall from the ...
Page 73
... likewise , the geometrical square constructed on a double line is evidently four times greater than the square on a single one ; on a triple line it is nine times great- er , & c . 10 G PROPOSITION V. THEOREM . The area of any ...
... likewise , the geometrical square constructed on a double line is evidently four times greater than the square on a single one ; on a triple line it is nine times great- er , & c . 10 G PROPOSITION V. THEOREM . The area of any ...
Page 79
... likewise the same altitude , are to each other as their bases BD , CD . But these rectangles are equivalent to the squares AH , AI ; there- fore we have AB2 : AC2 :: BD : DC . Hence the squares of the two sides containing the right ...
... likewise the same altitude , are to each other as their bases BD , CD . But these rectangles are equivalent to the squares AH , AI ; there- fore we have AB2 : AC2 :: BD : DC . Hence the squares of the two sides containing the right ...
Page 82
... likewise have OE :: OF : FH , or OE : OF EG : FH . And by reason of the common ratio OE OF , those two proportions give AE CF B : EG :: EG : FH . It may be proved in the G F same manner , that EG : FH :: GB : HD , and so on ; hence the ...
... likewise have OE :: OF : FH , or OE : OF EG : FH . And by reason of the common ratio OE OF , those two proportions give AE CF B : EG :: EG : FH . It may be proved in the G F same manner , that EG : FH :: GB : HD , and so on ; hence the ...
Page 92
... likewise CDE - HIK , & c . Moreover we shall have AB : FG :: BC : GH :: AC : FH :: CD : HI , & c .; hence the two polygons have their angles equal and their sides pro- portional ; consequently they are similar . PROPOSITION XXVII ...
... likewise CDE - HIK , & c . Moreover we shall have AB : FG :: BC : GH :: AC : FH :: CD : HI , & c .; hence the two polygons have their angles equal and their sides pro- portional ; consequently they are similar . PROPOSITION XXVII ...
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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