Elements of Geometry and Trigonometry |
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Page 40
... proportional , their squares or cubes will Let then will and For , or , and also be proportional . MN : P : Q , M2 : N2 : P2 : Q2 M3 N3 :: P3 : Q3 MxQ = NxP , since M : N :: P : Q - M2x Q2 N2x P2 , by squaring both members , M3 × Q3 ...
... proportional , their squares or cubes will Let then will and For , or , and also be proportional . MN : P : Q , M2 : N2 : P2 : Q2 M3 N3 :: P3 : Q3 MxQ = NxP , since M : N :: P : Q - M2x Q2 N2x P2 , by squaring both members , M3 × Q3 ...
Page 53
... proportional ( Book II . Prop . IV . ) ; and thus we find the angle ACD : angle ACI :: arc AO : arc AI . But the arc AO is greater than the arc AI ; hence , if this proportion is true , the angle ACD must be greater than the angle ACI ...
... proportional ( Book II . Prop . IV . ) ; and thus we find the angle ACD : angle ACI :: arc AO : arc AI . But the arc AO is greater than the arc AI ; hence , if this proportion is true , the angle ACD must be greater than the angle ACI ...
Page 54
... proportional to their angles ; hence , two sectors ACB , ACD , taken in the same circle , or in equal circles , are to each other as the arcs AB , AD , the bases of those sectors . It is hence evident that the arcs of the circle , which ...
... proportional to their angles ; hence , two sectors ACB , ACD , taken in the same circle , or in equal circles , are to each other as the arcs AB , AD , the bases of those sectors . It is hence evident that the arcs of the circle , which ...
Page 68
... proportional . 2. Any two sides , or any two angles , which have like po- sitions in two similar figures , are called homologous sides or angles . A 3. In two different circles , similar arcs , sectors , or segments , are those which ...
... proportional . 2. Any two sides , or any two angles , which have like po- sitions in two similar figures , are called homologous sides or angles . A 3. In two different circles , similar arcs , sectors , or segments , are those which ...
Page 71
... proportional ( Book II . Prop . IV . ) ; and we find AIKD AEFD :: AI AO . But AO is greater than AI ; hence , if this proportion is cor- rect , the rectangle AEFD must be greater than AIKD : on the contrary , however , it is less ...
... proportional ( Book II . Prop . IV . ) ; and we find AIKD AEFD :: AI AO . But AO is greater than AI ; hence , if this proportion is cor- rect , the rectangle AEFD must be greater than AIKD : on the contrary , however , it is less ...
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Common terms and phrases
adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone convex surface Cosine cylinder diagonal diameter dicular distance divided draw drawn 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 number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular perpendicular let fall 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 Cotang slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex