Elements of Geometry and Trigonometry |
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Page 29
... hence , the angle DEF is equal to BAC ( Ax . 1. ) . Scholium . The restriction of this proposition to the case where the side EF lies in the same direction with AC , and ED in the same direction with AB , is necessary , because if FE ...
... hence , the angle DEF is equal to BAC ( Ax . 1. ) . Scholium . The restriction of this proposition to the case where the side EF lies in the same direction with AC , and ED in the same direction with AB , is necessary , because if FE ...
Page 31
... hence , when a pentagon is equiangular , each angle is equal to the fifth part of six right angles , or to of one right angle . Cor . 3. The sum of the angles of a hexagon is equal to 2 × ( 6—2 , ) or eight right angles ; hence in the ...
... hence , when a pentagon is equiangular , each angle is equal to the fifth part of six right angles , or to of one right angle . Cor . 3. The sum of the angles of a hexagon is equal to 2 × ( 6—2 , ) or eight right angles ; hence in the ...
Page 33
... hence those triangles are equal ( Prop . VI . ) ; hence , AE , the side opposite the angle ADE , is equal to EC , opposite EBC ; hence also DE is equal to EB . Scholium . In the case of the rhombus , the sides AB , BC , being equal ...
... hence those triangles are equal ( Prop . VI . ) ; hence , AE , the side opposite the angle ADE , is equal to EC , opposite EBC ; hence also DE is equal to EB . Scholium . In the case of the rhombus , the sides AB , BC , being equal ...
Page 38
... hence , M ± N : M :: P + Q : P. PROPOSITION VII . THEOREM . Equimultiples of any two quantities , have the same ... hence , m . Mxn . Q = n . Nxm . P , by multiplying both members of the equation by mxn . But m . M and n . Q , may be ...
... hence , M ± N : M :: P + Q : P. PROPOSITION VII . THEOREM . Equimultiples of any two quantities , have the same ... hence , m . Mxn . Q = n . Nxm . P , by multiplying both members of the equation by mxn . But m . M and n . Q , may be ...
Page 44
... hence , the point D will fall on G ; therefore , the chord AD is equal to the chord EG . Conversely , supposing again the radii AC , EO , to be equal , if the chord AD is equal to the chord EG , the arcs AMD , ENG will also be equal ...
... hence , the point D will fall on G ; therefore , the chord AD is equal to the chord EG . Conversely , supposing again the radii AC , EO , to be equal , if the chord AD is equal to the chord EG , the arcs AMD , ENG will also be equal ...
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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