Elements of Geometry and Trigonometry |
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Page 32
... hence the two triangles are equal ( Prop . VI . ) ; therefore the side AB , opposite the an- gle ADB , is equal to the side DC , opposite the equal angle DBC ; and the third sides AD , BC , are equal : hence the op- posite sides of a ...
... hence the two triangles are equal ( Prop . VI . ) ; therefore the side AB , opposite the an- gle ADB , is equal to the side DC , opposite the equal angle DBC ; and the third sides AD , BC , are equal : hence the op- posite sides of a ...
Page 33
... hence the figure ABCD is a parallelogram . PROPOSITION XXXI . THEOREM . The two diagonals of a parallelogram divide ... hence those triangles are equal ( Prop . VI . ) ; hence , AE , the side opposite the angle ADE , is equal to EC ...
... hence the figure ABCD is a parallelogram . PROPOSITION XXXI . THEOREM . The two diagonals of a parallelogram divide ... hence those triangles are equal ( Prop . VI . ) ; hence , AE , the side opposite the angle ADE , is equal to EC ...
Page 38
... hence , M ± N : M :: P ± Q : P. PROPOSITION VII . THEOREM . Equimultiples of any two quantities , have the same ... hence , m . M × n . Q = n . N × m . 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 . M × n . Q = n . N × m . 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 ...
Page 45
... hence , AD is equal to DB ( Book I. Prop . XVII . ) . Again , since AD , DB , are equal , CG is a perpendicular erected from the mid- A H dle of AB ; hence every point of this perpendicular must be equally distant from its two ...
... hence , AD is equal to DB ( Book I. Prop . XVII . ) . Again , since AD , DB , are equal , CG is a perpendicular erected from the mid- A H dle of AB ; hence every point of this perpendicular must be equally distant from its two ...
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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 consequently convex surface cylinder diagonal diameter dicular distance draw drawn equal angles equally distant equation equiangular equivalent figure formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC let fall logarithm measured by half number of sides 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 solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex