Elements of Geometry and Trigonometry |
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Page 41
... passes through the centre , and is terminated on both sides by the circumference , is called a diameter . From the definition of a circle , it follows that all the radii are equal ; that all the diameters are equal also , and each ...
... passes through the centre , and is terminated on both sides by the circumference , is called a diameter . From the definition of a circle , it follows that all the radii are equal ; that all the diameters are equal also , and each ...
Page 45
... passes through two of the points just mentioned , will necessarily pass througli the third , and be perpendicular to the chord . It follows , likewise , that the perpendicular raised from the middle of a chord passes through the centre ...
... passes through two of the points just mentioned , will necessarily pass througli the third , and be perpendicular to the chord . It follows , likewise , that the perpendicular raised from the middle of a chord passes through the centre ...
Page 46
... pass through the three given points A , B , C. We have now shown that one circumference can always be made to pass through three given points , not in the same straight line : we say farther , that but one can be described through them ...
... pass through the three given points A , B , C. We have now shown that one circumference can always be made to pass through three given points , not in the same straight line : we say farther , that but one can be described through them ...
Page 49
... pass through each of the two centres C and D ( Prop . VI . Sch . ) . But no more than one straight line can be drawn through two points ; hence the straight line , which passes through the centres , will bisect the chord at right angles ...
... pass through each of the two centres C and D ( Prop . VI . Sch . ) . But no more than one straight line can be drawn through two points ; hence the straight line , which passes through the centres , will bisect the chord at right angles ...
Page 50
... pass through the point A , are tangent to each other . For , they have only the point A common , and it through the point A , AE be drawn perpendicular to AD , the straight line AE will be a common tangent to all the circles ...
... pass through the point A , are tangent to each other . For , they have only the point A common , and it through the point A , AE be drawn perpendicular to AD , the straight line AE will be a common tangent to all the circles ...
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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