Elements of Geometry and Trigonometry |
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Page 30
... evident , also , that the sum of all the angles in these triangles does not differ from the sum of all the angles in the polygon : hence the sum of all the angles of the polygon is equal to two right angles , taken as many times as ...
... evident , also , that the sum of all the angles in these triangles does not differ from the sum of all the angles in the polygon : hence the sum of all the angles of the polygon is equal to two right angles , taken as many times as ...
Page 47
... evident that CF is greater than CO , and CO than CI ( Book I. Prop . XV . ) ; therefore , CF is still greater than CI . But CF is equal to CG , because the chords AB , DE , are equal : hence we have CG > CI ; hence of two unequal chords ...
... evident that CF is greater than CO , and CO than CI ( Book I. Prop . XV . ) ; therefore , CF is still greater than CI . But CF is equal to CG , because the chords AB , DE , are equal : hence we have CG > CI ; hence of two unequal chords ...
Page 48
... from what has just been shown , we shall have MH - HP , MK = KP ; and hence the whole arc HMK = HPK . It is farther evident that each of these arcs is a semicircumference . PROPOSITION XI . THEOREM . If two circles cut each 48 GEOMETRY .
... from what has just been shown , we shall have MH - HP , MK = KP ; and hence the whole arc HMK = HPK . It is farther evident that each of these arcs is a semicircumference . PROPOSITION XI . THEOREM . If two circles cut each 48 GEOMETRY .
Page 50
... evident , as before , that they will have the point A common ; they can have no other ; because , if they had , the greater radius AD must be less than the sum of the radius AC and the distanceCD between the centres ( Prop . XII ...
... evident , as before , that they will have the point A common ; they can have no other ; because , if they had , the greater radius AD must be less than the sum of the radius AC and the distanceCD between the centres ( Prop . XII ...
Page 54
... evident that the arcs of the circle , which serve as a measure of the different angles , are proportional to the different sectors , in the same circle , or in equal circles . PROPOSITION XVIII . THEOREM . An inscribed angle is measured ...
... evident that the arcs of the circle , which serve as a measure of the different angles , are proportional to the different sectors , in the same circle , or in equal circles . PROPOSITION XVIII . THEOREM . An inscribed angle is measured ...
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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