Elements of Geometry and Trigonometry |
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Page 48
... 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 .
... 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 51
... whole , which is absurd ( Ax . 8. ) : hence , the angle ACB is equal to DCE . PROPOSITION XVI . THEOREM . In the same circle , or in equal circles , if two angles at the centre are to each other in the proportion of two whole numbers ...
... whole , which is absurd ( Ax . 8. ) : hence , the angle ACB is equal to DCE . PROPOSITION XVI . THEOREM . In the same circle , or in equal circles , if two angles at the centre are to each other in the proportion of two whole numbers ...
Page 52
... whole arc AB will be to the whole arc DE , as 7 is to 4. But the same reasoning would evidently apply , if in place of 7 and 4 any numbers whatever were employed ; hence , if the ratio of the angles ACB , DCE , can be expressed in whole ...
... whole arc AB will be to the whole arc DE , as 7 is to 4. But the same reasoning would evidently apply , if in place of 7 and 4 any numbers whatever were employed ; hence , if the ratio of the angles ACB , DCE , can be expressed in whole ...
Page 53
... whole numbers , and by the preceding theorem , we shall have , the angle ACB : angle ACI :: arc AB arc AI . Comparing these two proportions with each other , we see that the antecedents are the same : hence , the conse- quents are ...
... whole numbers , and by the preceding theorem , we shall have , the angle ACB : angle ACI :: arc AB arc AI . Comparing these two proportions with each other , we see that the antecedents are the same : hence , the conse- quents are ...
Page 55
... whole cir- cumference . Cor . 3. Every angle BAC , inscribed in a segment greater than a semicircle , is an acute angle ; for it is measured by half of the arc BOC , less than a semicircumference . And every angle BOC , inscribed in a ...
... whole cir- cumference . Cor . 3. Every angle BAC , inscribed in a segment greater than a semicircle , is an acute angle ; for it is measured by half of the arc BOC , less than a semicircumference . And every angle BOC , inscribed in a ...
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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