Elements of Geometry and Trigonometry |
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Page 20
... shown that the angle E is equal to B , and the angle F to C : hence the two triangles are equal ( Prop . VI . Sch . ) . Scholium . It may be observed that the equal angles lie op- posite the equal sides : thus , the equal angles D and A ...
... shown that the angle E is equal to B , and the angle F to C : hence the two triangles are equal ( Prop . VI . Sch . ) . Scholium . It may be observed that the equal angles lie op- posite the equal sides : thus , the equal angles D and A ...
Page 40
... shown that like powers or roots of proportional quantities are proportionals . PROPOSITION XIII . THEOREM . If there be two sets of proportional quantities , the products of the corresponding terms will be proportional . Let and then ...
... shown that like powers or roots of proportional quantities are proportionals . PROPOSITION XIII . THEOREM . If there be two sets of proportional quantities , the products of the corresponding terms will be proportional . Let and then ...
Page 46
... 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 . For , if there were a second circumference passing ...
... 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 . For , if there were a second circumference passing ...
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 51
... shown , we shall have AI = DE : but , by hypothesis , AB is equal to DE ; hence AI must be equal to AB , or a part to the whole , which is absurd ( Ax . 8. ) : hence , the angle ACB is equal to DCE . PROPOSITION XVI . THEOREM . In the ...
... shown , we shall have AI = DE : but , by hypothesis , AB is equal to DE ; hence AI must be equal to AB , or a part to the whole , which is absurd ( Ax . 8. ) : hence , the angle ACB is equal to DCE . PROPOSITION XVI . THEOREM . In the ...
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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