Elements of Geometry and Trigonometry |
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Page 38
... means of a proportion : hence , M ± N : M :: P + Q : P. PROPOSITION VII . THEOREM . Equimultiples of any two quantities , have the same ratio as the quantities themselves . Let M and N be any two quantities , and m any integral number ...
... means of a proportion : hence , M ± N : M :: P + Q : P. PROPOSITION VII . THEOREM . Equimultiples of any two quantities , have the same ratio as the quantities themselves . Let M and N be any two quantities , and m any integral number ...
Page 67
... means of it , their ratio in numbers . Let A and B be the given an- gles . D E B With equal radii describe the arcs CD , EF , to serve as mea- sures for the angles : proceed afterwards in the comparison of the arcs CD , EF , as in the ...
... means of it , their ratio in numbers . Let A and B be the given an- gles . D E B With equal radii describe the arcs CD , EF , to serve as mea- sures for the angles : proceed afterwards in the comparison of the arcs CD , EF , as in the ...
Page 73
... means the same thing as their rectangle , and this expression has passed into arithmetic , where it serves to designate the product of two unequal numbers , the expression square being employed to designate the product of a number ...
... means the same thing as their rectangle , and this expression has passed into arithmetic , where it serves to designate the product of two unequal numbers , the expression square being employed to designate the product of a number ...
Page 88
... mean propor- tional between the hypothenuse and the adjacent segment . 3d . The perpendicular will be a mean proportional between the two segments of the hypothenuse . Let BAC be a right angled triangle , and AD perpendicular to the ...
... mean propor- tional between the hypothenuse and the adjacent segment . 3d . The perpendicular will be a mean proportional between the two segments of the hypothenuse . Let BAC be a right angled triangle , and AD perpendicular to the ...
Page 89
... mean proportional between the segments BD , DC , of the hypothenuse . Scholium . Since BD : AB :: AB BC , the product of the extremes will be equal to that of the means , or AB2 = BD.BC . For the same reason we have AC2 = DC.BC ...
... mean proportional between the segments BD , DC , of the hypothenuse . Scholium . Since BD : AB :: AB BC , the product of the extremes will be equal to that of the means , or AB2 = BD.BC . For the same reason we have AC2 = DC.BC ...
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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