Elements of Geometry and Trigonometry |
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Page 57
... diameter AD . The angle BAD is a right angle ( Prop . IX . ) , and is measured by half the semicircumference AMD ; the angle DAC is measured by the half of DC : hence , BAD + DAC , or BAC , is measured by the half of AMD plus the half ...
... diameter AD . The angle BAD is a right angle ( Prop . IX . ) , and is measured by half the semicircumference AMD ; the angle DAC is measured by the half of DC : hence , BAD + DAC , or BAC , is measured by the half of AMD plus the half ...
Page 66
... diameter . PROBLEM XVII . To find the numerical ratio of two given straight lines , these lines being supposed to have a common measure . Let AB and CD be the given lines . From the greater AB cut off a part equal to the less CD , as ...
... diameter . PROBLEM XVII . To find the numerical ratio of two given straight lines , these lines being supposed to have a common measure . Let AB and CD be the given lines . From the greater AB cut off a part equal to the less CD , as ...
Page 90
... diameter BC , the triangle BAC will be right angled at A ( Book III . Prop . B D C XVIII . Cor . 2. ) ; hence , first , the perpendicular AD is a mean proportional between the two segments BD , DC , of the diameter , or what is the same ...
... diameter BC , the triangle BAC will be right angled at A ( Book III . Prop . B D C XVIII . Cor . 2. ) ; hence , first , the perpendicular AD is a mean proportional between the two segments BD , DC , of the diameter , or what is the same ...
Page 96
... diameter of the circum- scribed circle , and the perpendicular let fall upon the third side . In the triangle ABC , let AD be drawn perpendicular to BC ; and let EC be the diameter of the circumscribed circle ; then will AB.AC - AD.CE ...
... diameter of the circum- scribed circle , and the perpendicular let fall upon the third side . In the triangle ABC , let AD be drawn perpendicular to BC ; and let EC be the diameter of the circumscribed circle ; then will AB.AC - AD.CE ...
Page 99
... diameter , describe the semicircle DGF at the point E , erect upon the diameter the perpen- dicular EG meeting the circumfe- rence in G ; EG will be the mean AH proportional required . F E BH For , the perpendicular EG , let fall from a ...
... diameter , describe the semicircle DGF at the point E , erect upon the diameter the perpen- dicular EG meeting the circumfe- rence in G ; EG will be the mean AH proportional required . F E BH For , the perpendicular EG , let fall from a ...
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Common terms and phrases
adjacent altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone convex surface cosine cotangent cylinder diagonal diameter dicular distance divided draw drawn equal angles equally distant equations equivalent feet figure find the area formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC logarithm measured by half number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE PROBLEM proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABCDE Scholium secant segment similar sine slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex