Elements of Geometry and Trigonometry |
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Page 59
Adrien Marie Legendre Charles Davies. Let A be the given point , AB the given line , and IKL the given angle . From the vertex K , as a cen- tre , with any radius , describe the arc IL , terminating in the two sides of the angle ...
Adrien Marie Legendre Charles Davies. Let A be the given point , AB the given line , and IKL the given angle . From the vertex K , as a cen- tre , with any radius , describe the arc IL , terminating in the two sides of the angle ...
Page 60
... angles of a triangle being given , to find the third . Draw the indefinite line DEF ; at any point as E , make the an- gle DEC equal to one of the given angles , and the angle CEH equal to the other : the remaining angle HEF will be the ...
... angles of a triangle being given , to find the third . Draw the indefinite line DEF ; at any point as E , make the an- gle DEC equal to one of the given angles , and the angle CEH equal to the other : the remaining angle HEF will be the ...
Page 65
... angle , is measured by half the arc AKB : hence we have AMB = ABF = EBD = C : hence all the angles in- scribed in the segment AMB are equal to the given angle C. F * Scholium . If the given angle were a right angle BOOK III . 65.
... angle , is measured by half the arc AKB : hence we have AMB = ABF = EBD = C : hence all the angles in- scribed in the segment AMB are equal to the given angle C. F * Scholium . If the given angle were a right angle BOOK III . 65.
Contents
BOOK | 7 |
BOOK III | 41 |
Problems relating to the First and Third Books | 57 |
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adjacent altitude angle ACB ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone consequently convex surface cosine Cotang 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 number of sides opposite parallel parallelogram parallelopipedon pendicular perimeter perpen perpendicular perpendicular let fall plane MN polyedron polygon ABCDE PROBLEM 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