Elements of Geometry and Trigonometry |
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Page 43
... PROPOSITION IV . THEOREM . In the same circle , or in equal circles , equal arcs are subtended by equal chords ; and , conversely , equal chords subtend equal arcs . Note . When reference is made from one proposition to another , in the ...
... PROPOSITION IV . THEOREM . In the same circle , or in equal circles , equal arcs are subtended by equal chords ; and , conversely , equal chords subtend equal arcs . Note . When reference is made from one proposition to another , in the ...
Page 77
... proposition is equivalent to the algebraical formula , ( a - b ) 2 = a2 - 2ab + b2 . PROPOSITION X. THEOREM . The rectangle contained by the sum and the difference of two lines , is equivalent to the difference of the squares of those ...
... proposition is equivalent to the algebraical formula , ( a - b ) 2 = a2 - 2ab + b2 . PROPOSITION X. THEOREM . The rectangle contained by the sum and the difference of two lines , is equivalent to the difference of the squares of those ...
Page 94
... PROPOSITION XXIX . THEOREM . If from the same point without a circle , two secunts be drawn terminating in the ... proposition , it may be observed , bears a great analogy to the preceding , and differs from it only as the two chords AB ...
... PROPOSITION XXIX . THEOREM . If from the same point without a circle , two secunts be drawn terminating in the ... proposition , it may be observed , bears a great analogy to the preceding , and differs from it only as the two chords AB ...
Contents
BOOK | 7 |
Problems relating to the First and Third Books 57 | 57 |
BOOK IV | 68 |
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Common terms and phrases
adjacent adjacent angles altitude angle ACB angle BAC 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 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 number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE PROBLEM Prop proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant segment similar sine slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line TABLE OF LOGARITHMIC tang tangent THEOREM triangle ABC triangular prism vertex