...— Parallelograms on equal bases, and between the same parallels, are equal in area. 10. Theorem.— The angle formed by a tangent and a chord is measured by one-half the intercepted arc. NATURAL PHILOSOPHY. 1. Define specific gravity; how is it ascertained?...

...by half the circumference; hence their sum is equal to two right angles. PROPOSITION XVI. THEOREM. The angle formed by a tangent and a chord is measured by half the arc included between its sides. Let the straight line BE touch the circumference ACDF in the point A, and...

...by half the circumference; hence their sum is equal to two right angles. PROPOSITION XVI. THEOREM. The angle formed by a tangent and a chord is measured by half tlie arc included between its sides. Let the straight line BE touch the circumference ACDF in the point...

...inscribed angle is measured -by. half its intercepted arc. Ww^ 2Q3 . (E^ nL 2Q . Cv^ IL 57^ 26, An angle formed by a tangent and a chord is measured by half the intercepted arc. Ww. 209 ; (En. III. 32 ; Cv. II. 62). 27, An angle formed by two chords, intersecting...

...COR. 4. — Any angle inscribed in a segment greater than a semicircle is acute. THEOREM XV. 211. Any angle formed by a tangent and a chord is measured by half the intercepted arc. Let the Z. ABD be formed by the tangent CD and the chord AB. To prom that Z. ABD is...

...then the common tangent point C is in the line BD produced, and the chord CB = CD+BD. The angle OAD, formed by a tangent and a chord, is measured by half the arc ACD ; hence, R sin OAD = R sin IAD = \AD (see Legendrc, Trig. Arts. 64 and 30) ; hence, AD = 2R sin...

...semicircle is acute, and every angle inscribed in a segment less than a semicircle is obtuse. 103. Theorem. The angle formed by a tangent and a chord is measured by half the intercepted arc. 104. Theorem. An angle which has its vertex within the circle is measured by half...

...— a Since tan v = — tan |, v = JT — | by trigonometry. In the figure (see next page), PTO being formed by a tangent and a chord, is measured by half the arc PT, and therefore is equal to |. PTA, then, is equal to K, and the line PT is a normal. Hence the normal...

...semicircle is acute, and every angle inscribed in a segment less than a semicircle is obtuse. 103. Theorem. The angle formed by a tangent and a chord is measured by half the intercepted arc. 104. Theorem. An angle which has its vertex within the circle is measured by half...

...two secants is measured by half the difference of the included arcs. Proposition XXI. A Theorem. 184. The angle formed by a tangent and a chord is measured by half the intercepted arc. Proposition XXII. A Theorem. 185. An angle formed by two tangents is measured by half...