| Charles Hutton - Mathematics - 1811 - 406 pages
...because the lines AB, DF, are parallel, the alternate angles D and B are equal (th. 12). But the angle B, formed by a tangent and chord, is measured by half the arc BD (th. 48) ; and the other angle at the circumference D is measured by half the arc BF (th. 49) ;... | |
| Charles Hutton - Mathematics - 1812 - 620 pages
...because the lines AB, DF, are parallel, the alternate angles D ami B are equal (th. 12). But the angle H, formed by a tangent and chord, is measured by half the arc ED (th. 48) ; and the other angle at the circumference D is measured by half the arc BF(th. 49) ; therefore... | |
| Charles Hutton - Mathematics - 1822 - 616 pages
...because the lines AB, DF, are parallel, the alternate angles D and B are equal (tb. 12). But the angle B, formed by a tangent and chord, Is measured by half the arc BD (th. 48) ; and the other angle at the circumference D is measured by half the arc BF (th. 49) ;... | |
| Charles Davies - Geometry, Descriptive - 1840 - 260 pages
...intercepted between the point of contact and the primitive plane is equal to its projection. § 199. PL 3. Fig. 1. At the point of contact conceive a plane...: hence, the triangle EDD' is isosceles, and ED is II i equal to ED'. But DE', in space, is the hypothenuse of a triangle of which DE is the base and... | |
| Charles William Hackley - Geometry - 1847 - 248 pages
...to the tangent at the common point must pass through the center of each. THEOREM XXXVIII. The angle formed by a tangent and chord is measured by half -the arc of that chord. Let AB be a tangent to a circle, and ACB CD a chord drawn from the point of ~7~~ contact... | |
| George Roberts Perkins - Geometry - 1847 - 326 pages
...DF are parallel, the alternate angles DBA and BDF are equal ( B. I, Prop. xvn). But the angle DBA, formed by a tangent and chord, is measured by half the arc BD (B. lll, Prop. vn) ; and its equal angle BDF, being at the circumference, is measured by half the... | |
| George Roberts Perkins - Geometry - 1850 - 332 pages
...(Cor. 1, of this Proposition.) 84 '.•. ELEMENTS OF GEOMETRY. PROPOSITION VI. L , y THEOREM. The angle formed by a tangent and chord is 'measured by half the arc of that chord. Let AB be a tangent, and CD a chord drawn from the point of contact C; then the angle... | |
| Anthony Nesbit - Measurement - 1859 - 494 pages
...Any chords in a circle which are equally distant from the centre are equal to each other. 7. An angle formed by a tangent and chord is measured by half the arc of that chord. 8. An angle at the circumference of a circle, is measured by half the arc that subtends... | |
| Gerardus Beekman Docharty - Geometry - 1867 - 474 pages
...the lines AB, DF, are parallel, the alternate angles D and B are equal (th. 13, BI). But the angle B, formed by a tangent and chord, is measured by half the arc BD (th. 8), and the other angle at the circumference D is measured by half the arc BF (th. 9) ; therefore... | |
| Thomas Hunter - Geometry, Plane - 1878 - 142 pages
...The radius OK bisects the arc AKB. Therefore AK is equal to KB. PROPOSITION XII.—THEOREM. An angle formed by a tangent and chord is measured by half the arc of that chord. The angle EDB beirig a right angle is measured by half the semi-circumference—that... | |
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