 | Charles Hutton - Mathematics - 1811 - 406 pages
...therefore the arcs BD, BF, are equal. . <^ ED • THEOREM THEOREM LVIII. The Angle formed, Within a Circle, by the Intersection of two Chords, is Measured by Half the Sum of the Two Intercepted Arcs. ; . LET the two chords AB, CD, intersect at the point E: then the angle AEC,... | |
 | Charles Hutton - Mathematics - 1816 - 610 pages
...arcs UD, EF, arc equal. q. JE. B. Vol. T. SS THEOREM THEOREM LVIlt The Angle formed, Within a Circle, by the Intersection of two Chords, is Measured by Half the Sum of the Two Intercepted Arcs. LET the two chords AC, CD, intersect at the point E : then the angle ARC, or... | |
 | Nathan Scholfield - 1845 - 894 pages
...half of FDB; that is, by half of DB+DF, or half of DB+AC. Again, as the angle AEC=BKD, and that BED is measured by half the sum of the arcs AC and BD, the two angles are measured by the sum of those arcs ; and also as the sum of the four angles made... | |
 | George Roberts Perkins - Geometry - 1847 - 326 pages
...; therefore the arc BD is equal to BF. PROPOSITION XIII. THEOREM. The angle formed within a circle, by the intersection of two chords, is measured by half the sum of the two intercepted arcs. Let the two chords AB, CD intersect at the point F ; then will the angle AFC,... | |
 | Charles Davies - Geometry - 1850 - 218 pages
...equal, the arcs will be equal : hence DB is equal to BF. THEOREM XVI. The angle formed within a circle by the intersection of two chords, is measured by half the sum of the intercepted arcs. Let the two chords AB and CD intersect each other at the point E : then will the... | |
 | George Roberts Perkins - Geometry - 1850 - 332 pages
...Prop, xvn.) But the angle DBA, formed by a PROPOSITION XII. THEOREM. The angle formed within a circle, by the intersection of two chords, is measured by half the sum of the two intercepted arcs. Let the two chords AB, CD intersect at the point F; then will the angle AFC,... | |
 | Charles Davies - Geometry - 1850 - 238 pages
...equal, the arcs will be equal : hence DB is equal to BF. THKOREM XVI. The angle formed within a circle by the intersection of two chords, is measured by half the sum of the intercepted arcs. Lot the two chords AB and CD intersect each other at the point E : then will the... | |
 | Charles Davies - Geometry, Descriptive - 1851 - 254 pages
...through the eye, are circles. § 197. PI. 2. Fig. 3. Let the circle to be projected be a small cirole. Through the axis of the circle and the axis of the...equal. The triangles AED and AE'D' have the angle BAD common ; they are consequently equiangular, and have the angle ADE equal to the angle AE'D' : hence,... | |
 | Charles Davies - Geometry - 1855 - 340 pages
...equal, the arcs will be equal : hence DB is equal to BFTHEOREM XVIThe angle formed within a circle by the intersection of two chords, is measured by half the sum of the intercepted arcsLet the two chords AB and CD intersect each other at the point E : then will the angle... | |
 | George Roberts Perkins - Geometry - 1856 - 460 pages
...is, the angle FCB has for its measure one half the included arc CGEB. THEOREM XI. The angle formed ly the intersection of two chords is measured by half the sum of the included arcs. And the angle formed by the intersection of two secants is measured by half the difference... | |
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The angle formed by the intersection of two chords is measured by half the sum of the two intercepted arcs. Let the two chords AB, CD intersect each other at the point E ; then will the angle DEB, or its equal, AEC, be measured by half the two arcs DB... 
