 | Trinity College (Hartford, Conn.) - 1870 - 1008 pages
...the greater angle; and, conversely, the greater angle is opposite the greater side. :{. Prove that The angle formed by a tangent and a chord is measured by half the arc included between its sides. 4. Prove that If from a point without a circle a tangent and a secant are drawn, the square of the... | |
 | Charles Davies - Geometry - 1870 - 392 pages
...DAB by half the arc BD (Th. viii) : the two arcs AC and BD are themselves equal. hence THEOREM XIV. The angle formed by a tangent and a chord, is measured by half the arc of the chord. Let BAE be tangent to the circle at the point A, and А С any chord. From A, the point... | |
 | Eli Todd Tappan - Geometry - 1873 - 288 pages
...Corollary — All angles inscribed in the same arc are equal, for they have the same measure. 76 226. Theorem — The angle formed by a tangent and a chord is measured by half the intercepted arc. The angle CEI, formed by the tangent AC and the chord EI, is measured by half the... | |
 | Benjamin Greenleaf - Geometry - 1873 - 202 pages
...BAC is measured by half the arc BDC, and the angle B DC is measured by half the arc BAC; BOOK III. measured by half the circumference ; hence their sum is equal to two right angles. THEOREM XI. 165. The angle formed by the intersection of two chords is measured by half the sum of... | |
 | Wisconsin. Department of Public Instruction - Education - 1873 - 458 pages
...Theorem. — 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?... | |
 | Adrien Marie Legendre - Geometry - 1874 - 500 pages
...angle DAB is measured by half the arc DCB, the angle DCB by half the arc DAB : hence, the two angles, taken together, are measured by half the circumference...their sum is equal to two right angles. PROPOSITION XIX. THEOREM. Any angle formed by two chords, which intersect, is mca. sured by half the sum of the... | |
 | Benjamin Greenleaf - Geometry - 1874 - 206 pages
...for the angle BAC is measured by half the arc BDC, and the angle BDC is measured by half the arc BAG; measured by half the circumference ; hence their sum is equal to two right angles. THEOREM XI. 165. The angle formed by the intersection of two chords is measured by half the sum of... | |
 | Wisconsin - Wisconsin - 1874 - 1050 pages
...Theorem. — 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?... | |
 | Charles Scott Venable - 1881 - 380 pages
...half the arc BCD ; and the angle BCD is measured by half the arc BAD ; hence, the two angles BAD, BCD, taken together, are measured by half the circumference ; hence, their sum is equal to two right angles. This corollary may also be conveniently expressed as follows : Every angle, BAC (See Fig., Cor. 1),... | |
 | George Bruce Halsted - Measurement - 1881 - 258 pages
...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... | |
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BEC, taken together, are measured by half the circumference ; hence their sum is equal to two right angles. 
