 | Elias Loomis - Conic sections - 1861 - 254 pages
...The opposite angles of an inscribed quadrilateral, ABEC, are together equal to two right angles ; lor the angle BAC is measured by half the arc BEC, and...half the circumference ; hence their sum is equal to right angles. PROPOSITION XVI. THEOREM. The angle formed by a tangent and a chord, is measured half... | |
 | Benjamin Greenleaf - Geometry - 1862 - 518 pages
...half the arc BD C, and the angle BDC is measured by half the arc BAC; hence the two angles BAC, BDC, taken together, are measured by half the circumference ; hence their sum is equal to two right angles. 7 B PROPOSITION XIX. — THEOREM. 205. The angle formed by the intersection of two chords is measured... | |
 | Benjamin Greenleaf - Geometry - 1861 - 638 pages
...AEG, is measured by half the sum of the intercepted arcs DB and AC , PROPOSITION XX. — THEOREM. 206. The angle formed by a tangent and a chord is measured by half the intercepted arc. Let the tangent BE form, with the chord AC, the angle BAG; then BAG is measured by... | |
 | Benjamin Greenleaf - Geometry - 1863 - 502 pages
...half the arc BDC, and the angle BDC is measured by half the arc BAC; hence the two angles BAC, BDC, taken together, are measured by half the circumference;...their sum is equal to two right angles. PROPOSITION XIX. — THEOREM. 205. The angle formed by the intersection of two chords is measured by half the sum... | |
 | Benjamin Greenleaf - Geometry - 1863 - 504 pages
...half the arc BD C, and the angle BD C is measured by half the arc BAC; hence the two angles BAC, BDC, taken together, are measured by half the circumference ; hence their sum is equal to two right angles. ELEMENTS OF GEOMETRY. PROPOSITION XIX. — THEOREM. 205. The angle formed by the intersection of two... | |
 | Eli Todd Tappan - Geometry, Modern - 1864 - 288 pages
...angles inscribed in the same arc are equal, for they have the same measure. ELEMENTS OF GEOMETRY. 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 AG and the chord El, is measured by half the... | |
 | C. Davies - 1867 - 342 pages
...DAB by half the arc BD (Th- viii) : hence the two arcs AC and BD are themselves equalTHEOREM XIVThe angle formed by a tangent and a chord, is measured by half the arc of the chordLet BAE be tangent to the circle at the point A, and AC any chordFrom A, the point of contact,... | |
 | Eli Todd Tappan - Geometry - 1868 - 432 pages
...Corollary — All angles inscribed in the same arc are equal, for they have the same measure. 76 *-*'ilf. 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 El, is measured by half the... | |
 | Eli Todd Tappan - Geometry - 1868 - 444 pages
...than a semi-circumference, the angle is obtuse. If the arc is greater, the angle is acute. 76 226. Theorem — The angle formed by a tangent and a chord is measured by half (he intercepted arc. The angle CEI, formed by the tangent AC and the chord EI, is measured by half... | |
 | Benjamin Greenleaf - Geometry - 1868 - 340 pages
...EC, is measured by half the sum of the intercepted arcs DB and AC PROPOSITION XX. — THEOREM. 206. The angle formed by a tangent and a chord is measured by half the intercepted arc. Let the tangent BE form, with the chord AC, the angle BAC; then BAC is measured by... | |
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BEC, taken together, are measured by half the circumference ; hence their sum is equal to two right angles. 
