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" BEC, taken together, are measured by half the circumference ; hence their sum is equal to two right angles. "
Elements of Geometry, Conic Sections, and Plane Trigonometry - Page 64
by Elias Loomis - 1877 - 443 pages
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1822 - 367 pages
...measured by half the arc BAD ; hence the two angles BAD, BCD, taken together, are measured by the half of the circumference ; hence their sum is equal to two right angles. PROPOSITION XIX. THEOREM. The angle B AC, formed by a tangent and a chord, is measured by the half of the arc AMDC,...
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1828 - 316 pages
...measured by the half of the circumference ; hence their sum is equal to two right angles. THEOREM. 131. The angle formed by a tangent and a chord, is measured by the half of the arc included between its sides. Let BE be the tangent and AC the chord. From A, the...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1836 - 359 pages
...that is, by half the difference of BEC and EC, or half the difference of EEC and DF. PROPOSITION XXI. THEOREM. The angle formed by a tangent and a chord, is measured by half of the arc included between its sides. Let BE be the tangent, and AC the chord. From A, the point of...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1837 - 359 pages
...by half the arc BAD ; hence the two angles BAD, BCD, ta* ken together, are measured by the half of the circumference ; hence their sum is equal to two right angles. PROPOSITION XIX. THEOREM. The angle formed by two chords, which intersect each other, is measured by half the sum...
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Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...

Nathan Scholfield - 1845 - 894 pages
...by half the arc BAD; hence the two angles BAD, BCD, ta- _ ken together, are measured by the half of the circumference ; hence their sum is equal to two right angles. PROPOSITION XX. THEOREM. The angle formed by two chords, which intersect ench other, is measured by half (he sum...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1849 - 252 pages
...4. The opposite angles of an inscribed quadrilateral, ABEC, are together equal to two right angles; for the angle BAC is measured by half the arc BEC, and the angle BEG is measured by half the arc BAC; therefore the two angles BAC, BEC, taken together, are measured...
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Elements of Geometry and Trigonometry Translated from the French of A.M ...

Charles Davies - Trigonometry - 1849 - 384 pages
...measured by half the arc BAD ; hence the two angles BAD, BCD, taken together, are measured by the half of the circumference ; hence their sum is equal to two right angles. PROPOSITION XIX. THEOREM. Let AB, CD, be two chords intersecting each other at E: then will the angle AEC, or DEB,...
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Elementary Geometry: With Applications in Mensuration

Charles Davies - Geometry - 1850 - 216 pages
...DAB by half the arc BD (Th. viii) : hence, the two arcs AC and BD are themselves equal. THEOREM XIV. The angle formed by a tangent and a chord, is measured by halj the arc of the chord. Let BAE be tangent to the circle at the point A, and AC any chord. From...
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Elementary Geometry: With Applications in Mensuration

Charles Davies - Geometry - 1850 - 236 pages
...DAB by half the arc BD (Th. viii) : hence, the two arcs AC and BD are themselves equal. THEOREM XIV. The angle formed by a tangent and a chord, is measured by halj the arc of the chord. Let BAE be tangent to the circle at the point A, and AC any chord. From...
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Young Scientist: A Practical Journal for Amateurs, Volume 1

1851 - 716 pages
...half the angle at the centre of the same arc, and is therefore measured by the half of its arc. An angle formed by a tangent and a chord is measured by half the arc included between the tangent and the chord (fig. 73). Inscribed angles resting upon the same or upon similar arcs are...
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