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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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Iconographic Encyclopaedia of Science, Literature, and Art, Volume 1

Johann Georg Heck - Encyclopedias and dictionaries - 1851 - 712 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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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1852 - 436 pages
...by half the arc BCD, 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 (P. 17, S. 2). PROPOSITION XIX. THEOEEM. The angle formed by two chords, which intersect each other,...
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Elements of Geometry and Trigonometry: With Applications in Mensuration

Charles Davies - Geometry - 1886 - 340 pages
...DAB by half the arc BD (Th. viii) : hence the two arcs AC and BD are themselves equal. V THEOREM X1V. 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 AC any chord. From A, the point...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1854 - 436 pages
...by half the arc BCD, 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 (p. 17, s. 2). PROPOSITION XIX. THEOREM. The angle, formed by two chords, which intersect each other,...
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Elements of Geometry and Trigonometry: With Applications in Mensuration

Charles Davies - Geometry - 1855 - 340 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,...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1857 - 242 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,...half the circumference ; hence their sum is equal to twc right angles. -. PROPOSITION XVI. THEOREM. The angle formed by a tangent and a chord, is measured...
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Elements of Geometry and Trigonometry from the Works of A. M. Legendre ...

Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 442 pages
...by half the arc BCD, 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 (p. 17, s. 2). PROPOSITION x1x. THEOREM. The angle formed by two chords, which intersect each other,...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1858 - 256 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,...BAC, BEC, taken together, are measured by half the "Jrcumference ; hence their sum is equal to twe right angles. PROPOSITION XVI. THEOREM. The angle formed...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1860 - 246 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,...angle formed by a tangent and a chord, is measured bi, half the arc included between its sides. Let the straight line BE touch the circumTerence ACDF...
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Iconographic Encyclopaedia of Science, Literature & Art, Volume 1

Johann Georg Heck - Encyclopedias and dictionaries - 1860 - 332 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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