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" The angle formed by a tangent and a chord is measured by half the intercepted arc. "
Elements of Geometry and Trigonometry: With Applications in Mensuration - Page 49
by Charles Davies - 1886 - 324 pages
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1828 - 346 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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The Mechanics' Magazine, Museum, Register, Journal, and Gazette, Volume 12

Industrial arts - 1830 - 522 pages
...is the sine of the proposed arc AB, to the radius OA or OB. Also, since the angle included between a tangent and a chord, is measured by half the arc of that chord (Geom. Hutton's Course, th. 48.) therefore the angle 4AB=ABC (by the parallels Ab, CB,)...
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Iron: An Illustrated Weekly Journal for Iron and Steel ..., Volume 12

Perry Fairfax Nursey - Industrial arts - 1830
...is the sine of the proposed arc ЛВ, to the radius OA or OB. Also, since the angle included between a tangent and a chord, is measured by half the arc of that chord (Georn. Hutton's Course, th. 48.) therefore the angle frAB=t=ABC (by the parallels Ai, CB,)...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1836 - 359 pages
...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 plane (solid) geometry (Higher geometry) and trigonometry (and ...

Nathan Scholfield - 1845 - 896 pages
...those arcs, and also that either of them is measured by half of that sum. 73 PROPOSITION XXr. THEOREM. The angle formed by a tangent and a chord is measured by half the arc included between its sides. Let BE be the tangent, and AC the chord. From A, the point of contact,...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1849 - 252 pages
...by half the circumference ; hence their sum is equal to two right angles. PROPOSITION XVI. THEOREM. The angle formed by a tangent and a chord, is measured by half the arc included between its sides. Let the straight line BE touch the circumference ACDF in the point A, and...
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Elementary Geometry: With Applications in Mensuration

Charles Davies - Geometry - 1850 - 218 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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Iconographic Encyclopaedia of Science, Literature, and Art, Volume 1

Johann Georg Heck - Encyclopedias and dictionaries - 1851 - 714 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...
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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...
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