 | Adrien Marie Legendre - Geometry - 1822 - 394 pages
...which is the same thing, OAZ=OC.OD. For, joining AD and AC, the triangles « OAD, OAC have the angle O common ; also the angle OAD, formed by a tangent and a chord, has for its measure (19. II.) half of the arc AD; and the angleC has the same measure: hence the angle... | |
 | James Bates Thomson - Geometry - 1844 - 268 pages
...secant and its external segment ; that is, GEOMETRY. For, joining AD and AC, the triangles OAD, OAC have the angle 0 common ; also the angle OAD, formed by a tangent and a chord, has for its measure half of the arc AD ; (14. 2 ;) and the angle C has . the same measure : hence the... | |
 | Nathan Scholfield - 1845 - 894 pages
...OC : OA: :OA : OD, or OA"=OC.OD. For, drawing AD and AC, the triangles ° OAD, OAC, have the angle O common; also the angle OAD, formed by a tangent and a chord, has for its measure half of the arc AD (Prop. XXI. B. III.) ; and the angle C has the same measure... | |
 | Elias Loomis - Conic sections - 1849 - 252 pages
...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... | |
 | Charles Davies - Trigonometry - 1849 - 372 pages
...OA : : OA : OD, or OA 2 =OC.OD. For, drawing AD and AC, the triangles O OAD, OAC, have the angle O common; also the angle OAD, formed by a tangent and a chord, has for its measure half of the arc AD (Book III. Prop. XXI.); and the angle C has the same measure... | |
 | 1851 - 716 pages
...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... | |
 | Johann Georg Heck - Encyclopedias and dictionaries - 1851 - 712 pages
...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... | |
 | Adrien Marie Legendre - Geometry - 1852 - 436 pages
...consequently, by half the difference of BEC and DF. C GEOMETKY. PBOPOSITION XXI. THEOEEM. Either of the angles formed by a tangent and a chord, is measured by half the arc included between its sides. Let jRE'.be a tangent, and AC a chord. From JL, the- >x)int. of contact,... | |
 | Charles Davies - Geometry - 1886 - 340 pages
...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... | |
 | Charles Davies - Geometry - 1854 - 436 pages
...OC : OA :: OA : OD, or, OA*=oOCxOD. For, drawing AD and AC, the triangles DAO, CAO, have the angle O common ; also, the angle OAD, formed by a tangent...triangles are similar, and we have the proportion OC : OA : : OA : OD. which gives OZ2 o OCx OD. PROPOSITION XXXI. THEOREM. If either angle of a triangle... | |
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The angle formed by a tangent and a chord is measured by half the intercepted arc. 
