 | Nathan Scholfield - 1845 - 894 sider
...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,... | |
 | Elias Loomis - 1849 - 252 sider
...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... | |
 | Johann Georg Heck - 1851 - 712 sider
...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... | |
 | 1851 - 716 sider
...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... | |
 | Charles Davies - 1886 - 340 sider
...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... | |
 | Adrien Marie Legendre - 1852 - 436 sider
...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 - 1854 - 436 sider
...OA*=oOCxOD. For, drawing AD and AC, the triangles DAO, CAO, have the angle O common ; also, the angle OAD, formed by a tangent and a chord, is measured by half the arc AD (B. 1n., p. 21) ; and the angle C has the same measure (B. III., p. 18) ; hence, the angle OAD—... | |
 | Adrien Marie Legendre, Charles Davies - 1857 - 442 sider
...OD. For, drawing AD and AC, the triangles DA 0, CA O, have the angle 0 common ; also, the angle OAD, formed by a tangent and a chord, is measured by half the arc AD (B. 1n., p. 21) ; and the angle C has the same measure (B. III., P. 18) ; hence, the angle OAD=... | |
 | Elias Loomis - 1858 - 256 sider
...the triangles ABD and ABC are similar ; because they have the angle A in common ; also, the angle ABD formed by a tangent and a chord is measured by half the arc BD (Prop. XVI., B. III.) ; and the angle C is measured by half the same arc, therefore the angle ABD... | |
 | Johann Georg Heck - 1860 - 332 sider
...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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The angle formed by a tangent and a chord is measured by half the intercepted arc. 
