 | Charles Davies - Geometry - 1854 - 436 pages
...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—... | |
 | 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... | |
 | Elias Loomis - Conic sections - 1857 - 242 pages
...triangles ABD and ABC are similar ; because they B 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... | |
 | Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 442 pages
...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 - Conic sections - 1858 - 256 pages
...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... | |
 | 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... | |
 | Benjamin Greenleaf - Geometry - 1861 - 638 pages
...AEG, is measured by half the sum of the intercepted arcs DB and AC , PROPOSITION XX. — THEOREM. 206. The angle formed by a tangent and a chord is measured...the tangent BE form, with the chord AC, the angle BAG; then BAG is measured by half the arc AM C. From A, the point of contact, draw the diameter AD.... | |
 | Benjamin Greenleaf - Geometry - 1862 - 518 pages
...EC, is measured by half the sum of the intercepted arcs DB and AC PROPOSITION XX. — THEOREM. 206. The angle formed by a tangent and a chord is measured...the tangent BE form, with the chord AC, the angle BAG; then BAC is measured by half the arc AMC. From A, the point of contact, draw the diameter AD.... | |
 | Benjamin Greenleaf - Geometry - 1862 - 532 pages
...intercepted arcs DB and А С В PROPOSITION XX. — THEOREM. 206. The angle formed by a tangent and a chard is measured by half the intercepted arc. Let the tangent BE form, with the chord AC, the angle В А С ; then BAG is measured by half the arc A MC. From A, the point of contact, draw the diameter... | |
 | Benjamin Greenleaf - Geometry - 1863 - 502 pages
...AEC, is measured by half the sum of the intercepted arcs DB and AC PROPOSITION XX. — THEOREM. 206. The angle formed by a tangent and a chord is measured...the angle BAC; then BAC is measured by half the arc AMC. From A, the point of contact, draw the diameter AD. The angle BAD is a right angle (Prop. X.),... | |
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The angle formed by a tangent and a chord is measured by half the intercepted arc. 
