 | Sir Isaac Newton - Curves, Plane - 1863 - 316 pages
...chord of intersection of two consecutive positions of the circle described about that triangle. 9. Tangents are drawn to a circular arc at its middle point, and at its extremities, and the three chords are drawn. Prove that the triangle contained by the three tangents is ultimately... | |
 | Joseph Edwards - Differential calculus - 1886 - 540 pages
...be very small, show that its approximate value is 2 tan CD sin ^| 1 - tan2o> sin2- J. [ICS EXAM.] 6. Tangents are drawn to a circular arc at its middle point and at its extremities. Show that the area of the triangle formed by the chord of the arc and the two tangents at the extremities... | |
 | Joseph Edwards - Mathematics - 1892 - 550 pages
...drawn perpenEDC B dicular to the radius OA. Show that, in the limit, when P moves upto^, NA=AT. 5. Tangents are drawn to a circular arc at its middle point and at its extremities. Show that the area of the triangle formed by the chord of the arc and the two tangents at the extremities... | |
 | Joseph Edwards - Differential calculus - 1896 - 288 pages
...PN is drawn perpendicular to the radius OA. Show that, in the limit when P moves up to A, NA=AT. 5. Tangents are drawn to a circular arc at its middle point and at its extremities ; show that the area of the triangle formed by the chord of the arc and the two tangents at the extremities... | |
 | Isaac Newton - Curves, Plane - 1900 - 320 pages
...therefore, as before, £ satisfies all the con2 -1- x ditions of being a limit of . — — . 5 + ox (3) Tangents are drawn to a circular arc, at its middle point, and at its extremities. Shew that, when the arc diminishes, the area of the triangle formed by the chord of the arc, and the... | |
 | Godfrey Harold Hardy - Calculus - 1908 - 449 pages
...circle, touching it in P, and PN is drawn perpendicular to OA. Show that NAjAT-*~l as P moves up to A. 16. Tangents are drawn to a circular arc at its middle point and its extremities : A is the area of the triangle formed by the chord of the arc and the two tangents... | |
 | Canada. Topographical and Air Survey Bureau - 1908 - 758 pages
...+ 2r + 3r + . . . + nr when n is indefinitely in«'+1 creased, n being any positive number. . 20 2. Tangents are drawn to a circular arc at its middle point and its extremities, and the three chords are drawn. Shew that in the limit, when the arc is indefinitely... | |
 | G. H. Hardy - Mathematics - 2008 - 21 pages
...touching it in T, and TN is drawn perpendicular to OA. Show that NA/AP -*• 1 as P moves up to A. 13. Tangents are drawn to a circular arc at its middle point and its extremities; A is the area of the triangle formed by the chord of the arc and the two tangents... | |
 | 556 pages
...two consecutive positions of AB, and N the foot of the perpendicular from 0 on AB, then AP = NB. 12. Tangents are drawn to a circular arc at its middle...triangle whose vertices are the three points of contact. 13. If POP' be any fixed diameter of an ellipse, and QV any ordinate to this diameter ; and if the... | |
 | 558 pages
...two consecutive positions of AB, and N the foot of the perpendicular from OonAB, then AP = NB. 12. Tangents are drawn to a circular arc at its middle...triangle whose vertices are the three points of contact. 13. If POP' be any fixed diameter of an ellipse, and QV any Ordinate to this diameter ; and if the... | |
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A is the area of the triangle formed by the chord of the arc and the two tangents at the extremities, and A' the area of that formed by the three tangents. 