 | Harvey Goodwin - 1846 - 500 sider
...the directrix in L ; then SB = BK by definition, = SL = 2AS, since AS = AL by definition; PROP. II. The tangent at any point of a parabola bisects the angle between the focal distance and the diameter through the point. Let P be a point in the parabola, Pf a contiguous point... | |
 | William Elwood Byerly - 1879 - 300 sider
...cosPP'F= pp/' P' V cosPP'AS= ^ cosT'PF^ iimit rcps/Wl limit rP^TI cosT'PR P=P[_coaPP'Sj P' = P\_P'N] Art. 162; T'PR= T'PF, and the tangent at any point...question into smaller sectors, of which the sector FPP' in the figure of the last article may be taken as a type. Draw perpendiculars from the extremities... | |
 | William Elwood Byerly - 1880 - 288 sider
...P'N=P'Q. P'M cosPP'F= PP1' cos TPF= iimit fcosPP'jn limit rp^ cosT'PR P'=P[_cosPP'A'J P' = P\_P'N = 1' by Art. 162; .-. T'PR= T'PF, and the tangent at any point...area of the sector of a parabola included between tiuo focal radii. Take points of the parabola between the extremities of the bounding radii, and join... | |
 | Edward Albert Bowser - 1880 - 334 sider
...where the tangent is inclined at an angle of 30° to the axis of x. Ans. 12. Prove that the normal at any point of a parabola bisects the angle between the focal line and. the diameter passing through that point. [See Art. 56.] 13. Prove that the quantity 2p',... | |
 | Rufus B. Howland - 1887 - 76 sider
...triangles DPH and HPF have DP = PF and HP common ; hence they are equal, and the angle DPII equals HPF; or the tangent at any point of a parabola bisects the angle between a line perpendicular to the directrix and a line to the focus, both being drawn from the point of tangency.... | |
 | 1888 - 900 sider
...PQ become the tangent to the parabola at P, then the angle PSZ will become a right angle. PBOP. IV. The tangent at any point of a parabola bisects the angle between the focal distance of the point and the perpendicular from the point on the directrix. Let PZ (fig. 7) be the... | |
 | Royal Military College, Sandhurst - 1890 - 144 sider
...about three-quarters af this paper. Great importance will be attached to accuracy I\ i. Prove that the tangent at any point of a parabola bisects the angle between the focal distance and the perpendicular upon the directrix. If P be a point on the parabola, N the foot of the... | |
 | William Elwood Byerly - 1895 - 298 sider
..._ 'PF^ ii m i t rcosPP'PI limit [P^ 'PR P'= P (_cos PP'S J P' = P |_ P'^ .-. T'PR = T'PF, Art. 162; and the tangent at any point of a parabola bisects...question into smaller sectors, of which the sector FPP' in the figure of the last article may be taken as a type. Draw perpendiculars from the extremities... | |
 | Charles Briot, Bouguet (M., Jean Claude) - 1896 - 598 sider
...tangent is inclined at an angle of 30° to the axis of x. Ana. (lp, pV3). 12. Prove that the normal at any point of a parabola bisects the angle between the focal line and the diameter passing through that point. 13. On a parabola whose latus rectum is 10, a tangent... | |
 | 1907 - 794 sider
...PQ become the tangent to the parabola at P, then the angle PSZ will become a right angle. PROP. IV. The tangent at any point of a parabola bisects the angle between the focal distance of the point and the perpendicular from the point on the directrix. Let PZ (fig. 7) be the... | |
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Art. 162; T'PR= T'PF, and the tangent at any point of a parabola bisects the angle between the focal radius and the diameter through the given point. 164. To find the area of the sector of a parabola included between two focal radii. Take points of the... 
