...diameter of that circle, the whole of which is known; and the side CD perpendicular to AD and given. 47. If from one of the angles of a rectangle, a perpendicular be let fall on the diagonal D, and from the point of intersection perpendiculars P,p be let fall on the...

...one of £2,100 in eight months. Find the equated time of one payment, interest being 5 per cent. 3. If from one of the angles of a rectangle a perpendicular be let fall on the diagonal D, and from the point of intersection perpendiculars P, p, be let fall on...

...4, cos — = - = cos — , m 2 3 or m = 3, and the figure is an equilateral triangle. PROBLEM III. If from one of the angles of a rectangle a perpendicular be drawn to its diagonal, and from the point of their intersection lines be drawn perpendicular to the sides which contain the opposite...

...figure can be inscribed, whose area shall be I - I of the area of the former? W Ex. n = 2, n = 4. 3. If from one of the angles of a rectangle a perpendicular be drawn to its diagonal, and from the point of their intersection lines be drawn perpendicular to the sides which contain the opposite...

...similar recH tilineal figure can be inscribed whose area shall equal half that of the original ? 15. If from one of the angles of a rectangle a perpendicular be drawn to its diagonal, and from, the point of their intersection lines be drawn perpendicular to the sides which contain the opposite...

...that our problem includes question 8, No. 1 1, Leybourn's Math. Repository, which reads as follows : If from one of the angles of a rectangle a perpendicular...sides containing the opposite angle, then putting (P,p) for the last perpendiculars, and (D) for the diagonal, Cor. 2. Equation (5) is identical with...

...distance of the observer from the base, the height of the eye being five feet. Am. 99 '874922 feet. 20. If from one of the angles of a rectangle a perpendicular be drawn to its diagonal, and from the point of intersection' with the diagonal lines be drawn perpendicular to the sides which contain...

...cot» C)}], +Б _ /c2+ 4A{cot С + ./(1 + cot' C)} -'Б ~ V e + 4A{cot С - ^/(1 + cot2 C)j ' (12) If from one of the angles of a rectangle a perpendicular...opposite angle, then putting P and p for these last perpen22 2. culars, and D for the diagonal, P3 + p' = D*. Let the angle BAG = 6, then AD sin 0 = DE...

...and shew that they are in harmonic proportion with the area of a regular circumscribed pentagon. 6. If from one of the angles of a rectangle, a perpendicular be let fall on the diagonal d, and from the point of intersection, perpendiculars », a be let fall on...

...another square having its side equal to a given straight line. What are the limits of this line ? 42. If from one of the angles of a rectangle, a perpendicular be drawn to its diagonal d, and from the point of their intersection, lines p, q be drawn perpendicular to the sides which contain...