 | Euclid - Geometry - 1890 - 442 pages
...A 8 are reciprocally propl. .-. A : B = X : Y ; Proposition 17. THEOREMS — (a) If three straight lines are proportional the rectangle contained by the extremes is equal to the square on the mean : 264 B Let A, X, B be three st. lines such that A : X = X : B. Place them so that... | |
 | Euclid - Geometry - 1892 - 460 pages
...that is, AB : CD :: CL : AK; .'. AB : CD :: EF : GH. QE ri. PROPOSITION 17. THEOEEM. If three straight lines are proportional the rectangle contained by the extremes is equal to the squa/re on the mean: Conversely, if the rectangle contained by the extremes is equal to the square... | |
 | Henry Martyn Taylor - 1893 - 486 pages
...area. Wherefore, if two triangles &c. PROPOSITION 16. PART 1. If four straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means. Let the straight lines AB, CD, EF, GH be proportionals, so that AB is to CD as EF to GH: it is required... | |
 | Great Britain. Education Department. Department of Science and Art - 1894 - 894 pages
...sides, produced if necessary, proportionally. . 2. If four straight lines be proportionals, prove that the rectangle contained by the extremes is equal to the rectangle contained by the means. ACB is a straight line : circles are described on AC, CB as diameters. AP is a chord of the first circle,... | |
 | 1895 - 802 pages
...triangle. Apply this proposition to divide a given straight line into five equal parts. 4. If four straight lines are proportional the rectangle contained by...is equal to the rectangle contained by the means. Prove that the rectangle contained by the sides of a right-angled triangle is equal to the rectangln... | |
 | Henry Martyn Taylor - Euclid's Elements - 1895 - 708 pages
...area. Wherefore, if two triangles &c. PROPOSITION 16. PART 1. If four straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means. Let the straight lines AB, CD, EF, GH be proportionals, so that AB is to CD as EF to GH: it is required... | |
 | 1896 - 774 pages
...the points in which each diiigonal is divided into n + 1 equal parts. 4. If four straight lines be proportional, the rectangle contained by the extremes...rectangle contained by the means, and conversely. On a given straight line construct a rectangle equal to a given rectangle. 5. Shew how to solve two... | |
 | Edinburgh Mathematical Society - Electronic journals - 1899 - 340 pages
...altitude XY. [In the same way Euclid VI., 33, may be proved.] EUCLID VI. 16, 17. If four straight lines be proportional, the rectangle contained by the extremes...is equal to the rectangle contained by the means. Conversely : If the rectangle contained by the extremes be equal to the rectangle contained by the... | |
 | Euclid, Micaiah John Muller Hill - Euclid's Elements - 1900 - 190 pages
...38—49. Art. 132. PROPOSITION XXXVIII (i). (Euc. VI. 16, 1st Part.) ENUNCIATION. If four straight lines are proportional, the rectangle contained by...is equal to the rectangle contained by the means. Let K, L, M, P be the straight lines, such that K : L = M : P, it is required to prove that the rectangle... | |
 | Eldred John Brooksmith - Mathematics - 1901 - 368 pages
...proportionals ; prove that the triangles are similar. 11. Prove that if four straight lines are proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means. 12. Prove that in equal circles, sectors have the same ratio which the arcs on which they stand have... | |
| |
If four straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means... 
