 | Euclides - 1885 - 340 pages
...rectangle AB . F. In like manner, CK is equal to the rectangle CD . E. Hence AB . F = CD . E ; that is, the rectangle contained by the extremes is equal to the rectangle contained by the means. 2. If AB . F = CD . E, to prove AB : CD : : E : F. The same construction being made, because AB . F... | |
 | 1885 - 604 pages
...are opposite to the equal angles, are homologous sides. 5. If four straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means. 6. Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their... | |
 | Association for the Improvement of Geometrical Teaching - Euclid's Elements - 1888 - 208 pages
...in E. Shew that EM is parallel to BN. 169 SECTION II. AREAS. THEOR. 10. If four straight lines are proportional the rectangle contained by the extremes is equal to the rectangle contained by the means ; and, conversely, if the rectangle contained by the extremes is equal to the rectangle contained by... | |
 | E. J. Brooksmith - Mathematics - 1889 - 356 pages
...Find a fourth proportional to three given straight lines. 10. If four straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means ; and, if the rectangle contained by the means be equal to the rectangle contained by the extremes,... | |
 | New Brunswick. Board of Education - Education - 1889 - 1004 pages
...Йен. | PLANE AND SOLID GEOMETRY. Time, l hr. du min. 1. If four straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained bv the means. 2. Find a mean proportional between two given straight lines. 3. If two straight lines... | |
 | 1890 - 608 pages
...supplementary. If a circle can be described about a parallelogram the parallelogram must be a rectangle. 3. If four straight lines be proportional the rectangle...is equal to the rectangle contained by the means. Apply this theorem to shew that if two chords of a circle intersect the rectangle contained by the... | |
 | Euclid - Geometry - 1890 - 442 pages
...CAB = A EAD; .-. (0) is true. BOOK vi. Proposition 16. THEOREMS — (a) If four straight lines are proportional, the rectangle contained by the extremes is equal to the rectangle contained by the means : (/3) the converse of this is also true. Let A, B, X, Y be four st. lines such that A : B = X : Y.... | |
 | Edward Mann Langley, W. Seys Phillips - 1890 - 538 pages
...points of BD and CE nre collinear. PROPOSITION 16. THEOREM. (1) If four straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means. (2) Conversely : — If the rectangle contained by the extremes be equal to the rectangle contained... | |
 | Euclid - Geometry - 1892 - 460 pages
...DAZ ; and similarly that the A BXC = the A BDZ.] PROPOSITION 16. THEOREM. If four straight lines are proportional, the rectangle contained by the extremes...Conversely, if the rectangle contained by the extremes is equal to the rectangle contained by the means, the four straight lines are proportional. Let the... | |
 | 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... | |
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If four straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means. 
