 | London univ, exam. papers, John Edward A. Steggall - Mathematics - 1882 - 264 pages
...is 5d. Afternoon, 3 to 6. GEOMETRY AND TRIGONOMETRY. 1. If four right lines be proportional, prove that the rectangle contained by the extremes is equal to the rectangle contained by the means. [Euclid, vi. 16.] 2. Find a fourth proportional to three given right lines. If the first and second,... | |
 | Mathematical association - 1883 - 86 pages
...interior or exterior vertical angle. SECTION 2. 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... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 428 pages
...Wherefore, equal triangles &c. QED PROPOSITION 16. THEOREM. 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 extremes be equal to the rectangle contained by the means, tftefuur... | |
 | University of Cambridge - 1884 - 624 pages
...one, and whose vertical angle shall be half a right angle. 9. 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 extremes be equal to the rectangle contained by the means, the... | |
 | Euclides - 1884 - 434 pages
...case for a point in a side produced. PROPOSITION 16. THEOREMS. 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 means,... | |
 | 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 - 608 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... | |
 | Euclid, John Casey - Euclid's Elements - 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. 229 have the parallelogram AG = CK, and since these... | |
 | Association for the Improvement of Geometrical Teaching - Euclid's Elements - 1888 - 208 pages
...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,... | |
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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. 
