 | Robert Potts - 1865 - 528 pages
...the other, as the remaining side of the other is to the remaining side of the first." m. A straight line is said to be cut in extreme and mean ratio, when the whole is to the greater segment, as the greater segment is to the less. IV. The altitude of any figure is... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...the other, as the remaining side of this other is to the remaining side of the first. 3. A straight line is said to be cut in extreme and mean ratio, when the whole is to the greater segment as the greater segment is to the less. 4. The altitude of any figure is the... | |
 | Robert Potts - 1868 - 434 pages
...the other, as the remaining side of the other is to the remaining side of the first." m. A straight line is said to be cut in extreme and mean ratio, when the whole is to the greater segment, as the greater segment is to the less. IV. The altitude of any figure is... | |
 | Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...KGH is similar to ABC. Hence a figure KGH has been described as was required. QEF DEF. V. A straight line is said to be cut in extreme and mean ratio, when the whole is to the greater segment as the greater segment is to the less. PROPOSITION XXX. PROBLEM. (Eucl. vi.... | |
 | Euclid - Geometry - 1872 - 284 pages
...which have the angles in each respectively equal, and the sides about the equal angles proportional. 2. A right line is said to be cut in extreme and mean ratio, when, as the whole is to the greater segment, so is the greater to the less. 3. The altitude of any figure,... | |
 | Euclides - 1874 - 342 pages
...the other, as the remaining side of the other is to the remaining side of the first." 3. A straight line is said to be cut in extreme and mean ratio, when the whole is to the greater segment, as the greater segment is to the less. .4. The altitude of any figure is... | |
 | Euclid, James Bryce, David Munn (F.R.S.E.) - Geometry - 1874 - 236 pages
...remaining one of the second is to the remaining one of the first (vide App. VI., schol. 1). 3. A straight line is said to be cut in extreme and mean ratio when the whole is to one of the segments as that segment is to the other. 4. A straight line is said to be cut harmonically... | |
 | James Martin (of the Wedgwood inst, Burslem.) - 1876 - 334 pages
...Then the given line AB is divided in extreme and mean proportion in the point F. NOTE. — "A straight line is said to be cut in extreme and mean ratio, when the whole is to the greater segment as the greater segment is to the less " (Euo. VI., Def. 3). Problem 146.... | |
 | Robert Potts - Geometry - 1876 - 446 pages
...the other, as the remaining side of the other is to the remaining side of the first." in. A straight line is said to be cut in extreme and mean ratio, when the whole is to the greater segment, as the greater segment is to the less. IV. . The altitude of any figure... | |
 | Isaac Todhunter - Euclid's Elements - 1880 - 426 pages
...the other, as the remaining side of this other is to the remaining side of the first. 3. A straight line is said to be cut in extreme and mean ratio, when the whole is to the greater segment as the greater segment is to the less. 4. The altitude of any figure is the... | |
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A straight line is said to be cut in extreme and mean ratio, when the whole is to the greater segment as the greater segment is to the less. 
