 IN a right-angled triangle, if a perpendicular be drawn from the right angle to the base, the triangles on each side of it are similar to the whole triangle, and to one another.  Books 3-9 - Page 209by Euclid - 1908Full view - About this book
 | Robert Simson - Trigonometry - 1806 - 546 pages
...Wherefore, if two triangles, &c. QED G D 5.1. F PROP. VIII. THEOR. See N IN a right angled triangle, if a perpendicular be drawn from the right angle to the base, the triangles on each side of it are similar to the whole triangle, and to one another. Let ABC be a right angled... | |
 | John Playfair - Mathematics - 1806 - 320 pages
...first case. Therefore, if two triangles, &c. QED PROP. VIII. THEOR. IN a right angled triangle, if a perpendicular be drawn from the right angle to the base, the triangles on each side of it are similar to the whole triangle, and to each other* Let ABC be a right angled... | |
 | John Mason Good - 1813 - 714 pages
...angles equal about which the sities are proportionals. Prop. VllI.Thcor. In a right angled triangle, if a perpendicular be drawn from the right angle to the base; the triangles on each side of it are similar to the whole triangle, and to one another. Prop. IX. Prob. From a given... | |
 | Euclides - 1816 - 588 pages
...Wherefore, if the two triangles, &c. Q . ED 5. I. PROP. VIII. THEOR. Se«N. IN a right angled triangle, if a perpendicular be drawn from the right angle to the base ; the triangles on each side of it are similar to the whole triangle, and to one another. Let ABC be a right angled... | |
 | Thomas Leybourn - Mathematics - 1817 - 454 pages
...14470-0735 feet, the mountain's height required. in. QUESTION 1211, by Mr. S. Titlow, of Härtesten. If, in a right-angled triangle, a perpendicular be drawn from the right angle upon the hypothenuse, and circles inscribed, within the two smaller triangles on each side of it, their... | |
 | Miles Bland - Euclid's Elements - 1819 - 442 pages
...to the part produced the same ratio that the sum of the sides of the triangle has to the base. 29- If in a right-angled triangle, a perpendicular be drawn from the right angle to the hypothenuse, and circles inscribed within the triangles on each side of it ; their diameters will be... | |
 | Miles Bland - Euclid's Elements - 1819 - 444 pages
...BACD, FOGD being similar, and similarly situated, AD : OD :: AB + AC : FO + OG :: AB + AC : BC. (29.) If in a right-angled triangle, a perpendicular be drawn from the right angle to the hypothenuse, and circles inscribed within the triangles on each side of it ; their diameters will be... | |
 | John Playfair - Circle-squaring - 1819 - 350 pages
...equiangular to the triangle DEF, as in the first case. PROP. VIII. THEOR. In a right angled triangle, if a perpendicular be drawn from the right angle to the base; the triangles on each side of it are similar to the whole triangle, and to one another. Let ABC be a right angled... | |
 | George Lees - 1826 - 276 pages
...BD : : BD : BCC ; that is BD is a mean proportional between AB and BC. Which was to be found. Cor. If, in a right-angled triangle, a perpendicular be drawn from the right angle to the base, it is a mean proportional between the segments of the base ; the triangles on each side of it are similar... | |
 | Euclid - 1826 - 234 pages
...triangle DEF. If, therefore, two triangles, 8tc. QED PROPOSITION VIII. THEOREM. If in a right angled triangle a perpendicular be drawn from the right angle to the base, the triangles made by 'the perpendicular are similar to the whole and to one another. Let ABC be a right angled triangle,... | |
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