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, Sir Thomas Little Heath, Johan Ludvig Heiberg - 1908Full view - About this book
| John Playfair - Euclid's Elements - 1806 - 311 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... | |
| Euclid, Robert Simson - Euclid's Elements - 1806 - 518 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 Mason Good, Olinthus Gilbert Gregory - 1813
...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 - Euclid's Elements - 1816 - 528 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
...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 - Geometry - 1819 - 377 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 - Geometry - 1819 - 377 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 - 333 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 - Algebra - 1826 - 207 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, Phillips - 1826 - 180 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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