...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...

...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...

...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...

...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...

...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...

...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...

...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...

...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...

...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...

...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,...