 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
 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...triangle DEF. Wherefore, if two triangles &c. QED PROPOSITION 8. THEOREM. 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... | |
 | Euclid - 1868 - 138 pages
...кàQfтоç á^0jr тà irpbç тy кaQíтф Tpiofidá laTÍ Tif тf o\if Kai In a right-angled triangle, if a perpendicular be drawn from the right angle to the base, the triangles on each side of the perpendicular are similar to the whole and to Statement. — Let ABC be a right-angled... | |
 | Ontario Chief Superintendent of Education - Education - 1869 - 450 pages
...Inscribe an equiangular and equilateral pentagon in a given circle. 12. 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. No. 15. NATURAL PHILOSOPHY—... | |
 | Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...proportional to the lines BD, DH, AB. PROPOSITION XII. THEOREM. (Eucl. vi. 8.) 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. B a Let ABC be a right.angled... | |
 | William Alexander Myers - Circle-squaring - 1873 - 238 pages
...square root of the remaining || can be extracted exactly. THEOREM 3. In any right-angle triangle if a perpendicular be drawn from the right angle to the base the triangles on each side are similar to the whole triangle and to one another, and the perpendicular is a mean... | |
 | Francis Cuthbertson - Euclid's Elements - 1874 - 400 pages
...equal and the sides about the equal angles proportional. PROPOSITION VI. In a right-angled triangle, if a perpendicular be drawn from the right angle to the base; the triangles on each side of it shall be similar to the whole triangle and to one another. n Let ACB be a right-angled... | |
 | William Alexander Myers - Circle-squaring - 1874 - 207 pages
...lines AB, J5(7, a mean proportional DB is found. PROPOSITION 5. THEOREM. 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. See Plate 7 Fig. 1. Let DAG... | |
 | Euclides - 1874 - 342 pages
...DEF. Wherefore, if two triangles, &c. QED PROPOSITION 8.— Theorem. 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... | |
 | Euclid, James Bryce, David Munn (F.R.S.E.) - Geometry - 1874 - 236 pages
...to the hypotenuse divides the triangle into tico triangles, which are similar to the whole triangle and to one another. Let ABC be a right-angled triangle, having the angle A right, and let AD be the perpendicular on the hypotenuse; then shall the triangles ABD and ACD be... | |
 | Euclid - 1876 - 240 pages
...of a triangle. If from any angle of a triangle a straight line be drawn perpendicular to the base. If in a right-angled triangle, a perpendicular be drawn from the right angle to the Idem If a straight line drawn from any angle of a triangle divide the opposite side into segments which... | |
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