 | Euclides - 1855 - 230 pages
...unnecessarily prolix. K 3 PROPOSITION VIII. THEOREM. In a right-angled triangle (ABC), if a perpendicular (AD) be drawn from the right angle to the base; the triangles on each side of it are similar to the whole triangle, aud to one another. DEMONSTRATION. Because the angles BAG and ADB are equal, being both right... | |
 | Robert Potts - 1855 - 1050 pages
...about a given triangle. 9. Give Euclid's definition of proportional magnitudes. 10. 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. To what objection has this definition been... | |
 | John Playfair - Euclid's Elements - 1855 - 340 pages
...triangle ABC may be proved to 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 tc the base ; the triangles on each side of it are similar to the whole triangle, and to one another.... | |
 | Euclides - 1855 - 270 pages
...other pair of homologous gides are either equal or supplementary. PROP. VIIL THEOREM. In a right-angled triangle, if a perpendicular be drawn from the right angle to the opposite side, tin triangles on each side of the perpendicular tire similar to the whole triangle,... | |
 | John Playfair - Euclid's Elements - 1856 - 346 pages
...PROP. VIII. THEOR. In. a rigid angled triangle if a perpendicular be drawn from the right angle tc the base ; the triangles on each side of it are similar to t/ie whale triangle, and to one another. Let ABC be a right angled triangle, having the right angle... | |
 | Sandhurst roy. military coll - 1859 - 672 pages
...and the part of it without the circle, shall be equal to the square of the line which touches it. 2. In a right angled triangle if a perpendicular be drawn...triangles on each side of it are similar to the whole triangle, and to one another. 3. Find the sum of n terms of the arithmetical progression 1, 3, 5, 7,... | |
 | Thomas Stantial - Examinations - 1859 - 352 pages
...triangles are one to another in the duplicate ratio of their homologous sides. C. In a right-angled triangle, if a perpendicular be drawn from the right...triangles on each side of it are similar to the whole triangle and to one another. 6. EXERCISES IN GEOMETRY. I. 1. Trisect a given finite straight line.... | |
 | Euclides - 1860 - 288 pages
...triangle ABC may be proved to be equiangular to the triangle DEF, as in the first case. In a right-angled triangle, if a perpendicular be drawn from the right...triangles on each side of it are similar to the whole triangle, and to one another. Given ABC a right-angled triangle, having the right angle. BAC ; and... | |
 | Eucleides - 1860 - 396 pages
...unnecessarily prolix. PROPOSITION VIII. THEOREM. In a right-angled triangle (ABC), if a perpendicular (AD) 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. DEMONSTRATION. Because the angles BAC and ADB are equal, being both right... | |
 | Robert Potts - Geometry, Plane - 1860 - 380 pages
...PROPOSITION VIII. THEOREM. • In a right-angled triangle, if a perpendicular be drawn from the rightanyle 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-triangle, having the right angle BAC; and from... | |
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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. 
