| Euclides - 1855
...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
...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 - 318 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
...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 - 318 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 - 1869 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 - 1859
...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 - 361 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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