 In a right triangle, the perpendicular from the vertex of the right angle to the hypotenuse is a mean proportional between the segments of the hypotenuse: p2 = mn. Any two similar figures, in the plane or in space, can be placed in " perspective," that...  Text-book of Elementary Plane Geometry - Page 13by Julius Petersen - 1880 - 73 pagesFull view - About this book
 | John Radford Young - Euclid's Elements - 1827 - 246 pages
...: : AE : AC, consequently, Scholium. AD : AC; and from these proportions we infer (Prop. XII.) that the perpendicular from the vertex of the right angle to the hypothenuse divides the triangle into two similar ones, so that proposition XIV. is immediately deducible from... | |
 | Benjamin Greenleaf - Geometry - 1862 - 532 pages
...mean proportional between the hypothenuse and the part cut off adjacent to that side. 271. Cor. 2. The perpendicular from the vertex of the right angle to the hypothenuse is a mean proportional between the two parts into which it divides the hypothenuse. For, since the triangles... | |
 | Benjamin Greenleaf - Geometry - 1862 - 518 pages
...mean proportional between the hypothenuse and the part cut off adjacent to that side. 271. Cor. 2. The perpendicular from the vertex of the right angle to the hypothenuse is a mean proportional between the two parts into which it divides the hypothenuse. For, since the triangles... | |
 | Benjamin Greenleaf - Geometry - 1866 - 328 pages
...mean proportional between the hypothenuse and the part cut off adjacent to that side. 271. Cor. 2. The perpendicular from the vertex of the right angle to the hypothenuse is a mean proportional between the two parts into which it divides the hypothenuse, For, since the triangles... | |
 | Friedrich Ueberweg - Logic - 1871 - 686 pages
...which are similar to each other. 3. Those triangles, into which a right-angled triangle is divided by the perpendicular from the vertex of the right angle to the hypothenuse, are triangles whose angles are equal each to each. All triangles whose angles are equal each to each,... | |
 | Benjamin Greenleaf - Geometry - 1873 - 202 pages
...mean proportional between the hypothenuse and the part cut off adjacent to that side. 212. Cor. 2. The perpendicular from the vertex of the right angle to the hypothenuse is a mean proportional between the two parts into which it divides the hypothenuse. For, since the triangles... | |
 | Benjamin Greenleaf - Geometry - 1874 - 206 pages
...mean proportional between the hypothenuse and the part cut off adjacent to that side. 212. Cor. 2. The perpendicular from the vertex of the right angle to the hypothenuse is a mean proportional between the two parts into which it divides the hypothenuse. For, since the triangles... | |
 | Julius Petersen - Geometry, Modern - 1880 - 86 pages
...of the opposite side is half as great as this. 1 8. The side AB of a triangle ABC is produced to Z>, so that BD = BC. Prove that the line bisecting the...angle ABC, mark off any part AB, thereupon draw a line AD-&BC, and make AD = AB. Prove that the line BD bisects the given angle. 22. In a triangle ABC the... | |
 | George Irving Hopkins - Geometry, Plane - 1891 - 208 pages
...triangles BAD and ACE can be proved similar. 375. If one side of a right triangle is double the other, the perpendicular, from the vertex of the right angle to the hypothenuse, divides it into segments which are to each other as 1 to 4. 376. A line parallel to the bases of a... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 344 pages
...0 within each, and the triangles A1OB1, A2OB2 are similar, by th. 8. Theorem 13. In a right-angled triangle the perpendicular from the vertex of the right angle to the hypotenuse divides the triangle into two triangles which are similar to the whole and to each other.... | |
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