 | George Washington Hull - Geometry - 1807 - 408 pages
...a right triangle, I. The triangles formed are similar to the whole triangle, and to each other. II. The perpendicular is a mean proportional between the segments of the hypotenuse. III. Either leg is a mean proportional between the whole hypotenuse and the adjacent segment. AJ) "... | |
 | Euclides - 1821 - 294 pages
...and .-. equiangular and similar with one another. Cor. Hence it is evident that in every right angled triangle the perpendicular is a mean proportional between the segments of the side on which it falls ; also that the remaining sides are mean proportionals between their adjacent... | |
 | Pierce Morton - Geometry - 1830 - 584 pages
...that either side is a mean proportional between the hypotenuse and segment adjacent to il, and that the perpendicular is a mean proportional between the segments of the hypotenuse. Again, I. 38. in which it is demonstrated that, in every triangle, if a perpendicular be drawn from... | |
 | Mathematics - 1835 - 684 pages
...inferred that cither Me is a mean proportional between the hypotenuse and segment adjacent to it, and that the perpendicular is a mean proportional between the segments of the hypotenuse. Again, I. 38. in which it is demonstrated that, in every triangle, if a perpendicular be drawn from... | |
 | Horatio Nelson Robinson - Geometry - 1860 - 470 pages
...triangles have the sides about "the equal angles proportional, (Def. 16), we have BD : AD :: AD : CJ); or, the perpendicular is a mean proportional between the segments of the hypotenuse. 3. Again, BC :_BA :: BA : BD hence, BA2 = BC.BD (1) also, BC_i CA : : CA : CD hence, C!T - BC.CD (2)... | |
 | Trinity College (Hartford, Conn.) - 1870 - 1008 pages
...right triangle, (1) the triangles thus formed are similar to each other and to the whole triangle, (2) the perpendicular is a mean proportional between the segments of the hypotenuse, and (3) each side about the right angle is a mean proportional between the hypotenuse and its adjacent... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...triangle : 1st. The two triangles thus formed are similar to each other and to the whole triangle; 2d. The perpendicular is a mean proportional between the segments of the hypotenuse; 3d. Each side about the right angle is a mean proportional between the hypotenuse and the adjacent... | |
 | William Chauvenet - Geometry - 1872 - 382 pages
...triangle : 1st. The two triangles thus formed are similar to each other and to the whole triangle ; 2d. The perpendicular is a mean proportional between the segments of the hypotenuse ; 3d. Each side about the right angle is a mean proportional between the hypotenuse and the adjacent... | |
 | Edward Olney - Geometry - 1872 - 562 pages
...ACB, we have AD : AC :: AC : AB;* and from CDB and ACB, we have OB : CB :: CB : AB. 343. COR. 2. — The perpendicular is a mean proportional between the segments of the hypotenuse. DEM.— This is a consequence of the similarity of ACD and CDB. Thus, AD : CD : : CD : DB. Queries.... | |
 | Edward Olney - Geometry - 1872 - 472 pages
...we have AD : AC : : AC : AB ;* and from CDB and ACB, we have DB : CB :: CB : AB. , 345. COR. Й. — The perpendicular is a mean proportional between the segments of the hypotenuse. DEM. — This is a consequence of the similarity of ACD and CDB. Thus, AD : CD : : CD : DB. Queries.... | |
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In a right triangle, if a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I. 
