 | 1851 - 716 pages
...formed, is also to be similar to the original triangle, then must q= o, also n -f- q or bac = m -fo, which is only possible when bac is a right angle....hypothenuse will be equal to the sum of the squares of the other two sides. With respect to the similarity of such rectilineal figures as have more than... | |
 | Adrien Marie Legendre - Geometry - 1852 - 436 pages
...triangles on each side of the perpendicular are similar to the whole triangle, and to each other: 2d. Either side about the right angle is a mean proportional between the hypothenuse and the adjacent segment: 3d. The perpendicular is a mean proportional between the segments... | |
 | Charles Davies - Geometry - 1854 - 436 pages
...triangles on each side of the jxrpendicular are similar to the given triangle, and to each other: 2d. Either side about the right angle is a mean proportional between the hypothenuse and tl1e adiacent segment: 3d. The perpendicular is a mean proporti3nal bettveen the segments... | |
 | Charles Davies, William Guy Peck - Electronic book - 1855 - 592 pages
...the hypnlhenuse, 1st. The triangles formed arc similar to each other and to the whole triangle. 2d. Either side about the right angle is a mean proportional between the hypolhenuse and the adjacent segment. Ijd. The perpendicular is a mean proportional between the two... | |
 | Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 442 pages
...triangles on each side of the perpendicular are similat to the given triangle, and to each other: Zd. Either side about the right angle is a mean proportional between the hypothenuse and tlie adjacent segment: 3d The perpendicular is a mean proportional between the segments... | |
 | Johann Georg Heck - Encyclopedias and dictionaries - 1860 - 332 pages
...divide the triangle into two smaller ones, similar to each other and to the original triangle (fig. 39-41). From this may be easily deduced, 1, that the...hypothenuse will be equal to the sum of the squares of the other two sides. With respect to the similarity of such rectilineal figures as have more than... | |
 | William Frothingham Bradbury - Geometry - 1872 - 124 pages
...triangles AC :AB = AB :AD And since ABC and BCD are similar .AC : CB-=CB : CD that is, in a right triangle either side about the right angle is a mean proportional between the whole hypothenuse and tlie segment adjacent to that side cut off by the perpendicular drawn from the vertex of the rigM angle... | |
 | William Frothingham Bradbury - Geometry - 1872 - 262 pages
...:AB=AB :AD And since ABC and BCD are similar .AC : CB—CB: CD that is, in a right triangle eiIher side about the right angle is a mean proportional between the whole hypothenuse and the segment adjacent to that side cut off by the perpendicular drawn from the verIex of the right angle... | |
 | Edward Olney - Geometry - 1872 - 562 pages
...CDB are both similar to ACB, they are i; ED A^ DB Fio. 236. similar to each other. 344. COR. 1. — Either side about the right angle is a mean proportional between the whole hypotenuse and the adjacent segment. DEM. — This is a direct consequence of the similarity of the... | |
 | Edward Olney - Geometry - 1872 - 472 pages
...and CDB are both similar to ACB, they are QED DB FIG. 236. similar to each other. 344. COR. 1. — Either side about the right angle is a mean proportional between the whole hypotenuse and the adjacent segment. DEM. — This is a direct consequence of the similarity of the... | |
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Each side about the right angle is a mean proportional between the whole hypotenuse and the adjacent segment. 
