 | Thomas Hunter - Geometry, Plane - 1878 - 142 pages
...proportional between AE and EB; that is (Prop. XIV., Cor.), DE 2 =AE xEB. PROPOSITION XVH.—THEOREM. Similar triangles are to each other as the squares of their homologous sides. angle A equal to the angk i>, the angle B equal to the angle E, and the angle C equal to tht... | |
 | Horatio Nelson Robinson - Navigation - 1878 - 564 pages
...required, E, then if n : 1 be the ratio of ADE to the whole, we must have AD : AB : : Vn : 1, since similar triangles are to each other as the squares of their homologous sides. Therefore, if we take AD, having to the Hue AS the ratio of Vn : 1, and from D run a line parallel... | |
 | Surveying - 1878 - 534 pages
...AD 19 derived from the area of a triangle being equal to its base by half its altitude. (527) Since similar triangles are to each other as the squares of their homologous sides, ABC : DBE : : AB" : BD" ; whence BD = AB = AB — — . ABC M HI -f- n The construction of Fig.... | |
 | Isaac Sharpless - Geometry - 1879 - 282 pages
...from the longer side must it be drawn ? Ans. 2.84+. It will assist in solving this to remember that similar triangles are to each other as the squares of their homologous sides. 10. A man has three lots, each containing 10 acres; one is a square, one a circle, and one a... | |
 | Benjamin Gratz Brown - Geometry - 1879 - 68 pages
...to other analysis. The fountain from which flow most of the proportions respecting surfaces, is that similar triangles are to each other as the squares of their homologous sides. Others show that if four straight lines are pro ortional. similar rectilinear figures similarly... | |
 | William Mitchell Gillespie - Surveying - 1880 - 540 pages
...AD is derived from the area of a triangle being equal to its base by half its altitude. (52 T) Since similar triangles are to each other as the squares of their homologous sides, ABC : DBE : : AB" : BD« ; whence BD = AB J 5|? = AB <J — ^— . f ADU fn .f. 1fc The construction... | |
 | George Anthony Hill - Geometry - 1880 - 332 pages
...'2 * S ^ Since a and £ may be any two homologous sides taken as bases, therefore, — Theorem. — Similar triangles are to each other as the squares of their homologous sides. Exercises. — 1. If the homologous sides of one triangle are each one-fifth those of a similar... | |
 | William Frothingham Bradbury - Geometry - 1880 - 260 pages
...the squares of the sides is equivalent to the sum of the squares of the diagonals. THEOREM XXXII. 75. Similar triangles are to each other as the squares of their homologous sides. Let ABC and DEF be two T» similar triangles; then ABC:DEF=AC2:DJ A / \\ E Draw BG and EH perpendicular... | |
 | Simon Newcomb - Geometry - 1881 - 418 pages
...:: PB : BC. 4. Comparing with (1) and (2), AB : BR :: PB : BC. QED THEOREM XXII. 423. The areas of similar triangles are to each other as the squares of their homologous sides. Hypothesis. ABC and PQR, two triangles in which AB : BC : CA :: PQ : QR : RP. Conclusion. Area... | |
 | Franklin Ibach - Geometry - 1882 - 208 pages
...BD X DA for its equal DE X CD. ELEMENTS OF PLANE GEOMETRY. RELATION OF POLYGONS. THEOREM XXX. 290. Similar triangles are to each other as the squares of their homologous sides. Let the As ABC and EFG be similar. DH To prove that A ABC : A EFG :: A~ÏÏ : ËF\ Draw the... | |
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Since similar triangles are to each other as the squares of their homologous sides, ABC : DBE : : AB' : BD3 ; whence BD = AB J ^5| ~ AB A/— ^ — . j A150 f in -f- n The construction of Fig. 
