 | John Keill - 1723 - 444 σελίδες
...to AE asGFis to FL. Now fince ABE, FGL, are two Triangles, having one Angle of the one equal to one Angle of the other, and the Sides about the equal Angles proportional; the Triangle ABE will be * equiangular * 6 of tin's. to the Triangle FGL; and fo alfo fimilar to it.... | |
 | Euclid - 1728 - 236 σελίδες
...DEFINITIONS. [milar right-lined Figures, as ABC, DCE, are fuch chat have each Angle oí the one equal to each Angle of the other, and the Sides about the equal Angles proportional. в с" The Ang. В= DCE ; and AB : BC : : DC : CE. alfo the Ang. A = D ; and BA : AC : : CD : DE. and... | |
 | Euclid, John Keill - 1733 - 444 σελίδες
...AE as GF is to* FL. Now fmce ABE, FGL, are two Triangles, having one Angle of the one equal to One Angle of the other, and the Sides about the equal Angles proportional ; .the Triangle ABE will be * equiangular * doftbit. to the .Triangle FGL; and alfo fimilar to it,... | |
 | John Playfair - 1806 - 320 σελίδες
...Wherefore, if the sides, &c. QE *D. PROP. VI. THEOR. IF two triangles have one angle of one equal to one angle of the other, and the sides about the equal angles proportional, the triangles will be equiangular, and will have those angles equal which are opposite to the homologous... | |
 | Daniel Cresswell - 1817 - 454 σελίδες
...chord has to the aggregate of the two chords that are next to it. PROP. VI. (XVII.) If two trapeziums have an angle of the one equal to an angle of the other, and if, also, the sides of the two figures, about each of their angles, be proportionals, the remaining... | |
 | Adrien Marie Legendre - 1819 - 574 σελίδες
...general properties of triangles involve those of all figures, THEOREM. 208. Two triangles, whkh Iiave an angle of the one equal to an angle of the other and the sides about these angles proportional, are similar. Fig. 122. Demonstration. Let the angle A = D (Jig. 122), and... | |
 | Daniel Cresswell - 1819 - 486 σελίδες
...FAE, FH :HE::AF:AE; that is, FG is to GE in the given ratio. PROP. XVU. 23. THEOREM. If two trapeziums have an angle of the one equal to an angle of the other, and if, also, the sides of the two ^figures, about each of their angles, be proportionals, the remaining... | |
 | Peter Nicholson - 1823 - 210 σελίδες
...BC2 but, since AB is equal to the sum of the two lines AD, DB, therefore AB2 = AC2 THEOREM 63. 161. Two triangles, which have an angle of the one equal to an angle of the other, are to each other as the rectangle of the sides about the equal Suppose* the two triangles joined,... | |
 | Adrien Marie Legendre - 1825 - 276 σελίδες
...the sides FG, GH, so that AB:FG::BC: GH. It follows from this, that the triangles ABC, FGH, having an angle of the one equal to an angle of the other...sides about the equal angles proportional, are similar (208), consequently the angle BCA = GHF. These equal angles being subtracted from the equal angles... | |
 | Adrien Marie Legendre, John Farrar - 1825 - 280 σελίδες
...right-angled triangles. Thus the general properties of triangles involve those of all figures. THEOREM. 208. Two triangles, which have an angle of the one equal to an angle of the other and the sides about these angles proportional, are similar. Demonstration. Let the angle A = D (Jig. 122), and let Fig.... | |
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The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw... 
