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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. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C'... "
The Elements of Euclid, containing the first six books, with a selection of ... - Page 279
by Euclides - 1874
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An Elementary Treatise on the Geometrical and Algebraical Investigation of ...

Daniel Cresswell - Euclid's Elements - 1817 - 436 pages
...which any other 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...shall be equal to the remaining angles of the other. PROP. VIII. (xvin.) To divide a given finite straight line into two parts, such, that another given...
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A Supplement to the Elements of Euclid

Daniel Cresswell - Geometry - 1819 - 410 pages
...bisects the L 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...shall be equal to the remaining angles of the other. Let the two trapeziums ABCD, EFGH, which A ~~~--^ Tk E B CFG have the sides about each of their u....
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A Supplement to the Elements of Euclid

Daniel Cresswell - Geometry - 1819 - 410 pages
...bisects the L FAE, FH :HE::AF:AE; that is, FG is to GE in the given ratio. PROP. XVII. 23. THEOREM. If two trapeziums have an angle of the one equal to...angle of the other, and if, also, the sides of the two figvres, about each of tJieir angles, be proportionals, the remaining angles of the one shall be equal...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1819 - 208 pages
...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 =...
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The new practical builder, and workman's companion, Volume 2

Peter Nicholson - Building - 1823
...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,...
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Elements of Geometry...: Translated from the French for the Use of the ...

Adrien Marie Legendre - Geometry - 1825 - 224 pages
...AC : FH : : CD : HI; but we have seen that the angle ACD = FHI; consequently the triangles ACD, FHI, have an angle of the one equal to an angle of the other and the sides about the equal angles proportional ; they are therefore similar (208). We might proceed...
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Elements of Geometry

Adrien Marie Legendre - 1825 - 224 pages
...: FH : : CD : HI ; but we have seen that the angle ACD = FHI; consequently the triangles ACD, FHI, have an angle of the one equal to an angle of the other and the sides about the equal angles proportional ; they are therefore similar (208). We might proceed...
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Elements of Geometry...: Translated from the French for the Use of the ...

Adrien Marie Legendre, John Farrar - Geometry - 1825 - 224 pages
...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),...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1825 - 224 pages
...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 and the sides about the equal angles proportional, are similar (208), consequently the angle BCA = GHF....
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The Geometrical Companion, in which the Elements of Abstract Geometry are ...

George Darley - Geometry - 1828 - 169 pages
...equal." Here we have a criterion whereby to judge of the equality of two triangular surfaces, which have an angle of the one equal to an angle of the other. For example : ABCD is a road cutting off a triangular field AOB. It is desirable that the line of road...
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