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" Assuming that 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... "
SYLLABUS OF PLANE GEOMETRY - Side 17
1876
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An Elementary Treatise on the Geometrical and Algebraical Investigation of ...

Daniel Cresswell - 1817 - 436 sider
...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...
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Elements of Geometry

Adrien Marie Legendre - 1819 - 208 sider
...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...
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A Supplement to the Elements of Euclid

Daniel Cresswell - 1819 - 410 sider
...: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 an angle of the other, and if, also, the sides of the two figvres, about each of tJieir angles, be proportionals, the remaining...
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The New Practical Builder and Workman's Companion, Containing a Full Display ...

Peter Nicholson - 1823 - 596 sider
...CAG equal to D, take AG equal to DE or AB, and join CG ; and because the two triangles CAG, DEF, have an angle of the one equal to an angle of the other, and the sides which contain these angles are equal, CG shah1 be equal to EF (theorem 5). Now there...
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Elements of Geometry...: Translated from the French for the Use of the ...

Adrien Marie Legendre, John Farrar - 1825 - 224 sider
...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 anglgs proportional, are similar (208), consequently the angle BCA —...
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Elements of Geometry

Adrien Marie Legendre - 1825 - 224 sider
...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 (fig....
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The Geometrical Companion: In which the Elements of Abstract Geometry are ...

George Darley - 1828 - 169 sider
...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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Elements of Geometry Upon the Inductive Method: To which is Added an ...

James Hayward - 1829 - 172 sider
...BD . ... ABC ABXAC the common factor =-, we snail have —AE~V~AF' That is — If two triangles have an angle of the one equal to an angle of the other, their areas will be as the products of the sides containing the equal angles. Fig. 94. 17o if we take...
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Elements of Geometry: With Practical Applications, for the Use of Schools

Timothy Walker - 1829 - 129 sider
...vertices by the space of a quadrant, the sides will become parallel each to each. 3. — When they have an angle of the one equal to an angle of the other, and the sides including these angles proportional — . Thus if the F45 angle A=A (fig. 45), and if...
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Library of Useful Knowledge: Geometry, plane, solid, and spherical [by ...

1835
...interjacent side (c). 3. The three sides (/). 4. Two angles, and a side opposite to one of them . cor. 14 5. An angle of the one equal to an angle of the other, and the sides about two other angles, each to each, and the remaining angles of the same affection,...
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