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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... "
The elements of geometry, in eight books; or, First step in applied logic - Pagina 335
door L J V. Gerard - 1874
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An Elementary Treatise on the Geometrical and Algebraical Investigation of ...

Daniel Cresswell - 1817 - 436 pagina’s
...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...
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A Supplement to the Elements of Euclid

Daniel Cresswell - 1819 - 410 pagina’s
...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...
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Elements of Geometry

Adrien Marie Legendre - 1819 - 208 pagina’s
...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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The New Practical Builder and Workman's Companion, Containing a Full Display ...

Peter Nicholson - 1823 - 596 pagina’s
...triangle ABC ; therefore, also, the triangles DEF, ABC, are equiangular and similar. THEOREM 60. 158. Two triangles which have an angle of the one equal to an angle of the other, and the sides about them proportionals, are similar. Let the angle A equal D, and suppose that AB :...
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Elements of Geometry...: Translated from the French for the Use of the ...

Adrien Marie Legendre, John Farrar - 1825 - 224 pagina’s
...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....
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Elements of Geometry

Adrien Marie Legendre - 1825 - 224 pagina’s
...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 (fig....
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Elements of Geometry...: Translated from the French for the Use of the ...

Adrien Marie Legendre, John Farrar - 1825 - 224 pagina’s
...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 pagina’s
...: 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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The Geometrical Companion: In which the Elements of Abstract Geometry are ...

George Darley - 1828 - 169 pagina’s
...proportional, are 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 pagina’s
...suppress , 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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