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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'... "
Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ... - Página 126
por Euclides - 1840
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An Elementary Treatise on the Geometrical and Algebraical Investigation of ...

Daniel Cresswell - 1817 - 454 páginas
...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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Elements of Geometry

Adrien Marie Legendre - 1819 - 574 páginas
...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...
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A Supplement to the Elements of Euclid

Daniel Cresswell - 1819 - 486 páginas
...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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Euclid's Elements of Geometry: The Six First Books. To which are Added ...

Rev. John Allen - 1822 - 508 páginas
...FE, as FD to AC). And triangles (ABC, DEF), which have an angle (ACB) of one, equal to an angle (F) of the other, and the sides about the equal angles reciprocally proportional, are equal. Part 1.—On BC and AC produced, take CG equal to FE, CH to FD, and join AG and GH. The angle HCG is...
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The New Practical Builder and Workman's Companion, Containing a Full Display ...

Peter Nicholson - 1823 - 210 páginas
...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,...
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Elements of Geometry...: Translated from the French for the Use of the ...

Adrien Marie Legendre, John Farrar - 1825 - 294 páginas
...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 in the same manner to demonstrate,...
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Elements of Geometry

Adrien Marie Legendre - 1825 - 276 páginas
...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. 122), and let Fifr...
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Elements of Geometry...: Translated from the French for the Use of the ...

Adrien Marie Legendre, John Farrar - 1825 - 280 páginas
...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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Elements of Geometry

Adrien Marie Legendre - 1825 - 570 páginas
...properties of triangles involve those of all figures. THEOREM. 208. Two triangles, which have an ungle 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. 122), and let Kig....
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Euclid's Elements of geometry, transl. To which are added, algebraic ...

Euclides - 1826 - 226 páginas
...angles are reciprocally proportional; and if parallelogram* h.ave one angle of the one equal to one angle of the other, and, the sides about the equal angles reciprocally proportional; these parallelograms shall be equal to one another. • I*-1- foreFB, вс,аге in a direct line...
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