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" THEOR. If the sides of two triangles, about each of their angles, be proportionals, the triangles shall be equiangular, and have their equal angles opposite to the homologous sides. Let the triangles ABC, DEF have their sides proportionals, so that AB... "
Text book of geometry - Page 150
by Thomas Steadman Aldis - 1872
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Mathematics - 1806 - 320 pages
...h22. S. therefore, ex aequali, BA : AC : : CD ; DEh. Therefore, the sides, &c. QED PROP. ,V. THE OR. IF the sides of two triangles, about each of their angles, be proportional, the triangles will be equiangular, and have their equal angles opposite to the homologous sides. Let the triangles...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1806 - 546 pages
...ED, ex tcyuali*, BA is to AC, as CD to DE. Therefore, h 22. 5. the sides, Sic. QED PROP. V. THEOR. IF the sides of two triangles, about each of their angles, be proportionals, the triangles shall be equiangular, and have their equal angles opposite to the homologous...
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Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1813 - 714 pages
...angles are homologous sides, that is, are the antecedents Or consequents of the ratios. Prop. V. Theor. If the sides of two triangles, about each of their angles, be proportionals, the triangles shall be equiangular, and have their equal angles opposite to the homologous...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 588 pages
...ED, ex. squall h, BA is to AC, * t*. :,. as CD to DE. Therefore the sides, 8cu. QED PROP. V. THEOR. IF the sides of two triangles, about each of their angles, be proportionals, the triangles shall be equiangular, and have their equal angles opposite to the homologous...
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Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1819 - 800 pages
...angles lie homologous sides, that is, arc the antecedents or consequents of the ratios. Prop. V. Theor. If the sides of two triangles, about each of their angles, be proportional«, the trijiigles shall be equiangular, and have their Cjuil angles opposite to the homologous sides. Prop....
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 546 pages
...22. 5. CE to ED, ex aequali *, BA is to AC, as CD to DE. Therefore the sides, &c. QED PROP. V. THEOR. If the sides of two triangles, about each of their angles, be proportionals, the triangles shall be equiangular ; and the equal angles shall be those which are opposite...
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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - Geometry - 1829 - 210 pages
...sides have to each other. The sides about the equal angles of equiangular triangles are proportional. If the sides of two triangles about each of their angles be proportional, the triangles will be equiangular. If two triangles have,one angle of one triangle equal to one angle of the other,...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - Euclid's Elements - 1832 - 358 pages
...BC : CA : : CE : ED, ex aequali, BA : AC : : CD : DE. Therefore the sides, &c. QED PROP. V. THEOR. If the sides of two triangles, about each of their angles, be proportionals, the triangles shall be equiangular, and have their equal angles opposite to the homologous...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 pages
...ED, ex eequali ' BA is to i 22. 5. AC as CD to DE. Therefore, " the sides," &c. QED PROP. V. THEOR. If the sides of two triangles, about each of their angles be proportionals, the triangles shall be equiangular, and have their equal angles opposite to the homologous...
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

Mathematics - 1836 - 488 pages
...the equal angles are homologous sides, that is, are the antecedents or consequents of the ratios. V. If the sides of two triangles, about each of their angles, be proportional, the triangles shall be equiangular, and have their equal angles opposite to the homologous sides. VI. If two triangles...
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