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" If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar. "
The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ... - Page 141
by Robert Simson - 1827 - 513 pages
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The first six books of the Elements of Euclid, with numerous exercises

Euclides - Geometry - 1853 - 147 pages
...equiangular to the triangle def Wherefore, if two triangles, &c. QED PROPOSITION VII. — THEOREM. If two triangles have one angle of the one equal to one angle of tJie other, and the sides about two other angles proportionals, then if each of tlie remaining angles...
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Minutes of the Committee of Council on Education

Great Britain. Committee on Education - School buildings - 1855
...the other sides of the triangle have. 2. If two triangles have one angle of the one equal to one angh of the other, and the sides about the equal angles...equal which are opposite to the homologous sides. 3. If four straight lines be proportionals, the rectangle contained by the extremes is equal to the...
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National Society's Monthly Paper

1855
...segments of the hase shall have the same ratio which the other sides of thi; triangle have. 2. If two triangles have one angle of the one equal to one angle...about the equal angles proportionals, the triangles bhall be equiangular, and shall have those angles equal which are opposite to the homologous sides....
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855
...one of the parallels passes through the extremities of all the parallels. PROP VII. THEOREM. If two triangles have one angle of the one equal to one angle of the other, and the sides about another angle in each, proportionals ; and if the remaining angle in each be of the same affection...
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Liber Cantabrigiensis, an account of the aids afforded to poor students, the ...

Robert Potts - 1855
...triangle and the other two sides produced. 6. If two triangles have one angle of the one equal to otie angle of the other, and the sides about the equal angles proportionals, the triangle shall be equiangular, and shall have those angles equal which are opposite to the homologous...
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Elements of Geometry: Containing the First Six Books of Euclid with a ...

John Playfair - Geometry - 1855 - 318 pages
...equiangular to the triangle DEF. PROP. VI. THEOR. If two triangles have one angle of the one efnaH to one angle of the other, and the sides about the equal angles proportinnals, the triangles shall be equiangular, and shall have those angles equal which are opposite...
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The Calendar of King's College, London

1857
...angle ; and the angle in a segment less than a semicircle is greater than a right angle. 9. If two triangles have one angle of the one equal to one angle...equal which are opposite to the homologous sides. 10. If two triangles which have two sides of the one proportional to two sides of the other, be joined...
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The English Journal of Education, Volumes 11-13

Education - 1857
...the bent lever. BIGHEB MATHEMATICS AND MATHEMATICAL PHYSICS. SECOND YEAR. SECTION I. — 1. If two triangles have one angle of the one equal to one angle of the other and the sides about two other angles proportional ; then if each of the remaining angles be less or not less than a right...
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The Educational record, with the proceedings at large of the ..., Volumes 3-4

British and foreign school society - 1857
...improvements are due to the eighteenth century? HIGHER MATHEMATICS AND MATHEMATICAL PHfSCg. 1. If two triangles have one angle of the one equal to one angle of the other atid the sides "aboiift two other angles proportional ; then if each of the remaining angles be less...
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The Quarterly Journal of Pure and Applied Mathematics

Mathematics - 1871
...the proposition and reduces it to a case of ambiguous equality. Let the triangles ABC, DEF (fig. 9) have one angle of the one equal to one angle of the other; namely, L ВАС = DEF, and the sides about two other angles ABC, EDF proportionals, so that AB :...
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