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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. "
Elements of Plane Geometry According to Euclid - Page 129
by Andrew Bell - 1837 - 240 pages
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Papers for the Schoolmaster

1852
...2. About a given circle, to describe i triangle equiangular to a given triangle. 3. If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals the triangles shall be equiangular, and shall have...
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The Bible Question Decided in a Correspondence

Rev. William R. Williams - 1852
...A c : A b : : A" E": A" F". Now it is demonstrated in treatises on geometry,* that if two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals, the triangles are equiangular, and consequently...
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Public Education: As Affected by the Minutes of the Committee of Privy ...

Sir James Kay-Shuttleworth - Church and education - 1853 - 500 pages
...triangles on each side of it are similar to the whole triangle and to one another. 2. Equal triangles which have one angle of the one equal to one angle of the other, have their sides about their equal angles reciprocally proportional. 3. Equiangular parallelograms have to one another the...
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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - Mathematics - 1853
...equiangular to the triangle DEF. Wherefore, if the sides, etc. QED PROPOSITION VI. THEOR. If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals, the triangles shall be equiangular, and shall have...
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The first six books of the Elements of Euclid, with numerous exercises

Euclides - Geometry - 1853 - 147 pages
...other, have their sides about the equal angles reciprocally proportional ; and parallelograms that have one angle of the one equal to one angle of the other, and their sides about the equal angles reciprocally proportional, are equal to one another. LET ab,...
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The Elements of Euclid. Books I.-VI.; XI. 1-21 XII. 1-2. A New Text ..., Book 1

Euclides - Geometry - 1853
...straight lines A, B has been found a mean proportional HE. Which was to be done. PEOP. XIV. THEOE. If two parallelograms, which have one angle of the one equal to one angle of tie other, be equal : then they shall have their sides about this pair of equal angles reciprocally...
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Orr's Circle of the Sciences: The mathematical sciences

William Somerville Orr - Science - 1854
...PROPOSITION XV.— THEOKBM. Equal triangles (ABC, ADE), which have an angle (A) of the one equal to au angle of the other, have their sides about the equal angles reciprocally proportional ; and triangles which have an angle of the one equal to an angle of the other, and their sides about those...
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Elements of Geometry: Containing the First Six Books of Euclid with a ...

John Playfair - Geometry - 1855 - 318 pages
...wherefore the parallelogram AB is equal (9. 5.) to the parallelogram BC. PROP. XV. THEOR. Equal triangles which have one angle of the one equal to one angle of the other have their sfdes about the equal angles reciprocally proportional; And triangles which have one angle in the one...
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National Society's Monthly Paper

1855
...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 of the other, and the sides about the equal angles proportionals, the triangles bhall be equiangular, and shall have...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855
...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...
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