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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 Ago ... - Page 161
by Robert Simson - 1806 - 518 pages
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The English Journal of Education, Volume 6

Education - 1852
...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 paralellograras...
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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
...hence AB is to BC as DE to EF, and BC to CA as EF to FD. . Which was to be proved. PEOP. VII. THEOE. If two triangles have (!•) one angle of the one equal to one angle of the other ; (2) the sides about one of the other two pairs of angles proportionals ; and if each of the third...
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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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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 arc 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...
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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - Mathematics - 1853
...proportional DB is found. Which was to be done. PROPOSITION XIV. THEOR. Equal parallelograms which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional : and parallelograms that have one...
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National Society's Monthly Paper

1855
...the 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...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
...extremity of 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
...and the angle at A to the ;mgle at D. Therefore the triangle ABC is 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...
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Minutes of the Committee of Council on Education

Great Britain. Committee on Education - School buildings - 1855
...; the segments of the base shall have the same ratio which 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 proportionals, the triangles shall be equiangular,...
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