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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; viz. the first six books, together with the eleventh ... - Side 153
av Euclides - 1814
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Christian Pamphlets, Volum 7

1852 - 1080 sider
...: A b,. that is, 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...about the equal angles proportionals, the triangles are equiangular, and consequently similar ; we have seen that the two triangles A bc, A!' F"E" are...
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The English Journal of Education, Volum 6

1852 - 508 sider
...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 ..., Bok 1

Euclides - 1853 - 334 sider
...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 - 1853 - 176 sider
...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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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

...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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Public Education: As Affected by the Minutes of the Committee of Privy ...

Sir James Kay-Shuttleworth - 1853 - 522 sider
...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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National Society's Monthly Paper

1855 - 264 sider
...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 - 258 sider
...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 - 1050 sider
...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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Minutes of the Committee of Council on Education

...; 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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