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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. "
Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books - Seite 245
von Euclid - 1765 - 464 Seiten
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Christian Pamphlets, Band 7

1852 - 1080 Seiten
...: 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 one angle of the other, and the sides about the equal angles proportionals, the triangles are equiangular, and consequently similar...
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The English Journal of Education, Band 6

1852 - 512 Seiten
...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 ..., Bücher 1

Euclides - 1853 - 334 Seiten
...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 Seiten
...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

Royal Military Academy, Woolwich - 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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Public Education: As Affected by the Minutes of the Committee of Privy ...

Sir James Kay-Shuttleworth - 1853 - 522 Seiten
...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 Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855 - 270 Seiten
...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...
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National Society's Monthly Paper

1855 - 264 Seiten
...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 one angle of the other, and the sides about the equal angles proportionals, the triangles bhall be equiangular, and shall have those...
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Minutes of the Committee of Council on Education

Great Britain. Committee on Education - 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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The Calendar of King's College, London

1857 - 486 Seiten
...a right 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 of the other, and the sides about the equal angles proportionals, the triangles shall be equiangular, and shall have those...
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