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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 ... - Seite 165
von Robert Simson - 1806 - 518 Seiten
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Examination Papers

University of Toronto - 1900 - 1158 Seiten
...the other, have their sides about the equal angles reciprocally proportional ; and triangles which 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. Use this proportion...
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The Contents of the Fifth and Sixth Books of Euclid

Euclid, Micaiah John Muller Hill - 1900 - 143 Seiten
...about the equal angles reciprocally proportional, are equal in area. 49. (i) Equal triangles which have one angle of the one equal to one angle of the other have their sides about the equal angles reciprocally proportional. (ii) Triangles which have one angle...
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The Contents of the Fifth and Sixth Books of Euclid

Micaiah John Muller Hill - 1900 - 143 Seiten
...PROPOSITION XLVIII. (i). (Euc. VI. 14, 1st Part.) ENUNCIATION. Parallelograms having equal areas and having one angle of the one equal to one angle of the other have the sides about the equal angles reciprocally proportional. Let the two parallelograms be placed...
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Selected List of Educational Books for Secondary Schools

Macmillan & Co - 1901 - 776 Seiten
...; .:, by addition, . a + b+e+ ... x+y+z+ ... or a:x 338 EUCLID'S ELEMENTS. PROPOSITION 6. THEOREM. If two triangles have one angle of the one equal to...equal angles proportionals, the triangles shall be similar. In the A' BAG, EOF, let the L. BAG = the /_ EOF, and let BA : AC :: ED : DF. Then shall the...
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Woolwich Mathematical Papers for Admission Into the Royal Military Academy ...

Eldred John Brooksmith - 1901 - 368 Seiten
...diameters. 10. Describe a circle about a given equilateral and equiangular pentagon. 11. Triangles which have one angle of the one equal to one angle of the other and the sides about the equal angles reciprocally proportional, are equal to one another. , Two straight lines AOC, BOD intersect in 0 and...
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Elementary Geometry, Plane and Solid: For Use in High Schools and Academies

Thomas Franklin Holgate - 1901 - 440 Seiten
...vertex of the right angle which make equal angles with one of the sides. MISCELLANEOUS EXERCISES 1. If two triangles have one angle of the one equal to one angle of the other, and a second angle of the one supplementary to a second angle of the other, then the sides about the third...
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Report of the Committee of Council on Education in Scotland...[without Appendix]

1901
...A(f he bisected in fí, find the locus of R. 6. If two triangles have an angle of the one equal to an angle .of the other, and the sides about the equal angles proportionals, the triangles shall he similar. 13_ In the side ЛГ> of the triangle AUC a point I> is taken, and DE is drawn parallel...
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Report of the Committee of Council on Education in Scotland...[without Appendix]

1902
...pentagon is equal to the sum of a side and a diagonal of the smaller pentagon. 5. Equal triangles, which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional. 12, ABCD is a trapezium in which...
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Vectors and Rotors: With Applications

Olaus Henrici, George Charles Turner - 1903 - 236 Seiten
...negative. Geometrically the theorem is that of Euc. VI. vi., from which the general case follows at once. " If two triangles have one angle of the one equal to...equal angles proportionals, the triangles shall be similar." For if one triangle be applied to the other so that the proportional sides are in the same...
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Elementary Geometry: Practical and Theoretical

Charles Godfrey, Arthur Warry Siddons - 1903 - 355 Seiten
...§AB, OQ = J5 AC ; join PQ ; measure L.' P, Q, and compare them with L.' B, C. =o fig. 313. THEOREM 5. 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. fig. 314. Data ABC, DEF are two triangles...
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