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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, containing the first six books, with a selection of ... - Σελίδα 199
των Euclides - 1874
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Sessional Papers, Τόμος 22,Μέρος 2

Great Britain. Parliament. House of Commons - 1900 - 686 σελίδες
...submultiple, ratio, homologous, duplicate ratio. 8. If two triangles have one angle of the one equal to on« angle of the other, and the sides about the equal angles proportionals, the triangles shall lx) similar. In a given straight line PQ a point M is taken and PQ is produced to 0 so that MO is a...

Examination Papers

University of Toronto - 1900 - 1160 σελίδες
...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...

The Contents of the Fifth and Sixth Books of Euclid

Euclid, Micaiah John Muller Hill - 1900 - 190 σελίδες
...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...

The Contents of the Fifth and Sixth Books of Euclid

Euclid, Micaiah John Muller Hill - 1900 - 165 σελίδες
...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...

Selected List of Educational Books for Secondary Schools

Macmillan & Co - 1901 - 804 σελίδες
...kx, b = ky, c = kz, ... ; .:, by addition, . a + b+e+ ... x+y+z+ ... or a:x 338 EUCLID'S ELEMENTS. PROPOSITION 6. THEOREM. If two triangles have one...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...

Woolwich Mathematical Papers for Admission Into the Royal Military Academy ...

Eldred John Brooksmith - 1901 - 368 σελίδες
...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...

Elementary Geometry, Plane and Solid: For Use in High Schools and Academies

Thomas Franklin Holgate - 1901 - 462 σελίδες
...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...

Report of the Committee of Council on Education in Scotland...[without Appendix]

1901 - 808 σελίδες
...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...

Report of the Committee of Council on Education in Scotland...[without Appendix]

1902 - 942 σελίδες
...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...

Vectors and Rotors: With Applications

Olaus Henrici, George Charles Turner - 1903 - 236 σελίδες
...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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