 | Mathematics - 1868
...the point P to the points A and B cut a line in the points a, /3. The areas of triangles which have one angle of the one equal to one angle of the other, have to one another the ratio which is compounded of the ratios of the sides. Applying this to the... | |
 | Robert Potts - 1863
...produced. Also describe a circle touching three sides of a parallelogram. 6. 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, triangle shall be equiangular, and shall have... | |
 | Euclides - 1864
...(v. 9.) Therefore equal parallelograms, &c. QED PROPOSITION XV. THEOREM. Equal triangles which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocallg proportional : and converselg, triangles which... | |
 | Euclides - 1865
...BO. (v. 9.) Therefore equal parallelograms, &c. QED PROP. XV.— THEOREM. 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 ; and conversely, triangles which... | |
 | Isaac Todhunter - Euclid's Elements - 1880 - 400 pages
...Hence the result may be extended to triangles, and we have the following theorem, triangles which have one angle of the one equal to one angle of the other, have to one another the ratio which it compounded of the ratios of their tides. Then VI. 19 is an immediate... | |
 | Woolwich roy. military acad, Walter Ferrier Austin - 1880
...segments BG, GD, GC of the base shall be in harmonical proportion. 12. 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. ALGEBRA. 1. Prove that se и х... | |
 | Education, Higher - 1883
...other, have their sides about the equal angels reciprocally proportional ; and triangles which have one angle of the one equal to one angle of the other,...reciprocally proportional, are equal to one another. 15. If two straight lines be at right angles to the same plane, they shall be parallel to one another.... | |
 | Euclides - 1881
...reciprocally proportional ; and conversely, parallelograms which have an angle of the one equal to an angle of the other, and their sides about the equal angles reciprocally proportional ere equal to one another. First, Let AB and BC be equal parallelograms, which have their angles at... | |
 | George Bruce Halsted - Measurement - 1881 - 232 pages
...ratio m:n, and its area E. f^jj l^g « = •»/ ; 0=-\l — . Ans. \ n \ m 521. If two triangles have one angle of the one equal to one angle of the other, and the sides about a second angle in each equal, then the third angles will be either equal or supplemental.... | |
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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. 
