| 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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