 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 Geometry - Page 190by George Bruce Halsted - 1886 - 366 pagesFull view - About this book
 | Charles Butler - 1814 - 582 pages
...a6=the square of the product, wherefore ^ai^zthe product. 234. Prop. 23. Hence, if two triangles have one angle of the one equal to one angle of the other, they will have to each other the ratio compounded of the ratios of the sides about their equal angles;... | |
 | Daniel Cresswell - Geometry - 1816 - 352 pages
...is equal to FE, and the angle ABC to EFG. PROP. XIX. (114.) Theorem. If two spherical triangles have one angle of the one equal to one angle of the other, and have also the two sides about another angle in each severally equal, and if the third angle, in each,... | |
 | Euclides - 1816 - 588 pages
...: And because HE 'i«£ THE ELEMEtftS Booif Vl. PROP. XIV. TttEOR. 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... | |
 | Daniel Cresswell - Euclid's Elements - 1817 - 454 pages
...also touch the chord on the same side as the less circle touches it. (XI 1 1.) If two triangles have one angle of the one, equal to one angle of the other, and also another angle of the one, together with another angle of the other, equal to two right angles,... | |
 | John Playfair - Circle-squaring - 1819 - 350 pages
...to the triangle DEF. Wherefore, if two triangles, &c. QE D PROP. VII. THEOR. If two triangles have one angle of the one equal to one angle of the other, and the sides about two other angles proportionals, then, if each of the remaining angles be either less, or not less,... | |
 | Daniel Cresswell - Geometry - 1819 - 446 pages
...BC, and terminated by the given point D, is a rhombus. PROP. XI. 17. THEOREM. If two triangles have one angle of the one, equal to one angle of the other, and also another angle of the one, together with another angle of the other, equal to two right angles,... | |
 | Adrien Marie Legendre - Geometry - 1819 - 574 pages
...involve those of all figures, THEOREM. 208. Two triangles, whkh Iiave an angle of the one equal to an angle of the other and the sides about these angles proportional, are similar. Fig. 122. Demonstration. Let the angle A = D (Jig. 122), and let AB : DE ::•AC: DF, the triangle... | |
 | John Playfair - 1819 - 354 pages
...parallelogram BC. Therefore equal parallelograms, &c. Q, ED PROP, XV. THEOR. triangles 'which have one angle of the one equal to one angle of the other, have their sides about >k> equal angles reciprocally proportional : And triangles mhich have one angle... | |
 | Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 pages
...involve those of all figures. THEOREM. 208. Two triangles, which have an angle of the one equal to an angle of the other and the sides about these angles proportional, are similar. Demonstration. Let the angle A = D (Jig. 122), and let Fig. 122. £g . DE ..£c. Dp, tne triangie £gc... | |
 | Adrien Marie Legendre - Geometry - 1825 - 276 pages
...involve those of all figures. THEOREM. 208. Two triangles, which have an angle of the one equal to an angle of the other and the sides about these angles proportional, are similar. Demonstration. Let the angle A-=D (fig. 122), and let Fifr 122. ^g . DE ..£C. QF^ the triangie ^BC... | |
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