 | E. M. Reynolds - 1868 - 172 pàgines
...their sides about their equal angles reciprocally proportional, these triangles are equal, DBF. Similar figures are those which have their several angles...and the sides about the equal angles proportionals. It has been shewn that equiangular triangles have their sides about their equal angles proportionals... | |
 | Isaac Todhunter - 1869 - 312 pàgines
...feet. 70. From similar triangles we pass naturally to the consideration of similar rectilineal figures. Similar rectilineal figures are those which have their...and the sides about the equal angles proportionals. 71. Take for example two five-sided figures ABODE and abcde ; these are similar if the angles at A,... | |
 | Thomas Steadman Aldis - 1872 - 84 pàgines
...joining the two given points and produced. DBF. Similar rectilineal figures are such as have their angles equal each to each and the sides about the equal angles proportional. DEF. In proportion the antecedents or consequents of the ratios are said to be homologous.... | |
 | Euclid, James Bryce, David Munn (F.R.S.E.) - 1874 - 236 pàgines
...each of each, whatever multiple one of the magnitudes is of one, the same shall all be of all, .... BOOK VI. DEFINITIONS. 1. Similar rectilineal figures...and the sides about the equal angles proportionals. 2. Two magnitudes are said to be reciprocally proportional to two others, when one of the first pair... | |
 | Euclides - 1874 - 342 pàgines
...1, CM m to p (V. 11). QED BOOK VI. DEFINITIONS. 1. SIMILAR rectilineal figures are those which hare their several angles equal, each to each, and the sides about the equal angles proportionals. 2. " Reciprocal figures, viz., triangles and parallelograms, are such as have their sides about two... | |
 | James Martin (of the Wedgwood inst, Burslem.) - 1876 - 334 pàgines
...given straight line AB is divided in the point (7, so thatAB :AC: :5 :3. SECTION X.— SIMILAR FIGURES. DEFINITIONS. 1. " Similar rectilineal figures are...and the sides about the equal angles proportionals" (Euc. VI., Def. 1). NOTE 1. — The following rectilineal figures are similar, viz. : — All equilateral... | |
 | Robert Potts - 1876 - 446 pàgines
...Euclid's Elements > BOOK VL DEFINITIONS. I. SIMILAR rectilineal figures are those which have tlieir several angles equal, each to each, and the sides about the equal angles proportionals. n. " Reciprocal figures, viz. triangles and parallelograms, are such as have their sides about two... | |
 | Thomas Hunter - 1878 - 142 pàgines
...relation of A to B may be very vague. BOOK V. DEFINITIONS. 1. SIMILAR polygons are those which have their angles equal, each to each, and the sides about the equal angles proportional. 2. In similar polygons the sides adjacent to the equal angles are called homologous sides,... | |
 | Isaac Sharpless - 1879 - 282 pàgines
...A therefore A : B :: A+C+E+etc. : B+D + F+etc. BOOK V. SIMILAR POLYGONS.—MEASUREMENT OF POLYGONS. DEFINITIONS. 1. Similar rectilineal figures are those...each to each, and the sides about the equal angles proportional. 2. A straight line is cut in extreme and mean ratio when the whole is to the greater... | |
 | Isaac Todhunter - 1880 - 426 pàgines
...Z>/T, then and .F together are greater than CD and E together. Wherefore, if four magnitudes &c. QED BOOK VI. DEFINITIONS. 1. SIMILAR rectilineal figures...and the sides about the equal angles proportionals. 2. Reciprocal figures, namely, triangles and parallelograms, are such as have their sides about two... | |
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Reciprocal figures, viz. triangles and parallelograms, " are such as have their sides about two of their " angles proportionals in such a manner, that a side 
