 | Dennis M'Curdy - 1846 - 166 pagina’s
...same unit, &c. QED BOOK SIXTH. Definitions. 1. Similar rectilineal figures are those which have their angles equal, each to each ; and the sides about the equal angles proportionals. 2. Reciprocal figures, viz. triangles and parallelograms, are those which have their sides about two... | |
 | Euclides - 1846 - 292 pagina’s
...four magnitudes Sfc. BOOK VI. DEFINITIONS. i. SIMILAR rectilineal figures are those which have their 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 of... | |
 | Euclides - 1848 - 52 pagina’s
...remaining of the last, each to each, or with the remaining ratio of the last. BOOK VI. DEFINITIONS. SIMILAR rectilineal figures are those which have their...and the sides about the equal angles proportionals. II. " Reciprocal figures, viz. triangles and parallelograms are such as have their sides about two... | |
 | Thomas Tate (mathematical master.) - 1848 - 284 pagina’s
...PROBLEMS RELATIVE TO THE CIRCLE. 56. THEOREM. A straight line c D, drawn from the * Def. Similar figures have their several angles equal, each to each, and the sides about the equal angles proportional. D 2 centre c of a circle, to the middle point D of a chord AB, is perpendicular to that... | |
 | Joseph Jones - 1849 - 370 pagina’s
...Circumference X the Diameter. When are areas said to be similar ? or What are similar rectilineal figures. Those which have their several angles equal, each to each, and the sides about the equal angles proportional. How do you compare similar areas? They are to each other as the squares of their like... | |
 | Royal Military Academy, Woolwich - 1853 - 400 pagina’s
...duplicate, both triplicate, etc.), be the same, then the fundamental ratios will be also the same. BOOK VI. DEFINITIONS. 1. SIMILAR rectilineal figures...and the sides about the equal angles proportionals. 2. •• Reciprocal figures, viz. triangles and parallelograms, are such " as have their sides about... | |
 | Euclides - 1853 - 176 pagina’s
...according as the first and second are equal to, greater, or less than each other. BOOK VI. DEFINITIONS. I. SIMILAR rectilineal figures are those which have their...and the sides about the equal angles proportionals. Definition I. II. Reciprocal figures, viz. triangles and parallelograms, are such as have their sides... | |
 | Euclides - 1855 - 230 pagina’s
...-L = —, T am JS. a J> therefore - = -T, 7> « and m : p .. h : I. »» A THE ELEMENTS OF EUCLID. BOOK VI. DEFINITIONS. 1. Similar rectilineal figures...and the sides about the equal angles proportionals. SCHOLIUM. In the cnse of triangles it would have been sufficient to state that ' similar triangles... | |
 | Euclides - 1855 - 270 pagina’s
...g. BOOK VI. DEFI3ÍITIONS. £, SIMILAR rectilineal figures are those which have their several angle equal, each to each, and the sides about the equal angles proportionals. In the case of triangles, this definition is redundant. For it ¡9 proved in Prop. IV. of this Book, that... | |
 | Robert Rawson - 1856 - 178 pagina’s
...another dimension in one figure; to find its corresponding dimension in the other. NB — "Similar figures are those which have their several angles...each to each, and the sides about the equal angles proportional." (Euclid, vi.) 3 Rule.— AD : ad:: DC : dc. J> The same proportion holds in respect... | |
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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 
