| Euclid - 1822 - 179 pages
...EF to GH(7). (5)Hypotii. 5Fig. \T. See N. PROP. XXIII. THEOR. Equiangular parallelograms (AB and CG) **are to each other in a ratio compounded of the ratios of** their sides. Let two of the sides AB and BC about the equal angles be placed so that they may form... | |
| Peter Nicholson - Architecture - 1823 - 596 pages
...the two lines AD, DB, therefore AB2 = AC2 THEOREM 63. 161. Two triangles, which have an angle of the **one equal to an angle of the other, are to each other** as the rectangle of the sides about the equal Suppose* the two triangles joined, so as to have a common... | |
| Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 324 pages
...subduplicates will also be equal. PROPOSITION XXIII. THEOREM. (640) Equiangular parallelograms (AD and CG) **are to each other in a ratio compounded of the ratios of** their sides. Let two of the sides AB and BC about the equal angles be placed so that they may form... | |
| John Playfair - Geometry - 1829 - 186 pages
...sides about the equal angles. ED. CoR. 2. Two parallelograms, which have one angle of one equal to one **angle of the other, are to each other in a ratio compounded of the ratios of the sides** of one to the sides of the other, each to each, about their equal angles. For two parals. having one... | |
| Euclid - Euclid's Elements - 1833 - 183 pages
...compounded of the ratios of the sides containing the equal angles. Cor. 3. Any parallelograms or triangles **are to each other in a ratio compounded of the ratios of** their bases and altitudes ; for they are equal to rectangles, or to right-angled triangles, on the... | |
| Robert Mudie - Mathematics - 1836 - 496 pages
...ratio of their bases. Therefore, again — Triangles or parallelograms which have different bases, **are to each other in a ratio compounded of the ratios of** their bases and altitudes. Thus, for instance, if the base of the triangle or parallelogram A is 12,... | |
| Robert Mudie - Mathematics - 1836 - 496 pages
...of their bases. Therefore, again — ••Triangles or parallelograms which have different bases, **are to each other in a ratio compounded of the ratios of** their bases and altitudes. Thus, for instance, if the base of the triangle or parallelogram A is 12,... | |
| Dennis M'Curdy - Geometry - 1846 - 138 pages
...5. NOTE. — The opposite sides and angles of a parallelogram are equal : p. 34ofb. 1. 15 Th. Equal **triangles which have an angle of one equal to an angle of the other,** have their sides about the equal angles reciprocally proportional : and triangles are equal, which... | |
| Euclides - 1846
...equal angles are reciprocally proportional (AB to BC as 1.I! to BD. And if two triangles (ABD and CBL), **have an angle of one equal to an angle of the other,** and the sides about the equal angles reciprocally proportional, they will be equal to one another.... | |
| Thomas Lund - Geometry - 1854 - 192 pages
...be : BC ; and by making C the centre, that be : BC :: ac : AC. COR. 1. Conversely, if two triangles **have an angle of one equal to an angle of the other,** and the sides forming the equal angles proportionals, the triangles will be similar. COR. 2. Hence,... | |
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