Books Books If two triangles have an angle of one equal to an angle of the other... Euclid's Elements of Geometry: The Six First Books. To which are Added ... - Page 176
by Euclid, Rev. John Allen - 1822 - 494 pages ## The First Six Books with Notes

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... ## The New Practical Builder and Workman's Companion, Containing a Full Display ...

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... ## The First Six Books of the Elements of Euclid, with a Commentary and ...

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... ## Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

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... ## The First Six Books of the Elements of Euclid: With Notes

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... ## Popular Mathematics: Being the First Elements of Arithmetic, Algebra, and ...

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,... ## Popular Mathematics: Being the First Elements of Arithmetic, Algebra, and ...

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,... ## Euclid's Elements, Or, Second Lessons in Geometry: In the Order of Simson's ...

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... ## Euclid's Elements of geometry, the first three books (the fourth, fifth, and ...

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.... 