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 Books Books Two triangles having an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. Elements of Plane and Solid Geometry - Page 188
by George Albert Wentworth - 1877 - 398 pages ## An Elementary Treatise on the Geometrical and Algebraical Investigation of ...

Daniel Cresswell - Euclid's Elements - 1817 - 436 pages
...has to the aggregate of the two chords that are next to it. PROP. VI. (XVII.) If two trapeziums have an angle of the one equal to an angle of the other, and if, also, the sides of the two figures, about each of their angles, be proportionals, the remaining... ## Elements of Geometry

Adrien Marie Legendre - Geometry - 1819 - 208 pages
...proportional to the sides FG, GH, so that AB:FG::BC:GH. It follows from this, that the triangles ABC, FGH, having an angle of the one equal to an angle of the other and the sides about the equal angles proportional, are similar (208), consequently the angle ECA —... ## A Supplement to the Elements of Euclid

Daniel Cresswell - Geometry - 1819 - 410 pages
...:HE::AF:AE; that is, FG is to GE in the given ratio. PROP. XVII. 23. THEOREM. If two trapeziums have an angle of the one equal to an angle of the other, and if, also, the sides of the two figvres, about each of tJieir angles, be proportionals, the remaining... ## Euclid's Elements of Geometry: The Six First Books. To which are Added ...

Rev. John Allen - Astronomy - 1822 - 508 pages
...BL oy HE. Cor. 1.—By a similar reasoning it may be proved, that triangles, which have an angle of one, equal to an angle of the other, are to each other, in a ratio, compounded of the ratios, of the sides including the equal angles, Cor. 2.—A right line... ## The New Practical Builder and Workman's Companion, Containing a Full Display ...

Peter Nicholson - Architecture - 1823 - 596 pages
...CAG equal to D, take AG equal to DE or AB, and join CG ; and because the two triangles CAG, DEF, have an angle of the one equal to an angle of the other, and the sides which contain these angles are equal, CG shah1 be equal to EF (theorem 5). Now there... ## Elements of Geometry

Adrien Marie Legendre - Geometry - 1825 - 280 pages
...putting CM in the place of CA we shall have CP : CM : : CM : CQ ; consequently the triangles CPM, CQM, having an angle of the one equal to an angle of the other and the sides about the equal angles proportional, are similar (20") ; therefore MP:MQ::CP : CM or... ## Elements of Geometry...: Translated from the French for the Use of the ...

Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 pages
...putting CM in the place of CA we shall have CP : CM : : CM : CQ ; consequently the triangles CPM, CQM, having an angle of the one equal to an angle of the other and the sides about the equal angles proportional, are similar (203) ; therefore MP : MQ : : CP : CM... ## The Geometrical Companion, in which the Elements of Abstract Geometry are ...

George Darley - Geometry - 1828 - 190 pages
...equal." Here we have a criterion whereby to judge of the equality of two triangular surfaces, which have an angle of the one equal to an angle of the other. For example : ABCD is a road cutting off a triangular field AOB. It is desirable that the line of road... ## Elements of Geometry: With Practical Applications, for the Use of Schools

Timothy Walker - Geometry - 1829 - 129 pages
...vertices by the space of a quadrant, the sides will become parallel each to each. 3. — When they have an angle of the one equal to an angle of the other, and the sides including these angles proportional — . Thus if the F45 angle A=A (fig. 45), and if... 