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" If two sides and the included angle of the one are respectively equal to two sides and the included angle of the other... "
Elements of Geometry: With, Practical Applications - Page 28
by George Roberts Perkins - 1850 - 320 pages
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Elements of Geometry: With Notes

John Radford Young - Euclid's Elements - 1827 - 246 pages
...and join GH. fa/ V Then the triangles GBH, DEF are equal, since two sides and the included angle in the one are respectively equal to two sides and the included angle in the other ; hence, and by hypothesis, AB : BC : : GB : BH, that is, the sides BA, BC of the triangle...
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An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1837 - 216 pages
...the equal angles in the second, are called homologous. 51. Theorem. Two triangles are equal, when two sides and the included angle of the one are respectively equal to two sides and the included angle of the other. Demonstration. In the two triangles ABC, DJP(ng.31), let the angle A be equal to the...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid - Geometry - 1837 - 410 pages
...respect equal. They are proved to be such in the fourth proposition, u In , tivo sides and the contaHied angle of the one are respectively equal to two sides and the contained angle of the other : in the eighth, when the three sides of the one are equal to the three...
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Elements of Geometry: On the Basis of Dr. Brewster's Legendre : to which is ...

James Bates Thomson - Geometry - 1844 - 237 pages
...consequently they are equal. (Ax. 13.) Hence, universally, Any two triangles are every way equal, when two sides and the included angle of the one, are respectively equal to two sides and the included angle of the other. PROPOSITION VI. THEOREM. If two triangles ABC, DEF, have two angles and the interjacent...
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Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...

Nathan Scholfield - 1845 - 896 pages
...has been proved (Prop. VIII.) that two triangles are equal, when two sides and the included angle in the one, are respectively equal to two sides and the included angle in the oilier ; we may now infer further, that two triangles are equivalent or equal in surface, when...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1845 - 380 pages
...respect equal. They are proved to be such in the fourth proposition, when two sides and the contained angle of the one are respectively equal to two sides and the contained angle of the other: in the eighth, when the three sides of the one are equal to the three...
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Elements of Geometry: With Practical Applications ...

George Roberts Perkins - Geometry - 1847 - 308 pages
...greater than CB ; then take AD equal to BC, and join DB. Now in the two triangles DAB and CBA, we have DA equal to CB by construction, the side AB common, and...CB and CA, and therefore the triangle is isosceles. PROPOSITION VIII. THEOREM. When two triangles have all the three sides of the one equal to all the...
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An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1847 - 150 pages
...the equal angles in the second, are called homologous. 51. Theorem. Two triangles are equal, when two sides and the included angle of the one are respectively equal to two sides and the included angle of the other. Proof. In the two triangles ABC, DEF, (fig. 31), let the angle Jl be equal to the angle...
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Elemento of Geometry, Theoretical and Practical: Containing a Full ...

George Clinton Whitlock - Mathematics - 1848 - 324 pages
...and a increase or decrease together. Cor. 2. Two spherical triangles are equal : (537) 1. When two sides and the included angle of the one are respectively equal to the two sides and the included angle of the other ; and therefore, FOR A SIDE. 265 Fig. 120a. 2....
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1849 - 252 pages
...to DF, and join GH. Then the triangles AGH, DEF are equal, since two sides and the included angle in the one, are respectively equal to two sides and the included angle in the other (Prop. VI., BI). But, by hypothesis, AB : DE : : AC : DF; therefore AB : AG : : AC : AH;...
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