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" If two triangles have two sides and the included angle of the one, equal to two sides and the included angle of the other, each to each, the two triangles will be equal in all their parts." Axiom 1. "Things which are equal to the same thing, are equal... "
Manual of Geometry and Conic Sections: With Applications to Trigonometry and ... - Page 273
by William Guy Peck - 1876 - 366 pages
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Mathematical Dictionary and Cyclopedia of Mathematical Science: Comprising ...

Charles Davies, William Guy Peck - Mathematics - 1855 - 628 pages
...themselves will bo equal." Prop. V. " When two triangles have two sides, and the included angle of the une equal to two sides and the included angle of the other, each to each, the two triangles will be equal. "Axiom 1. Things which are equal to tho same thing are equal to each...
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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - Geometry - 1856 - 460 pages
...the sum of the interior angles less than two right angles. OF TRIANGLES. THEOREM XX. If two triangles have two sides and the included angle of the one, equal to the two sides and the included angle of the other, the triangles will fie identical, or equal in all...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1857 - 242 pages
...because AB is equal to CD, and BC is common to the two triangles ABC, BCD, the two triangles ABC, BCD have two sides and the included angle of the one, equal to two sides and the included angle of the other ; therefore, the side AC is equal to BD (Prop. VI.), and the angle ACB to the angle CBD....
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Elements of Geometry and Trigonometry from the Works of A. M. Legendre ...

Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 442 pages
...by construction, AG=DE: DF, Q D B AH. CEP DF; hence AH=DF. Therefore, the two triangles A GH, DEF, have two sides and the included angle of the one equal to two sides and the included angle of the other : hence, they are equal (BI, p. 5) ; but the triangle A GH is similar to ABC : therefore,...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1858 - 256 pages
...because AB is equal to CD, and BC is common to the two triangles ABC, BCD, the two triangles ABC, BCD have two sides and the included angle of the one, equal to two sides and the included angle oi the other ; therefore, the side AC is equal to BD (Prop. VI.), and the angle ACB to the angle CBD....
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Carpentry Made Easy: Or, The Science and Art of Framing, on a New and ...

William E. Bell - Bridge building - 1857 - 250 pages
...FAGE is equivalent to the square P. Again, the two triangles ABH rod CBI are equal, having also two sides and the included angle of the one equal to two sides and the included angle of the other ; and AHB is half of 'he square X, and CBI is half of the rectangle FBIG : therefore,...
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Carpentry Made Easy, Or, The Science and Art of Framing, on a New and ...

William E. Bell - Bridges - 1859 - 226 pages
...quantities ; 8; AXS:BX8:: A:B; (AX8)XB=(BX8)XA, AX8:BX8::A:B. Proposition VIII. Theorem. Wlien two triangles have two sides and the included angle of the one equal to two sides and the included angle of tJn other, each to each, the two triangles are equal. 1n the triangles ABC and DEF, let AB=DE, AC=DF,...
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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - Geometry - 1860 - 474 pages
...sum of the interior angles less than two right angles. OF TRIANGLES. • THEOREM XX. If two triangles have two sides and the included angle of the one, equal to the two sides and the included angle of the other, the triangles will be identical, or equal in all...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1861 - 244 pages
...right angles. PROPOSITION VI. THEOREM. If two triangles have two sides, and the included angle of t/ie one, equal to two sides and the included angle of the other > each to each, the two triangles will be equal, their third sides will be equal, and their other angles will be equal,...
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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 532 pages
...construction, AG is equal to DE ; hence А П is equal to D F. Therefore the two triangles AGH, DEF, having two ¡sides and the included angle of the one equal to...and the included angle of the other, each to each, are themselves equal (Prop. V. Bk. I.). But the triangle AGH is similar to А В С ; therefore DEF...
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