| Adrien Marie Legendre - Geometry - 1857 - 448 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,... | |
| Elias Loomis - Conic sections - 1858 - 234 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.... | |
| Bridges - 1857 - 134 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,... | |
| William E. Bell - Bridges - 1859 - 134 pages
...two 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...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,... | |
| George Roberts Perkins - Geometry - 1860 - 443 pages
...which has 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 be identical, or equal in all... | |
| Benjamin Greenleaf - Geometry - 1862 - 490 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... | |
| Benjamin Greenleaf - Geometry - 1862 - 490 pages
...sides of the same square ; and BF equal to BC, for the same reason ; therefore the triangles ABF, HBC **have two sides and the included angle of the one equal to two sides and the included angle** of the other ; hence they are themselves equal (Prop. V. Bk. I.). G ELEMENTS OF GEOMETRY. EG same altitude... | |
| Benjamin Greenleaf - Geometry - 1863 - 320 pages
...sides of the same square ; and BF equal to BC, for the same reason ; therefore the triangles ABF, HBC **have two sides and the included angle of the one equal to two sides and the included angle** of the other ; hence they are themselves equal (Prop. V. Bk. I.). ELEMENTS OF GEOMETRY. K same altitude... | |
| Evan Wilhelm Evans - Geometry - 1862 - 98 pages
...similar. • Take AG equal to DE, and AH to DF ; also, join GH. Then the triangles AGH, DEF, having two **sides and the included angle of the one equal to two sides and the included angle** of the other, are equal throughout (Theo. VII, B. I). Now,- by hypothesis, AB : DE : : AC : DF. Therefore,... | |
| CHARLES DAVIES, LL.D. - 1863
...be greater nor less than D : hence, it must be equal to it. The two triangles have, therefore, two **sides and the included angle of the one equal to two sides and the** inclu* ded angle of the other, each to each ; and, consequently, they are equal in all their parts... | |
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