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... Plane and Solid Geometry - Page 176by Seth Thayer Stewart - 1891 - 406 pagesFull view - About this book
| 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... | |
| Elias Loomis - Conic sections - 1857 - 242 pages
...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.... | |
| Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 442 pages
...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,... | |
| 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,... | |
| Elias Loomis - Conic sections - 1858 - 256 pages
...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.... | |
| William E. Bell - Bridges - 1859 - 226 pages
...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,... | |
| Horatio Nelson Robinson - Geometry - 1860 - 470 pages
...draw the line C'Elf. Take AD, equal to AE, and draw BD and DC. Now, the two triangles, CAD and CAE, having two sides and the included angle of the one equal to the two sides and included angle of the other, each to each, are equal, and CE = CD; but in the triangle,... | |
| 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,... | |
| 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...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 is... | |
| Benjamin Greenleaf - Geometry - 1861 - 638 pages
...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 arc themselves equal (Prop. V. Bk. I.). EG ELEMENTS OF GEOMETRY. same altitude... | |
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