| Adrien Marie Legendre - 1871 - 490 pągines
...their parts (I., D. 14) ; which was to be proved. PROPOSITION VI. THEOREM. If two triangles have t1oo angles and the included side of the one equal to two...and the included side of the other, each to each, the triangles will be equal in all their parts. In the triangles ABC and DEF, let the angle B be equal... | |
| Elias Loomis - 1871 - 302 pągines
...to the angle AGE (Prop V.) ; and, by construction, BG is equal to GA ; hence the triangles BGF, AGE have two angles and the included side of the one,...equal to two angles and the included side of the other ; they are, therefore, equal (Prop. VII.) ; and the angle BFG is equal to the angle AEG. But AEG is,... | |
| Charles Davies - 1872 - 464 pągines
...in all their pa1ls (I., D. 14) ; which was to be proved. PROPOSITION VI. THEOREM. If two tria11gles have two angles and the included side of the one equal...and the included side of the other, each to each, the triangles mill be equal in all their parts. In the triangles ABC and DEF, let the angle />' be... | |
| Edward Olney - 1872 - 270 pągines
...Then b'c' = be, and Ac' = ac, since the triangles aba and A&V have two angles and the included side of one equal to two angles and the included side of the other. In like manner draw c'd' making angle b'c'd' — bed, c'd'— ed, and Ad'= ad. So, also, making angle... | |
| Edward Olney - 1872 - 472 pągines
...Ai'c' = b. Then b'c' = be, since the triangles abe, and Ai'c' have two angles and the included side of one equal to two angles and the included side of the other. In like manner draw c'd' making angle b'c'd'= bed, and c'd'= cd. So, also, making angle c'd'c' = cde,... | |
| Adrien Marie Legendre - 1874 - 500 pągines
...to be proved. PROPOSITION IX. THEOREM. If two spherical triangles on the same, or on equal spheres, have two angles and the included side of the one equal...and the included side of the other, each to each, the remaining parts will be equal, each to each Let the spherical triangles ABC and EFG, have the angle... | |
| Aaron Schuyler - 1875 - 284 pągines
...T'"0 is the supplement of ОT'; hence, ОT --= T'"О, and the angle ОCT is equal to the angle ОCT'". The angle COR is equal to the angle COR', since each...OR is estimated upward, and OR' downward, they have contrary signs; hence, OR = — OR'. But OR is the tangent of the arc ОT, and OR' is the tangent of... | |
| B. Marks - 1875 - 176 pągines
...does the line de fall exactly upon the line ab? DEMONSTRATION. We wish to prove that, // two triangles have two angles, and the included side of the one...and the included side of the other, each to each, the two triangles are equal to each other in all respects. Let the triangles abc and d ef have the... | |
| William Guy Peck - 1876 - 412 pągines
...GEOMETRY. PROPOSITION VIII. THEOREM. If two spherical triangles have two angles and the included side of one, equal to two angles and the included side of the other, each to each, their remaining parts are equal, each to each. Let FGH and ACD be two spherical triangles, in which... | |
| Edward Olney - 1876 - 354 pągines
...on equal spheres, two sphev'cal triangles having two angles and the included side of the one eqval to two angles and the included side of the other, each to each, areequal, or symmetrical and equivalent. DEM.—Using the same triangles as in the preceding proposition,... | |
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