 | Elias Loomis - Conic sections - 1849 - 252 pages
...intersection, are together equal to four right angles. PROPOSITION VI. THEOREM. 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, their third sides will be equal, and their... | |
 | Charles Davies - Logic - 1850 - 390 pages
...each, and the triangles themselves will be equal." Prop. V. " When two triangles have two Proposition 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." Axiom I. " Things which are equal to... | |
 | Charles Davies - Logic - 1850 - 402 pages
...to each, and the triangles themselves will be equal." Prop. V. " When two triangles have two tides 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." Axiom I. " Things which are equal to... | |
 | George Roberts Perkins - Geometry - 1850 - 332 pages
...BAC is equal to its alternate angle DCA, (Prop, xvu;) hence the two triangles, having two sides^and the included angle of the one equal to two sides and the included angle of the other, namely, the side equal to the side CD, the side AC common, and the contained angle BAC... | |
 | Charles Davies - Geometry - 1850 - 218 pages
...Triangles. ACD+BCD=ADC+BDC that is, the angle ACB=ADB. Now, the two triangles ACB and ADB have two sides and the included angle of the one equal to two sides and the ineluded angle of the other, each to each: hence, the remaining angles will be equal (Th. iv) : consequently,... | |
 | Charles Davies - Geometry - 1850 - 238 pages
...Triangles. ACD+BCD=ADC+BDC that is, the angle ACB=ADB. Now, the two triangles ACS and ADB have two sides and the included angle of the one equal to two sides and the in. eluded angle of the other, each to each : hence, the remaining angles will be equal (Th. iv) :... | |
 | Adrien Marie Legendre - Geometry - 1852 - 436 pages
...to the successive angles ACB, BCD, DCE, ECF, FCA. PROPOSITION V. THEOEEM. 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 the two triangles EDF and BAC, let... | |
 | Charles Davies - Geometry - 1886 - 340 pages
...Triangles. ACD+BCD=ADC+BDC that is, the angle ACB=ADB. Now, the two triangles ACB and ADB have two sides and the included angle of the one equal to two sides and the in. eluded angle of the other, each to each: hence, the remaining angles will be equal (Th. iv) : consequently,... | |
 | Charles Davies - Geometry - 1854 - 436 pages
...angle A CB, by hypothesis ; and the side BC , common: therefore, the two triangles, BDC, BAC, have two sides and the included angle of the one, equal to two sides and the included angle of the other, each to each : hence they are equal (p. 5). But the part cannot be equal to the whole... | |
 | Mathematics - 1866 - 426 pages
...Euclid in his Demonstration of I. G anything else ? by supposing BG = AC. he obtains two triangles having two sides and the included angle of the one equal to two sides and the included angle of the other ; two triangles, which, if the supposition BG = AG is correct should, applied one upon... | |
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DEF, having two sides and the included angle of the one equal to two sides and the included angle of the other, each to each, are themselves equal (Prop. 
