 | 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... | |
 | 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...and the included angle of the other, each to each, the two triangles will be equal. In the two triangles EDF and BAC, let the side ED be equal to the... | |
 | 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...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 (A. 8) ; hence, there is no... | |
 | Anthony Dumond Stanley - Sphere - 1854 - 130 pages
...these two sides. Now DCE is equal to this triangle, two sides and the included angle of the one being equal to two sides and the included angle of the other, each to each ; since CE and DE are supplements of AE and BE, and the angle CED is equal to AEB. Since then CDE is... | |
 | Charles Davies - Geometry - 1855 - 340 pages
...the angle B to the angle E : then will AB : AC : : DE : DF96 BOOK IVProportions of TrianglesFor, on the sides of the larger triangle DEF, make Dl equal...Hence, the angles'/ and G are equal to C and B, and consequently, to the angles F and E : therefore, IG is parallel to EF (Bk- I- Th- xiv, Cor- 1)Now,... | |
 | Charles Davies, William Guy Peck - Electronic book - 1855 - 592 pages
...equal, each to each, and the triangles themselves will bo equal." Prop. V. " When two triangles have two sides, and the included angle of the one equal to...and the included angle of the other, each to each, the two triangles will be equal. " Axiom 1. Things which are equal to the same thing are equal to each... | |
 | 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... | |
 | Samuel Simon Schmucker, S. S. (Samuel Simon) Schmucker - History - 1855 - 332 pages
...demonstration of the theorem of Euclid known as Prop. IV. of Book I., viz.: If two triangles have two sides, and the included angle of the one equal to two sides and the included angle of the other, they must be identical or equal in all respects. For it virtually consists in supposing... | |
 | 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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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... 
