 | 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...other, each to each, the two triangles will be equal." Axiom I. " Things which are equal to the same thing, are equal to each other." Axiom X. (of Legendre).... | |
 | Charles Davies - Geometry - 1850 - 218 pages
...angle BDC. Of 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
...angle BDC. Of 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) :... | |
 | George Roberts Perkins - Geometry - 1850 - 332 pages
...(Ax. III.) And in the same manner it may be shown that the angle AFD is equal to BFC. PROPOSITION III. THEOREM. 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... | |
 | Charles Davies - Geometry - 1886 - 340 pages
...we have Of 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,... | |
 | Adrien Marie Legendre - Geometry - 1852 - 436 pages
...have, AB : DE :: AC : and by construction, AG=DE: hence, AH=DF. Therefore, the two triangles AGH, DEF, have two sides and the included angle of the one equal to the sides and the included angle of the other : hence, they are equal (B. L; p. 5) ; but the triangle... | |
 | 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 - 1854 - 436 pages
...: DE : : AC : DF; and by construction, AG=DE : hence AN=DF. Therefore, the two triangles A GH, DEF, have two sides and the included angle of the one equal to twd sides and the included angle of the other: hence, they are equal (BI, p. 5); but the triangle AGH... | |
 | Charles Davies, William Guy Peck - Electronic book - 1855 - 592 pages
...angles will also be equal, each to each, and the triangles themselves will bo equal." Prop. V. " When two triangles have two sides, and the included angle...other, each to each, the two triangles will be equal. " Axiom 1. Things which are equal to the same thing are equal to each other.'' Axiom 10 (of Legendre)... | |
 | Samuel Simon Schmucker, S. S. (Samuel Simon) Schmucker - History - 1855 - 332 pages
...the nature, eg, of the demonstration of the theorem of Euclid known as Prop. IV. of Book I., viz.: If two triangles have two sides, and the included...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... | |
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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. 
