 | Adrien Marie Legendre - Geometry - 1836 - 394 pages
...contradicts the hypothesis: therefore, BAC is greater than EDF. PROPOSITION X. THEOREM. If two triangles have the three sides of the one equal to the three sides of the other, each to each, the three angles will also b« equal, each to each, and the triangles themselves will... | |
 | John Playfair - Geometry - 1836 - 148 pages
...proved. COR. Hence, every equiangular triangle is also equilateral. PROP. VII. THEOR. If two triangles have the three sides of the one equal to the three sides of the other, each to each ; the angles opposite the equal sides are also equal. Let the two triangles ABC, DEF,... | |
 | Euclides - 1840 - 192 pages
...agree in having two sides, and the angle contained by those sides, equal (as in Prop. 4); or, in having the three sides of the one equal to the three sides of the other (as in Prop. 8) ; or, finally, in having two angles and a side, similarly placed with respect to the... | |
 | Adrien Marie Legendre - Geometry - 1841 - 288 pages
...AMD will be equal to the arc ENG. For, if the radii CD, OG, be drawn, the two triangles A CD, EOG, will have the three sides of the one equal to the three sides of the other, each to each, namely, AC = EO, CD =. OG and AD = EG; therefore these triangles are equal (43) ; hence... | |
 | Nicholas Tillinghast - Geometry, Plane - 1844 - 108 pages
...are equal (Def. 4), therefore AD=DB (BI Prop. 19, Cor. 2); hence the two triangles ACD, BCD, having the three sides of the one equal to the three sides of the other, are equal, (B. I. Prop. 22), and the angles ACD, BCD, are equal ; and therefore the arcs AE, EB,are... | |
 | George Roberts Perkins - Geometry - 1847 - 326 pages
...AP, since PB = PC, the oblique line AB = AC (B. VI, Prop, v) ; therefore the two triangles ADB, ADC have the three sides of the one equal to the three sides of the other ; consequently they are equal (BI, Prop, vm), and the angle ADB is equal to ADC ; therefore each is... | |
 | Elias Loomis - Conic sections - 1849 - 252 pages
...greater than the angle EDF. Therefore, if two triangles, &c. PROPOSITION XV. THEOREM. If two triangles have the three sides of the one equal to the three sides of the other, each to each, the three angles will also be equal, each to each, and the triangles themselves will... | |
 | Charles Davies - Logic - 1850 - 398 pages
...need the following, which have been before proved ; viz. : Prop. X. (of Legendre). "When two triangles have the three sides of the one equal to the three sides of the other, each to each, the three angles will also be equal, each to each, and the triangles themselves will... | |
 | George Roberts Perkins - Geometry - 1850 - 332 pages
...AP, since PB = PC, the oblique line AB = AC, (B. VI, Prop. v;) therefore the two triangles ADB, ADC have the three sides of the one equal to the three sides of the other; consequently they are equal, (B. I, Prop, viu,) and the angle ADB is equal to ADC ; therefore each... | |
 | Charles Davies - Geometry - 1850 - 218 pages
...chord, and the arc AE equal to EB. First. Draw the two radii CA, CB. Then the two triangles A CD, DCB, have the three sides of the one equal to the three sides of the *Note. When reference is made from one theorem to another, in the same Book, the number of the theorem... | |
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If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent. 
