| Charles Davies - Geometry - 1850 - 218 pages
...and consequently, AE is equal to BF. Hence, the two triangles ACE and BDF have the three sides of the **one equal to the three sides of the other, each to each,** and therefore the angle ACE is equal to the angle BDF (Bk. I. Th. viii). THEOREM XII. BOOK V , Of Planes.... | |
| Charles Davies - Geometry - 1850 - 238 pages
...and consequently, AE is equal to BF. Hence, the two triangles ACE and BDF have the three sides of the **one equal to the three sides of the other, each to each,** and therefore the angle A CE is equal to the angle BDF (Bk. I. Th. viii). THEOREM XII. 1:21 Of Plane*.... | |
| Adrien Marie Legendre - Geometry - 1852 - 436 pages
...therefore, BA C is greater than EDF. PROPOSITION X. THEOEEM. If two triangles have the three sides of the **one equal to the three sides of the other, each to each, the triangles are equal.** Let EDF and BAC be two triangles, having the side ED=BA, the side EF^BC, and the side DF=AC; then will... | |
| Charles Davies - Geometry - 1886 - 340 pages
...angle K. For, draw the chord DE. Then the two triangles IKL and EAD, having the three sides of the **one equal to the three sides of the other, each to each, the** angle EAD will be equal to the angle K (Bk. I. Th. viii). PROBLEM 1X. Through a g1ven po1nt to draw... | |
| Charles Davies - Geometry - 1854 - 436 pages
...therefore, BA C is greater than EDF. PROPOSITION X. THEOREM. If two triangles have ihe three sides of the **one equal to the three sides of the other, each to each, the triangles are equal.** Let EDF and BA C be two triangles, having the side ED=BA, the side EF=BC, and the side DF=AC; then... | |
| Thomas Lund - Geometry - 1854 - 520 pages
...equal, in all respects, as stated above. COR. Hence, also, if two triangles have the three sides of the **one equal to the three sides of the other, each to each,** in the same order, the two triangles will be equal, and their angles likewise will be equal, each to... | |
| Charles Davies, William Guy Peck - Electronic book - 1855 - 592 pages
...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 bo equal." Prop. V.... | |
| Charles Davies - Geometry - 1855 - 340 pages
...consequently, AE is equal to BF- Hence, the two triangles ACE and BDF have the' three sides of the **one equal to the three sides of the other, each to each,** and therefore the angle ACE is equal to the angle BDF (Bk- I- Th- viii)- \ THEOREM XII121 BOOK V Of... | |
| Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 442 pages
...therefore, BA C 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 triangles are equal.** Let EDF and BAC be two triangles, having the side ED=BA, the side EF=BC, and the side DF=AC\ then will... | |
| Euclides - 1858 - 248 pages
...given lines, any two of which are greater than the third, to make a triangle. DEMONSTRATION. — P. 8. **If two triangles have the three sides of one equal to the three sides of** another, each to each, the angle contained by two equal and conterminous sides of the one, shall be... | |
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