| George Roberts Perkins - Geometry - 1850 - 332 pages
...will intersect in two points G and H, thus giving two triangles, DGF and DHF; but these two triangles, **having the three sides of the one equal to the three sides of the other,** are identical. (Prop, vin.) If two of the given lines are equal, the triangle will be isosceles; when... | |
| Charles Davies - Geometry - 1850 - 218 pages
...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... | |
| Charles Davies - Geometry - 1850 - 236 pages
...and the arc AE equal to EB. First. Draw the two radii CA, CB. Then the two triangles A CD, DCS, have **the three sides of the one equal to the three sides of the** Of the Circle. B other, each to each : viz. AC equal to CB, being radii, AD equal to DB, by hypothesis,... | |
| Charles Davies - Geometry - 1886 - 334 pages
...angle EAD will be equal to tho 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... | |
| Adrien Marie Legendre - Geometry - 1852 - 436 pages
...the hypothesis : 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... | |
| Thomas Lund - Geometry - 1854 - 192 pages
...coincide, and are 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 - Geometry - 1854 - 436 pages
...hypothesis : 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,... | |
| Charles Davies, William Guy Peck - Mathematics - 1855 - 630 pages
...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 bo equal." Prop.... | |
| Charles Davies - Geometry - 1855 - 336 pages
...and the arc AE equal to EB- ^ First- Draw the two radii CA, CBThen 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... | |
| George Roberts Perkins - Geometry - 1856 - 460 pages
...equal, as in the case of a rhombus, we have AB — AD, and the two triangles AEB and AED will have **the three sides of the one equal to the three sides of the other** respectively, consequently they will be equal (T. XXV.), and the angle AEB = AED, that is, in a rhombus... | |
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