| Elias Loomis - Conic sections - 1858 - 256 pages
...throughout. Thus, two circles having equal radii are equal ; and two triangles, having the three sides of the **one equal to the three sides of the other, each to each,** are also equal. 2. Equivalent figures are such as contain equal areas. Two figures may be equivalent,... | |
| Horatio Nelson Robinson - Geometry - 1860 - 470 pages
...between any two sidei of a triangle, etc. THEOREM XXI. If two triangles have the three sides of the **one equal to the three sides of the other, each to each, the** two triangles are eqml, and the equal angles are opposite the equal sides. In two triangles, as ABC... | |
| Benjamin Greenleaf - Geometry - 1862 - 532 pages
...equal. For, if the radii CD, OG are drawn, the triangles А С D, EOG, having the three sides of the **one equal to the three sides of the other, each to each,** are themselves equal (Prop. XVIII. Bk. I.) ; therefore the angle А С D is equal to the angle EOG... | |
| Benjamin Greenleaf - Geometry - 1862 - 518 pages
...are equivalent. ELEMENTS OF GEOMETRY. Let ABC, DEF be two triangles, having the three sides of the **one equal to the three sides of the other, each to each,** namely, AB to DE, AC to DF, andCBtoEF; then their triangles will be equivalent. Let 0 he the pole of... | |
| Benjamin Greenleaf - Geometry - 1863 - 504 pages
.... — THEOREM . ELEMENTS OF GEOMETRY. Let ABC, DEF be two triangles, having the three sides of the **one equal to the three sides of the other, each to each,** namely, AB to DE, AC toDF, andCB toEF; then their triangles will be equivalent. Let 0 be the pole of... | |
| Horatio Nelson Robinson - Conic sections - 1865 - 474 pages
...= AC, and AF = BD, (Th. 24); hence we have two A's, CAF and EBD, which have the three sides of the **one equal to the three sides of the other, e,ach to each;** therefore, the two A's are equal, (Th. 21). If, from the whole figure ABDC, we take away the A CAF,... | |
| Benjamin Greenleaf - Geometry - 1866 - 328 pages
...than the angle D. PROPOSITION XVIII. — THEOREM. 80. If two triangles have the three sides of the **one equal to the three sides of the other, each to each, the triangles** themselves will be equal. Let the triangles ABC, DEF have the side AB equal to DE, AC to DP, and BC... | |
| Charles Davies - Mathematics - 1867 - 186 pages
...have been before proved ; viz. : Prop. X. (of Legendre). "If two triangles have the three sides of the **one equal to the three sides of the other, each to each, the triangles** will be equal in all their parts." Prop. V. " If two triangles have two sides and the included angle... | |
| Education - 1868 - 516 pages
...Rhet. This structure is very often neglected. Examples : "If two triangles have the three sides of the **one equal to the three sides of the other, each to each, the triangles** will be equal in all their parts." The article before one here is improper, because the reference is... | |
| Benjamin Greenleaf - Geometry - 1868 - 340 pages
...34, Ax. 14). Thus circles having equal radii are equal ; and triangles having the three sides of the **one equal to the three sides of the other, each to each,** are also equal. Equal figures are always similar ; but similar figures may be very unequal. BOOK IV.... | |
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