| Francis James Jameson - Mathematics - 1851 - 144 pages
...the same parallels,* are equal to one another. Hence AECD - ABCE - ABEA = AAED. 1851. (A]. Triangles **upon equal bases and between the same parallels are equal to one another,** (i. 38.) (E). Let ABC, ABD be two equal triangles upon the same base AB, and on opposite sides of it... | |
| Sir Henry Edward Landor Thuillier - Surveying - 1851 - 826 pages
...proved that ABCD being a parallelogram, AB = CD and AD =BC. THEO. XII. All parallelograms on the same or **equal bases and between the same parallels are equal to one another,** that is if BD — GH, and the lines BH and AF are parallel, then the paralellogram ABD C = BDFE = EFGH.... | |
| Euclides - 1852 - 152 pages
...equal to the triangle DEC. Wherefore triangles, &c. QED OF EUCLID. PROP. XXXVIII. THEOR. Triangles **upon equal bases, and between the same parallels, are equal to one another. Let** the triangles ABC, DEF be upon equal bases EC, EF, and between the same parallels BF, AD: The triangle... | |
| Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...the parallelogram DBCF, because the diameter DC bisects it : PROPOSITION XXXVIII. THEOR. Triangles **upon equal bases, and between the same parallels, are equal to one another. Let** the triangles ABC, DEF be upon equal bases BC, EF, and between the same parallels BF, AD : the triangle... | |
| Euclides - 1853 - 146 pages
...ABC is equal to the triangle DBC. Wherefore, triangles, &c. QED PROP. XXXVIII. — THEOREM. Triangles **upon equal bases and between the same parallels, are equal to one another, Let** the triangles ABC, DEF, be upon equal bases BC, EF, and between the same parallels BF, AD. The triangle... | |
| Euclides - Geometry - 1853 - 176 pages
...parallelogram eb С f Therefore parallelograms upon the same base, &c. QED PROPOSITION XXXVI. — THEOREM. **Parallelograms upon equal bases, and between the same parallels, are equal to one** anotJier. a de ЬЕТ abСd, efgh, be parallelograms upon equal bases bС, fg, and between the same... | |
| Thomas Lund - Geometry - 1854 - 520 pages
...parallelograms as the unit is contained in AB, and BEFC into as many as the unit is contained in BE. Then since **parallelograms upon equal bases and between the same parallels are equal to one another** (41 Cor. 1), the smaller parallelograms which make up ABCD, and BEFC, are all equal. Therefore the... | |
| Euclides - 1855 - 270 pages
...upon the same base and on the same side of it, are between the same parallels. PROP. XXXVL THEOREM. **Parallelograms upon equal bases and between the same parallels, are equal to one another. Let** AC, EG be parallelograms upon equal bases BC, FG, and between the same parallels AH, BG. The parallelogram... | |
| Cambridge univ, exam. papers - 1856 - 200 pages
...lines, make the alternate angles equal to each other, these two straight lines shall be parallel. 4. **Parallelograms upon equal bases, and between the same parallels, are equal to one another.** 6. If a straight line be divided into any two parts, the rectangle contained by the whole and one of... | |
| Euclides - 1856 - 168 pages
...parallelogram DBCF (Prop. 37) ; wherefore the triangle ABC is equal to the triangle DEC. XL. Triangles **upon equal bases and between the same parallels are equal to one another. Let** the triangles ABC, DEF (Fig. 32) be upon equal bases BC, EF, and between the same parallels BF, A D.... | |
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