| Hugo Reid - Mathematics - 1872 - 148 pages
...to meet CD or that line produced. 142. If ote. — This illustrates the important geometrical truth, **that — Parallelograms on the same base and between the same parallels are equal** to one another; that is, equal in area. Fic.34 AEFD and ABCD are on the same base AD and between the... | |
| Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...which a paral. .am is divided by its diagonals, are equal to each other. PROPOSITION XXXV. THEOREM. **Parallelograms on the same base and between the same parallels are equal.** Let the OĞ ABCD, EBCF be on the same base BC, and between the same \\aAF, BC. Then must £]ABCD=E]EBCF.... | |
| Lewis Sergeant - 1873 - 182 pages
...the same base and between the same parallels are equal to one another. (10.) (This appears to mean **that parallelograms on the same base and between the same parallels are equal,** and also that triangles on the same base and between the same parallels are equal. See Geometry, Props.... | |
| Euclides - 1874 - 120 pages
...is a parallelogram. 3. The diagonals of a parallelogram bisect each other. PROPOSITION 35. THEOREM. **Parallelograms on the same base, and between the same parallels, are equal** to one another. .. Let the parallelograms ABCD, EBCFbe on the '• same base BC, and between the same... | |
| Francis Cuthbertson - Euclid's Elements - 1874 - 400 pages
...(i. 27) the O ^^T is both equilateral and rectangular, and is .-. a square. AREAS. PROPOSITION XXXI. **Parallelograms on the same base and between the same parallels are equal.** TJ E -BC Let the O s A BCD, EBCF be on the same base BC, and between the same parallels AF, BC. Then... | |
| Braithwaite Arnett - 1874 - 130 pages
...straight line perpendicular to a given straight line of unlimited length from a given point without it. 2. **Parallelograms on the same base and between the same parallels are equal** to one another. 3. If a straight line be bisected, and produced to any point, the rectangle contained... | |
| William Alexander Willock - Circle - 1875 - 196 pages
...parallelograms OQt and O,Q, which are the complementary parallelograms, are (Ax. 3) equal in area, as stated. 6. **Parallelograms on the Same Base and between the Same Parallels are equal** in area. Bl Ot Let AB be the common base, and ABA.B, and ABA B2 two such parallelograms on AB and between... | |
| Association for the improvement of geometrical teaching - Geometry, Modern - 1876 - 66 pages
...difference of identically equal magnitudes are equal, although they may not be identically equal. THEOR. i. **Parallelograms on the same base and between the same parallels are equal.** COR. i. The area of a parallelogram is equal to the area of a rectangle, whose base and altitude are... | |
| Education Department,London - 1876 - 1010 pages
...opposite angle on the same side of the line, the two straight lines shall be parallel to one another. 2. **Parallelograms on the same base and between the same parallels are equal** to each other. If the angular points of two equal parallelograms which stand on the same base but on... | |
| Queensland. Department of Public Instruction - Education - 1909 - 144 pages
...equal to three given straight lines, any two of which are together greater than the third. 4. Prove **that parallelograms on the same base and between the same parallels are equal.** 5. Prove that if a straight line lie divided into two parts, the squares on the whole line and on one... | |
| |