| Euclid, Charles Peter MASON - 1872
...ABCD and EFGH, being each equal to the parallelogram ABGH, Are equal to each other. PBOPOSITION XXXVU. **Triangles upon the same base and between the same parallels are equal to** each other. For the construction in this proposition we must be ableto draw a straight line from a... | |
| Hugo Reid - 1872 - 124 Seiten
...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 same parallels... | |
| Lewis Sergeant - 1873
...decimals. (10.) 21 41 21 228 2000 _1824 1~7G, <fcc. (See Arith., § 61.) * 3. Show that parallelograms and **triangles upon 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... | |
| Henry Major - 1873
...and DEC is the half of DBCF ; therefore ABC is equal to DEC. XXXVIII. — 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. Produce AD both ways to the... | |
| Edward Atkins - 1874
...same base, and between the same parallels, are equal to one anot/ier. Let the triangles ABC, DBC be on **the same base BC, and between the same parallels AD, BC ; The triangle ABC shall be equal** to the triangle DBC. CONSTRUCTION. — Produce AD both ways, to the points E, F. Through B draw BE... | |
| Euclides - 1874
...divides the parallelogram ACDB into two equal parts. ~ QED PROPOSITION 35. — Theorem. Parallelograms **upon the same base, and between the same parallels, are equal to one another. Let the** parallelograms ABCD, EBCF be upon the same base BC, and between the same parallels AF, BC. Then the... | |
| Edward Atkins - 1874
...two equal parts. Therefore, the opposite sides, <fec. QED Proposition 35. — Theorem. Parallelograms **upon the same base, and between the same parallels, are equal to one another. Let the** parallelograms A BCD, EBCF be on the same base BC, and between the same parallels AF, BC; The parallelogram... | |
| Euclides - 1874
...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 parallels AF, BC: the parallelogram... | |
| Braithwaite Arnett - 1874
...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 by the whole... | |
| Edward Atkins - 1876 - 119 Seiten
...two equal parts. Therefore, the opposite sides, &c. QED Proposition 35. — Theorem. Parallelograms **upon the same base, and between the same parallels, are equal to one another. Let the** parallelograms ABCD, EBCF be on the same base BC, and between the same parallels AF, BC; The parallelogram... | |
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