| Thomas Fowler - Logic - 1870 - 372 pages
...equal to one another,' is derived from, or is the total result of, the previous deductions (i) that ' **Parallelograms upon equal bases, and between the same parallels, are equal to one another,'** (2) that 'Triangles formed by the diagonal of a parallelogram are each of them equal to half the parallelogram'... | |
| Edinburgh univ - 1871 - 392 pages
...each 6 feet by 5, and 2 doors, each 9 feet by four, with paper I £ yards wide, at 5jd. a yard. 4. **Parallelograms upon equal bases and between the same parallels are equal to one another.** Prove this ; and modify the enunciation, so as to extend it to the case where the parallelograms are... | |
| Henry William Watson - Geometry - 1871 - 320 pages
...therefore the area .of the parallelogram AF is equal to the area of the parallelogram AD. PROPOSITION 5. **Parallelograms upon equal bases and between the same parallels are equal to one another** in area. Let ABFE and CDHG be two parallelograms upon equal Fig. 13. bases AB and CD EKFL o H and between... | |
| Euclides - 1871 - 136 pages
...: Bach of the £7» is double of A BDC; i. 34. QEI). PROPOSITION XXXVI. THEOREM. Parallelograms on **equal bases, and between the same parallels, are equal to one another.** 9Let the Os ABCD, EFGH be on equal bases BC, FG, and between the same IIs AH, BG. Then must O ABCD... | |
| Popular educator - 1872 - 848 pages
...a to any point in the straight line HE, produced both ways indefinitely. Triangles also which stand **upon equal bases and between the same parallels are equal to one another.** Thus, the triangles t, H o, M ot, which B _ stand on equal c bases, H o, ro, and H _ L.-'' P "-..MK... | |
| Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...reason thus : Each of the O« is double of &BDC; 1.34. QED PROPOSITION XXXVI. THEOREM. Parallelograms on **equal bases, and between the same parallels, are equal to one another.** A. J) M !_-. JT Let the Os A BCD, EFGH be on equal bases BC, FG, and between the same II s AH, BG.... | |
| Henry Major - Student teachers - 1873 - 588 pages
...AB bisects it ; 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... | |
| Euclides - 1874 - 342 pages
...is equal to the triangle DBC. Wherefore, triangles, &c. QED PROPOSITION 38. — 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. Then the... | |
| Edward Atkins - 1874 - 426 pages
...equal to the parallelogram EBCF. Therefore, parallelograms, <fec. QED Proposition 36. — Theorem. **Parallelograms upon equal bases, and between the same parallels, are equal to one** anot/ier. Let ABCD, EFGH be parallelograms on equal bases BC, FG, and between the same parallels AH,... | |
| Euclides - 1874 - 120 pages
...the square shall be less than that of the parallelogram. PROPOSITION 36. THEOREM. Parallelograms on **equal bases, and between the same parallels, are equal to one another.** j Let ABCD, EFGH be parallelograms on equal ' • bases BC, FG, and between the same parallels AH,... | |
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