 | 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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Triangles upon equal bases, and between the same parallels, are equal to one another. 
