 | 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
...diameter 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
...triangle ABC 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... | |
 | Braithwaite Arnett - 1874 - 130 pages
...consecutive angles of a quadrilateral is half the sum of the two remaining angles. 2. Parallelograms -on equal bases, and between the same parallels, are equal to one another. 3. Divide a given straight line into two parts, so that the rectangle contained by the whole and one... | |
 | Edward Atkins - 1874 - 426 pages
...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,... | |
 | Edward Atkins - 1876 - 130 pages
...triangle ABC is equal to the triangle DBC. Therefore, triangles, &c. QED Proposition 38. — Theorem. Triangles upon equal bases, and between the same parallels, are equal to one another. Let tho triangles ABC, DEF, bo on equal bases BC, EF, and between the same parallels BF, AD. The triangle... | |
 | James Martin (of the Wedgwood inst, Burslem.) - 1876 - 334 pages
...therefore the triangles are equal, as ' ' the halves of equal things are equal." — Euc. I., Ax. 7. (D.) " Triangles upon equal bases and between the same parallels are equal to one another" (in area). — Euc. I.. 38. Ex. ABC, KEFNOTE. -It can be readily seen that A BC is a half of the parallelogram... | |
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Triangles upon equal bases, and between the same parallels, are equal to one another. 
