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" Triangles upon equal bases, and between the same parallels, are equal to one another. "
Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ... - Page 26
by Dennis M'Curdy - 1846 - 138 pages
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The elements of inductive logic

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'...
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The Edinburgh university calendar

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...
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The Elements of Plane and Solid Geometry

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...
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Elements of geometry, containing the first two (third and fourth ..., Part 1

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...
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The popular educator, Volume 1; Volume 29

Popular educator - 1872 - 850 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...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

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....
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The Acting Teacher's and Student's in Training Guide and Text Book for ...

Henry Major - Student teachers - 1873 - 592 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...
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The Elements of Euclid, containing the first six books, with a selection of ...

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...
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Pure mathematics, Volume 1

Edward Atkins - 1874 - 424 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,...
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A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes ...

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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