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" Parallelograms upon the same base and between the same parallels, are equal to one another. "
Geometry Without Axioms; Or the First Book of Euclid's Elements. With ... - Page 111
by Thomas Perronet Thompson - 1833 - 150 pages
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Elements of geometry, containing the first two (third and fourth ..., Part 1

Euclides - 1871 - 136 pages
...[3EBCH= EJEFGH, i. 35. V they are on the same base EH and between the same IIs ; .-. O ABCD =o EFGH. Triangles upon the same base, and between the same parallels, are equal to one another. Let A s ABC, DBC be on same base BC and between same lis AD. BC. Then must &ABC= &DBC. From B draw BE \\...
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The Elements of Plane and Solid Geometry

Henry William Watson - Geometry - 1871 - 320 pages
...proved equal to the area of AF, therefore the area of AF is equal to the area of GD. PROPOSITION 6. Triangles upon the same base and between the same parallels are equal to one another in area. Fig. 14. j) AD P Let the triangles ABC and DBC be upon the same base BC, and between the same...
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Key to the Irish commissioners' Treatise on mensuration

William Kennedy Maxwell - 1871 - 148 pages
...ft. 13. Here, as 4-1 : 65 : : 5 : 79-26, the height of the pole. Ans. 14. Now, triangles that stand upon the same base, and between the same parallels are equal to each other ; therefore, this question will, as shown in the figure, admit of two answers. Here, the...
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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
...same II s ; and CJEBCH= CJEFGH, i. 35. v they are on the same base EH and between the same IIs ; QED PROPOSITION XXXVII. THEOREM. Triangles upon the same...the same parallels, are equal to one another. Let A s ABC, DBC be on same base BC and between same IIs AD, BC. Then must &ABC= A DBC. From B draw BE...
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The first and second books of Euclid explained to beginners, by C.P. Mason

Euclid, Charles Peter MASON - Geometry - 1872 - 216 pages
...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...
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First book of mathematics

Hugo Reid - Mathematics - 1872 - 146 pages
...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...
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Elementary Mathematics: Embracing Arithmetic Geometry, and Algebra

Lewis Sergeant - 1873 - 182 pages
...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...
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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
...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...
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Pure mathematics, Volume 1

Edward Atkins - 1874 - 424 pages
...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...
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The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874 - 342 pages
...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...
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