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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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Woolwich mathematical papers [aftwerw.] Mathematical papers for admission ...

Woolwich roy. military acad - 1884 - 148 pages
...this proposition. How many of the exterior angles of any triangle must be obtuse ? 4. Parallelograms upon the same base, and between the same parallels, are equal to one another. 5. Describe a square that shall be equal to a given rectilineal figure. Divide a given straight line...
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Stewart's guide-book to the queen's scholarship and certificate examinations ...

Stewart W. and co - 1884 - 146 pages
...respectively, then PR and liV are respectively parallel to straight lines KM. and MN. QED SliCTION III. 1. (a) Triangles upon the same base and between the same parallels are equal. (b.) Construct a triangle equal to a given triangle and having a base three times as great (a) See...
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The text of Euclid's geometry, book 1, uniformly and systematically arranged ...

Euclides - 1884 - 214 pages
...Therefore, the opposite sides &c. Proved. I. 4. E. r. PROPOSITION XXXV. THEOREM. Parallelograms on the same base, and between the same parallels, are equal to one another. GIVEN that the parallelograms ABCD and EBCF are on the same base BC, and between the same parallels...
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Cambridge University Examination Papers.Michaelmas Term,1884 to Easter Term ...

Cambridge University Examination Papers.Michaelmas Term,1884 to Easter Term,1885.Volume XIV - 1885 - 652 pages
...a given straight line of unlimited length, from a given point without it. 3. Parallelograms on the same base, and between the same parallels, are equal to one another. 4. If a straight line be divided into two equal parts and also into two unequal parts, the rectangle...
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Woolwich Mathematical Papers for Admission Into the Royal Military Academy ...

E. J. Brooksmith - Mathematics - 1889 - 354 pages
...this proposition. How many of the exterior angles of any triangle must be obtuse ? 4. Parallelograms upon the same base, and between the same parallels, are equal to one another. Of all triangles that can be drawn upon a given base and between the same parallels, shew that an isosceles...
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The Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 538 pages
...that 'the three medians of a triangle are concurrent.' PROPOSITION 35. THEOREM. Parallelograms on the same base and between the same parallels are equal to one another. Let ||gms A BCD, EBCF be on the same base and between the same ||s AF, BC, ABCD shall be equal to EBCF....
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Rider Papers on Euclid: Books i and Ii, Graduated and Arranged in Order of ...

Rupert Deakin - Euclid's Elements - 1891 - 102 pages
...the diameter bisects the parallelogram, ie divides it into two equal parts. 35. Parallelograms on the same base and between the same parallels are equal to one another. 36. Parallelograms on equal bases and between the same parallels are equal to one another. 37. Triangles...
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The First Book of Euclid's Elements: Arranged for Beginners

Euclid, John Bascombe Lock - Euclid's Elements - 1892 - 184 pages
...of equal area. 6. Rectangles having two adjacent sides equal are of equal area. Proposition 37. 139. Triangles upon the same base and between the same parallels are equal, Let ABC, DBC represent triangles upon the same base BC and between the same parallels AD, BC ; it is...
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Mathematics: Mechanic's bids and estimates. Mensuration for beginners. Easy ...

Seymour Eaton - 1899 - 362 pages
...ABC is equal to the triangle BCD (Proposition 4). PROPOSITION 35. THEOREM 323 Parallelograms on the same base and between the same parallels are equal to one another. Let the parallelograms ABCD, EBCF be on the same base BC, and between the same parallels AF, BC; then the parallelogram...
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Proceedings, Volume 48

American Association for the Advancement of Science - American periodicals - 1899 - 646 pages
...part a strict treatment of equivalence. Even Euclid, in proving his I. 35, " Parallelograms on the same base, and between the same parallels, are equal to one another," does not show that the parallelograms can be divided into pairs of pieces admitting of superposition...
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