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" TRIANGLES upon the same base, and between the same parallels, are equal to one another. "
Euclid's Elements [book 1-6] with corrections, by J.R. Young - Seite 45
von Euclides - 1838
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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
...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 - 1889
...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 - 515 Seiten
...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 - 1891 - 79 Seiten
...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 Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1892 - 518 Seiten
...PROPOSITION 37. THEOREM. Triangles on the same base, and between the sanie parallels, are equal in area. Let the triangles ABC, DBC be upon the same base BC, and between the same parallels BC, AD. Then shall the triangle ABC be equal to the triangle DBC. Construction. Through B draw BE parallel...
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The First Book of Euclid's Elements: Arranged for Beginners

Euclid, John Bascombe Lock - 1892 - 167 Seiten
...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 - 340 Seiten
...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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Summarized Proceedings ... and a Directory of Members, Band 48

American Association for the Advancement of Science - 1899
...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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Summarized Proceedings ... and a Directory of Members, Band 48

American Association for the Advancement of Science - 1899
...third 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 notshowthat the parallelograms can be divided into pairs of pieces admitting of superposition...
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Engineering Drawing and Design (A Text-book Of): Including Practical ...

Sidney Herbert Wells - 1900
...irregular figure to a triangle of equal area. The principle of this reduction depends upon the fact that triangles upon the same base and between the same parallels are equal (Euclid, i., 37), and the method consists of converting certain triangles, obtained from the figure,...
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