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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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Woolwich Mathematical Papers for Admission Into the Royal Military Academy ...

Eldred John Brooksmith - 1901
...are equal in every respect. 3. Define parallel straight lines ; and show that parallelograms on the same base and between the same parallels are equal to one another. 4. Enunciate the proposition which is represented in algebraical symbols by and give the construction...
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Annual Report of the Commissioners ..., Band 68

1902
...another upon the same side of it are together equal to two right angles. 2. Prove that parallelograms upon the same base and between the same parallels are equal to one another. 3. Prove that if one side of a triangle be produced, the exterior angle is greater than either of the...
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Agnosticism

Robert Flint - 1903 - 664 Seiten
...is a state of mind which has various stages. I may believe, for instance, that parallelograms on the same base and between the same parallels are equal to one another because I know that Euclid and other mathematicians say so, or because I have measured such parallelograms...
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A Text-book of Euclid's Elements for the Use of Schools, Bücher 1

Euclid - 1904 - 456 Seiten
...PROPOSITION 37. THEOREM. Triangles on the same base, and between the same 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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Calendar

University of Sydney - 1905
...GEOMETRY. TWO HOURS AND A HALF. THREE HOURS ALLOWED FOH CANDIDATES FOE THE PN RUSSELL SCHOLARSHIP. 1. Triangles upon the same base and between the same parallels are equal to one another. Upon a base line measuring 4 units, parallelograms of area 12 units are described. Find the locus of...
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A text-book of engineering drawing and design

Sidney Herbert Wells - 1905
...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 convertingcertain triangles, obtained from the figure,...
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Practical Surveying and Elementary Geodesy, Including Land Surveying ...

Henry Adams - 1913 - 276 Seiten
...piece added on to the triangle at Ac. The solution really depends upon the proposition of Euclid, " Triangles upon the same base and between the same parallels are equal." The triangles are ABC and AeC, and the parallels SYSTEMS OF SURVEYING 5 Fio. 6.— To make a triangle...
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A Treatise on Mine-surveying

Bennett Hooper Brough - 1920 - 477 Seiten
...meeting CD produced, at G. Join A G. The method depends upon Euclids' theorem that triangles on the same base and between the same parallels are equal to one another. By using a parallel ruler and a pricker the drawing in of all the constructional lines, except the...
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Euclid's Elements in Greek: Vol. I:

Richard Fitzpatrick - 2005 - 296 Seiten
...equal to one another.]15 Thus, triangle ABC is equal to triangle DEC. Thus, triangles which are on the same base and between the same parallels are equal to one another. (Which is) the very thing it was required to show. 15This is an additional common notion. Xrf H A В...
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