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" TRIANGLES upon the same base, and between the same parallels, are equal to one another. "
Inventional Geometry: A Series of Problems, Intended to Familiarize the ... - Página 43
por William George Spencer - 1877 - 97 páginas
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Annual Report of the Commissioners ..., Volumen68

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 páginas
...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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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 páginas
...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 páginas
...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 páginas
...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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Geometrical Drawing: With Notes and Examples ...

William Henry Blythe - 1900
...making AE = AB then the triangle EBC is equal in area to ABCD. It is proved in (Euclid, Bk. 1.) that triangles upon the same base and between the same parallels are equal to one another, by means of this proposition any rectilineal figure can be reduced to a triangle of equal area. A triangle...
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Examination,Midsummer,1879

Education Department - 1879
...and CD, "rect. AB. CD." Other abbreviations, if employed, must not be ambiguous. 1. Parallelograms upon the same base and between the same parallels are equal to one another. Construct an isosceles triangle equal to a given parallelogram. 2. In obtuse-angled triangles, if a...
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Journal, Volumen13

1865
...propositions : — (1) The angles of a triangle are together equal to two right angles. (2) Parallelograms upon the same base, and between the same parallels, are equal to one another. (3) The squares on the sides containing the right angle of a right-angled triangle are equal to the...
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