| 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... | |
| 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... | |
| 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... | |
| 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,... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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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