| American Association for the Advancement of Science - Science - 1899 - 650 pages
...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... | |
| Sidney Herbert Wells - Machine design - 1900 - 200 pages
...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,... | |
| Eldred John Brooksmith - Mathematics - 1901 - 368 pages
...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... | |
| 1902 - 482 pages
...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 - Agnosticism - 1903 - 698 pages
...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 - 716 pages
...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 - Machine design - 1905 - 246 pages
...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,... | |
| Joseph Gregory Horner - Engineering - 1909 - 560 pages
...three interior angles of every triangle are equal to two right angles. (Prop. 32.) Triangles on the **same base and between the same parallels are equal to one another.** (Prop. 37.) Triangles on equal bases and between the same parallels are equal to one another. (Prop.... | |
| St. George William Joseph Stock - Philosophy, English - 1912 - 246 pages
...of them is equal to the same thing. But we have now to ask how it can be known that parallelograms **upon the same base and between the same parallels are equal to one another.** This truth itself is not manifest at sight, but it becomes manifest when we succeed in showing that... | |
| Henry Adams - Geodesy - 1913 - 300 pages
...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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