 | 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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Parallelograms upon the same base and between the same parallels, are equal to one another. 
