 | Joseph Gregory Horner - Engineering - 1907 - 560 pages
...form of an equation : 2DOA + 2DOC - 2DOB. Now the triangle DOA equals triangle BCO (for triangles on equal bases and between the same parallels are equal to one another— Euclid, I. 38). Therefore, 2DOA + 2DOC = 2BCO + 2DOC = 2DOB. Therefore the sum of the moments of P... | |
 | 1907 - 566 pages
...form of an equation : 2DOA + 2DOC .-= 2DOB. Now the triangle DOA equals triangle BCO (for triangles on equal bases and between the same parallels are equal to one another— Euclid, 1.38). Therefore, 2DOA + 2DOC = 2BCO + 2DOC = 2DOB. Therefore the sum of the moments of P and... | |
 | Euclid - Mathematics, Greek - 1908 - 550 pages
...makes them all equal to one another." PROPOSITION 36. Parallelograms which are on equal bases and in the same parallels are equal to one another. Let ABCD, EFGH be parallelograms which are on equal bases BC, FG and in the same parallels AH, BG ; I say that the parallelogram... | |
 | Paul Carus - Electronic journals - 1909 - 682 pages
...of the article in a universal sense is regular in Greek. Euclid does not say "All parallelograms on equal bases and between the same parallels are equal to one another" but "the parallelograms" (TO. TOpoAAiyAoypo/t/aa) ; so in the famous 47th it is not "in all" but "In... | |
 | Sir Gooroodass Banerjee - Education - 1910 - 380 pages
...relations of magnitudes to one another. Thus while in the fiirst Book we have it proved that triangles upon equal bases and between the same parallels are equal to one another, it is proved in the Sixth Book that triangles upon equal bases and between the same parallels are related... | |
 | St. George William Joseph Stock - Philosophy, English - 1912 - 246 pages
...same parallels. By the intervention of this idea the mind is able intuitively to perceive that the parallelograms upon equal bases and between the same parallels are equal to one another, since each of them is equal to the same thing. But we have now to ask how it can be known that parallelograms... | |
 | John William Gordon - Perspective - 1922 - 244 pages
...parallel lines coplanar with the lines An0, Bw0, and Cn0. Furthermore, the triangles ABD and BCE, being on equal bases and between the same parallels, are equal to one another. If to each of those triangles we add the triangle BDE we obtain the quadrilaterals ABED and BCED. Therefore... | |
 | R. H. Warn, John G. Horner - Crafts & Hobbies - 2002 - 292 pages
...parallels, are equal to one another. (Euc. I. 37, and I. 38.) (jr) Parallelograms upon the same base, or upon equal bases, and between the same parallels, are equal to one another. (Enc. I. 35, and I. 36.) (7i) If a parallelogram and a triangle be upon the same base, and between... | |
 | Richard Fitzpatrick - Mathematics - 2005 - 298 pages
...[Prop. 1.34]. So that the parallelogram ABCD is also equal to EFGH. Thus, parallelograms which are on equal bases and between the same parallels are equal to one another. (Which is) the very thing it was required to show. В Г Ta Tpíycova та еш TTJÇ аитг]с ßaascoc... | |
 | Euclid - 454 pages
...makes them all equal to one another." PROPOSITION 36. Parallelograms which are on equal bases and in the same parallels are equal to one another. Let ABCD, EFGH be parallelograms which are on equal bases BC, FG and in the same parallels AH, BG ; I say that the parallelogram... | |
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Triangles upon equal bases, and between the same parallels, are equal to one another. 
