 | 1894 - 330 sider
...EBCF be two parallelograms. Then ABCD is equal in area to EBCF. IX. Triangles upon the same base, or upon equal bases, and between the same parallels are equal to one another. Thus the triangle ABC, Fig. 25, is equal in area to the triangle DEF. X. A triangle is equivalent to... | |
 | Thomas Fowler - 1895 - 620 sider
...which our deductive reasoning proceeds. The proposition proved in Euclid, Book i. Prop. 38, that ' Triangles upon equal bases, and between the same parallels, are equal to one another,' is derived from, or is the total result of, the previous deductions (i) that ' Parallelograms upon... | |
 | Northwest Territories Council of Public Instruction - 1897 - 628 sider
...right angles. I. 32. Cor. 2. (6) Divide a right angle into five equal parts. 10. ('/) Parallelograms on equal bases and between the same parallels are equal to one another. I. 36. (6) Extend the proof of proposition (a) to any number of parallelograms. (c) Distinguish "equal... | |
 | Seymour Eaton - 1899 - 362 sider
...square shall be less than that of the parallelogram. Lesson No. 17 PROPOSITION 38. THEOREM Triangles on equal bases, and between the same parallels, are equal to one another. Let the triangles ABC, DEF be on equal bases BC, EF, and between the same parallels BF, AD : then the... | |
 | Manitoba. Department of Education - 1900 - 558 sider
...so that ED is equal to twice BA. Prove that the angle DBC is equal to onethird of the angle ABC. 5. Triangles upon equal bases and between the same parallels are equal to one another. If E and D are the points of trisection (nearest to A) of the sides AB, AC of a triangle, and F the... | |
 | 1907 - 566 sider
...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... | |
 | Joseph Gregory Horner - 1907 - 560 sider
...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... | |
 | Paul Carus - 1909 - 682 sider
...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 - 1910 - 380 sider
...of the 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 - 1912 - 246 sider
...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... | |
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Triangles upon equal bases, and between the same parallels, are equal to one another. 
