 | Northwest Territories Council of Public Instruction - 1897 - 628 pągines
...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... | |
 | Augustus De Morgan - 1898 - 316 pągines
...equal to two angles of the other, and the interjacent sides equal, are equal in all respects. f, g Parallelograms on the same or equal bases, and between the same parallels, are equal. The explanation of this is as follows : the whole proposition is divided into distinct assertions,... | |
 | Seymour Eaton - 1899 - 362 pągines
...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 pągines
...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... | |
 | Joseph Gregory Horner - 1907 - 560 pągines
...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 pągines
...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... | |
 | Paul Carus - 1909 - 682 pągines
...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 pągines
...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... | |
 | Henry John Spooner - 1911 - 196 pągines
...Parallelogram. — The working of this problem depends upon the geometrical fact that parallelograms upon the same or equal bases, and between the same parallels, are equal in area (Euc. I. 35, 3(i). Thus, the parallelogram ABCH (Fig. 128) is on the base AB, and if on this... | |
 | St. George William Joseph Stock - 1912 - 246 pągines
...provided that we know the parallelograms to be equal. The knowledge however that parallelograms upon equal bases and between the same parallels are equal to one another does not come from intuition, but itself rests upon a prior demonstration. This (Jemonstralioji consists... | |
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Triangles upon equal bases, and between the same parallels, are equal to one another. 
