 | Lewis Sergeant - 1873 - 182 pages
...appears to mean that parallelograms on the same base and between the same parallels are equal, and also that triangles on the same base and between the same parallels are equal. See Geometry, Props. 35, 37.) * 6. Divide a6 - 3 aV + 3 aV - a? by a? - 3 a?x + 3 oo? -a?. (10.) as... | |
 | Euclid, James Bryce, David Munn (F.R.S.E.) - Geometry - 1874 - 236 pages
...parallelogram BD is equal to the parallelogram FH. (Ax. 1.) PROP. XXVIII.— THEOREJL (Euc. I. 37.) Triangles on the same base and between the same parallels are equal in area. r. D c -v „ Let ABC and ABD be two triangles on the same base AB and between the same parallels,... | |
 | Euclides - 1874 - 120 pages
...equal to the parallelogram EFGH. [Ax. i.] Therefore, parallelograms, &c. QED PROPOSITION 37. THEOREM. Triangles on the same base, and between the same parallels, are equal. * Let the triangles ABC, DBC be on the same ' • base BC, and between the same parallels AD, BC: the... | |
 | William Alexander Willock - Circle - 1875 - 196 pages
...which are the complementary parallelograms, are (Ax. 3) equal in area, as stated. 6. Parallelograms on the Same Base and between the Same Parallels are equal in area. Bl Ot Let AB be the common base, and ABA.B, and ABA B2 two such parallelograms on AB and between the... | |
 | University of Madras - 1876 - 580 pages
...side BC is produced to D. Prove that the exterior angle ACD is greater than the angle ABC. III. Prove that triangles on the same base and between the same parallels are equal to one another. (a) Two equal triangles have two sides of the one equal to two sides of the other.... | |
 | Popular educator - 1876 - 854 pages
...DE, н к, and they are what we may term symmetrical triangles. From this we learn that symmetrical triangles on the same base and between the same parallels are equal to one another ; and this is true, not for symmetrical Fig. 32. triangles only, but for any triangles,... | |
 | William George Spencer - Geometry - 1877 - 108 pages
...322. Take an inch to represent a foot, and make a scale of feet and inches. 323. From the theorem, that triangles on the same base, and between the same parallels^ are equal in surface, can you change a trapezium into a triangle ? 324-. Can you change a triangle into a rectangle... | |
 | Euclides - 1879 - 146 pages
...ABCD = /— 7 EFGH. (ax. i) Therefore, parallelograms on equal, &c. QED PROPOSITION XXXVII. THEOREM. Triangles on the same base, and between the same parallels, are equal to one another. Let the As ABC, DEC be on the same base BC, and between the same ||s AD, BC. Then shall... | |
 | University of Madras - 1879 - 674 pages
...coefficient of a,u in the expansion of 1/"(\ + x)3 7.9.11.23 ' -TT - w in ascending powers of x is R / A VII. Triangles on the same base and between the same parallels are equal to one another. ABCD is a quadrilateral figure whose diagonals intersect in E. AD BC are produced to... | |
 | Euclides, Frederick Burn Harvey - Geometry - 1880 - 178 pages
...= the parallelogram EFGH. Wherefore, Parallelograms on equal bases, &c. QED PROP. XXXVII. THEOREM. Triangles on the same base and between the same parallels are equal to one another. Let ABC and DBC be triangles on the same base BC, and between the same parallels AD... | |
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Prove that parallelograms on the same base and between the same parallels are equal in area. 
