 | War office - 1861 - Liczba stron: 260
...— — . MATHEMATICS. REV. CANON HEAVISIDE, MA Voluntary Paper, No. II. 1. Parallelograms upon the same base and between the same parallels are equal to one another. 2. If a straight line be divided into two equal and also into two unequal parts, the rectangle contained... | |
 | Dublin city, academic inst - 1862 - Liczba stron: 32
...line apply a parallelogram equal to a given triangle, and having an angle equal to a given one. 3. Parallelograms on the same base and between the same parallels are equal. 4. Suclid says the external angles of any rectilinear figure are together equal to two right angles... | |
 | Euclides - 1862 - Liczba stron: 172
...parallelogram EFGH. (ax. 1.) Wherefore, parallelograms, &c. QED PROP. XXXVII.— THEOREM. Triangles upon the same base, and between the same parallels, are equal to one another. (References — Prop. i. 31, 34, 35 ; ax. 7.) Let the triangles ABC, BBC, be on the same base BC, and... | |
 | University of Oxford - 1863 - Liczba stron: 316
...three given straight lines, of which any two whatever must be greater than the third. 5. Triangles on the same base and between the same parallels are equal to each other. 6. Describe a parallelogram which shall be equal to a given triangle, and have one of its... | |
 | Euclides - 1863 - Liczba stron: 74
...ft" _± ± ± 1 ± t -I f 1 [ / <' -T ' it 9 \ l)s 8 a Cl .PROP. 37. — THEOR. Triangles upon the same base and between the same parallels are equal to one another. consequently, half the product of the base ana altitude gives the area of a triangle. PROP. 38. —... | |
 | Euclides - 1864 - Liczba stron: 448
...(ax. 1.) Therefore, parallelograms upon equal, &c. QED PROPOSITION XXXVII. THEOREM. Triangles upon the same base and between the same parallels, are equal to one another. Let the triangles ABC, DBCbe upon the same base BC, and between the same parallels AD, BC. Then the triangle... | |
 | Euclides - 1864 - Liczba stron: 262
...(ax. 1.) Therefore, parallelograms upon equal, &c. QED PROPOSITION XXXVII. THEOREM. Triangles upon the same base and between the same parallels, are equal to one another. Let the triangles ABC, DBCbe upon the same base BC, and between the same parallels AD, BC. Then the triangle... | |
 | 1864 - Liczba stron: 370
...Find the limits of a hyperbola when it is produced by an Irish member. IV. Similar figures upon the same base, and between the same parallels, are equal to one another. Apply this theorem to show the base similarity of certain persons who cut similar figures in Parliament.... | |
 | Joseph Hughes - 1883 - Liczba stron: 568
...respect, and . •. the angle HFE = the angle GEF, and.'. DE = DF. Q.ED. 3. Parallelograms upon the same base and between the same parallels are equal to one another. Prop. 35, Bk. I. Algebra. MALES. Answer hi-o Questions, including (if possible) No. 2. I. Subtract... | |
 | Euclides - 1884 - Liczba stron: 214
...bisects the parallelogram ACDB. Therefore, the opposite sides &c. Proved. I. 4. E. r. PROPOSITION XXXV. THEOREM. Parallelograms on the same base, and between the same parallels, are equal to one another. GIVEN that the parallelograms ABCD and EBCF are on the same base BC, and between the same parallels... | |
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Triangles upon the same base, and between the same parallels, are equal to one another. 
