 | Robert Potts - 1860 - Liczba stron: 380
...the parallelogram A CDB into two equal parts. QED PROPOSITION XXXV. THEOREM. Parallelograms upon the same base, and between the same parallels, are equal to one another. Let the parallelograms AB CD, EBCF be upon the same base 2? C, and between the same parallels AF, BC. Then... | |
 | Royal college of surgeons of England - 1860 - Liczba stron: 332
...angles equal to each other, these two straight lines shall be parallel. 5. Parallelograms upon the same base and between the same parallels are equal to one another. The perimeter of a square is less than that of any other parallelogram of equal area. 6. If a straight... | |
 | Henry William Watson, Edward John Routh - 1860 - Liczba stron: 240
...contained by AB and CD, the rect. AB, CD. 1. DEFINE parallel straight lines. Parallelograms upon the same base, and between the same parallels, are equal to one another. If a straight line DME be drawn through the middle point M of the base BC of a triangle ABC, so as... | |
 | Euclides - 1860 - Liczba stron: 288
...therefore (Ax. 1) the parallelogram ABCD is equal to EFGH. PROPOSITION XXXVII. THEOREM. Triangles upon the same base, and between the same parallels, are equal to one another. Given the triangles ABC and DEC upon the same base BC, and between the same parallels AD and BC ; to... | |
 | Henry William Watson, Edward John Routh - 1860 - Liczba stron: 240
...contained by AB and CD, the rect. AB, CD. 1. DEFINE parallel straight lines. Parallelograms upon the same base, and between the same parallels, are equal to one another. If a straight line DME be drawn through the middle point M of the base BC of a triangle ABC, so as... | |
 | 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... | |
 | 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
...right angles are equal to twice as many right angles as the figure has sides. 7. Parallelograms on the same base and between the same parallels are equal to one another. 8. The complements of the parallelograms which are about the diameter of any parallelogram are equal... | |
 | 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: 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 ABC shall be... | |
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Parallelograms upon the same base and between the same parallels, are equal to one another. 
