 | War office - 1861 - 260 Seiten
...— — . 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 - 32 Seiten
...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 - 172 Seiten
...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 - 316 Seiten
...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 - 74 Seiten
...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 - 448 Seiten
...(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 - 262 Seiten
...(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 - 370 Seiten
...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 - 568 Seiten
...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 - 214 Seiten
...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. 
