 | W. PEASE - 1846 - 86 sider
...triangle required. The reason of this is (Prob. XXXVII. Bk. I. Euclid,) because triangles upon the same base, and between the same parallels, are equal to one another : ie the triangles ACB and AE B, being upon the base, AB, to which the line EC is parallel, therefore... | |
 | Euclid, John Playfair - 1846 - 334 sider
...angles of a parallelogram is equal to two right angles. PROP. XXXV. THEOR. Parallelograms upon, the same base and between the same parallels, are equal to one another. > (SEE THE 2d AND 3d FIGURES.) 34 If the sides AD, DF of the parallelograms ABCD, DBCF opposite to... | |
 | William Whewell - 1847 - 708 sider
...with the first twenty-six propositions of Euclid, and not till then, it becomes evident to him, that parallelograms on the same base and between the same parallels are equal ; and he cannot even conceive the contrary. When he has a little further cultivated his geometrical... | |
 | Charles William Hackley - 1847 - 248 sider
...cases is left as an exercise for the learner. THEOREM XXII. Parallelograms, as also triangles, standing on the same base, and between the same parallels, are equal to each other. Let ABCD, ABEF be two parallelograms, and ABC, ABF two triangles, ABAB standing on the... | |
 | Thomas Gaskin - 1847 - 301 sider
...Nov. 1847. GEOMETRICAL PROBLEMS. ST JOHN'S COLLEGE. DEC. 1830. (No. I.) 1. PARALLELOGRAMS upon the same base and between the same parallels are equal to one another. 2. Of unequal magnitudes,, the greater has a greater ratio to the same than the less. 3. If the diameter... | |
 | Cambridge univ, exam. papers - 1847 - 40 sider
...and x both lie between 0 and 1, prove that >x. i — a 3. In the figure of Euclid, Book i. Prop. 35, (Parallelograms on the same base and between the same parallels are equal,) if two diagonals be drawn to the two parallelograms respectively, one from each extremity of the base,... | |
 | Euclides - 1847 - 128 sider
...BMNC. Wherefore the sum of the areas &c. — QED PEOP. XXXVII. THEOR. GEN. ENUN. — Triangles upon the same base, and between the same parallels, are equal to one another. PART. ENUN. — Let the A ABC, DBC be upon the same base BC, and between the same || s AD, BC ; then... | |
 | J. Goodall, W. Hammond - 1848 - 390 sider
...Given the value of two angles of a triangle, how is the value of the third ascertained ? 2. Prove that parallelograms on the same base and between the same parallels are equal to one another. 3. In any right angled-triangle, the square which is described upon the side subtending the right angle... | |
 | 1848 - 542 sider
...Bell's Euclid," prop. 32, book i. ; (a) and (6). See " Tate's Geometry," &c. page 27. 2. Prove that parallelograms on the same base and between the same parallels are equal to one another. — See " Bell's Euclid," prop. 35, book i. ; or " Tate's Geometry," &c. p. 33. 3. In any right-angled... | |
 | Great Britain. Council on Education - 1848 - 596 sider
...the construction fails when that condition is not fulfilled. 2. Prove that parallelograms upon the same base and between the same parallels are equal to one another. Shew hence that the area of a parallelogram is properly measured by the product of the numbers that... | |
| |
Triangles upon the same base, and between the same parallels, are equal to one another. 
