 | Robert Routledge - Science - 1881 - 748 pages
...the reasoning can easily be followed by any one conversant with tht geometrical fact that triangks on the same base and between the same parallels are equal in area. Let a body be moving unacted on by any F force along the line AD, Fig. 85 ; in that line its positions... | |
 | Arthur Sherburne Hardy - Quaternions - 1881 - 252 pages
...the order of the factors, hence TV(a + /3)(a-/3)=2TVj8a, which is the proposition (Art. 41, 7). 13. Parallelograms on the same base and between the same parallels are equal. We have (Fig. 45) BE = BA + AE = BA + xBC. Operating with V . BC x V(BC . BE)=V(BC . BA), since VaBC2... | |
 | John Gibson - 1881 - 64 pages
...Propositions 33-40. 1. The opposite sides and angles of a parallelogram are equal to one another. 2. Parallelograms on the same base and between the same parallels are equal to one another. 3. Triangles on the same base and between the same parallels are equal. 4. Equal triangles... | |
 | William George Spencer - Geometry - 1881 - 116 pages
...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 trapezi um into a triangle ? 324. Can you change a triangle into a rectangle... | |
 | Education, Higher - 1883 - 536 pages
...and in it take any point P. Join P, A and P, B. The angle APB shall be greater than the angle ACB. 5. Parallelograms on the same base and between the same parallels are equal to one another. 6. Divide a given straight line into two parts, such that the difference of the squares... | |
 | College of preceptors - 1882 - 528 pages
...the difference of two sides of a triangle and the third side. 3. Define a parallelogram ; and show that parallelograms on the same base and between the same parallels are equal in area. Enunciate a converse of this proposition. 4. Define an acute-angled triangle, an obtuse-angled triangle,... | |
 | Great Britain. Education Department. Department of Science and Art - 1882 - 510 pages
...Show how to draw a straight line through a given point, parallel to a given straight line. 11. Show that parallelograms on the same base and between the same parallels are equal. Show how to construct an isosceles triangle equal to a given triangle. '10.) 12. ABC is a triangle... | |
 | Marianne Nops - 1882 - 278 pages
...parallelograms are equal. It is plain that we want a connecting link in order to compare them. We know that parallelograms on the same base and between the same parallels are equal ; can •we construct a parallelogram on BC and between these parallels, which will then be equal to... | |
 | Mary W I. Shilleto - 1882 - 418 pages
...students are advised not to confine themselves to one paper, but to make use of the whole set. (a) 1. Parallelograms on the same base and between the same parallels are equal. AOC is an isosceles triangle, of which A is the vertex : AB, AC are bisected in D & E respectively... | |
 | John Robertson (LL.D., of Upton Park sch.) - Examinations - 1882 - 152 pages
...kind being worth £10 each. Find how many he has of each kind. 1. Write down the three postulates. 2. Parallelograms on the same base, and between the same parallels are equal to one another. 3. If a straight line be bisected, and produced to any point, the squares of the whole... | |
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Prove that parallelograms on the same base and between the same parallels are equal in area. 
