| William E. Bell - Bridges - 1859 - 226 pages
...Theorem. Parallelograms having equal loses and equal altitudes, contain equal areas, or are equivalent. Let the two parallelograms, ABCD and ABEF, have the same base, AB, and the same altitude P8 ; then they will be equivalent. 1n the triangles BCE and ADF, the sides BC and... | |
| Sandhurst roy. military coll - 1859 - 672 pages
...the greater angle shall be greater than the base of the other. 2. Define a parallelogram ; prove that parallelograms upon the same base and between the same parallels are equal to one another. 3. If a straight line be divided into any two parts, the squares of the whole line... | |
| Royal college of surgeons of England - 1860 - 336 pages
...lines make the alternate 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.... | |
| Henry William Watson, Edward John Routh - Mathematics - 1860 - 240 pages
...and for the rectangle 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... | |
| Robert Potts - Geometry, Plane - 1860 - 380 pages
...the diameter -BCdivides 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... | |
| William Whewell - Philosophy - 1860 - 604 pages
...understood, and the proof being gone through, the truth of the proposition must be assented to. That parallelograms upon the same base and between the same parallels are equal ; — that angles in the same segment are equal ; — these are propositions which we learn to be true... | |
| War office - 1861 - 260 pages
...— ax — bx (a — b)(x — a) (b — a)(x—b] Solve the equation x + y = 9^ a? + 2y* = 66 J 7. Parallelograms upon the same base and between the same parallels are equal to one another. 8. The angles in the same segment of a circle are equal to one another. 9. Inscribe... | |
| Euclides - 1862 - 172 pages
...the triangle ABC is equal to the triangle BCD ; (l. 4) 44 THE SCHOOL EUCLID. PROP. XXXV.— THEOREM. Parallelograms upon the same base, and between the same parallels, are equal to each other. (References— Prop. i. 4, 29, 34 ; ax. 1, 3, 6.) Let the parallelograms ABCD, EBCF,... | |
| Euclides - 1863 - 74 pages
...tiJ the next two divisions coincide, it will have moved 2-100th of an inch, &e. PEOP. 35.— THEOK. Parallelograms upon the same base and between the same parallels are equal, or rather equivalent to one another. DEK:-P. 84, Ax. 6, Ax. 1, Ax. 3, P. 29, P. 2*. ADE CASE L Sup.... | |
| University of Oxford - Education, Higher - 1863 - 328 pages
...length from a given point without it. 5. Describe a square equal to a given rectilineal figure. 6. Parallelograms upon the same base and between the same parallels are equal to one another. 7. Divide a straight line into two parts, so that the rectangle contained by the whole... | |
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