 | University of Oxford - Education, Higher - 1863 - 316 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 and one part... | |
 | 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.... | |
 | Euclides - 1864 - 448 pages
...triangle BCD ; (l. 4.) and the diameter BC divides the parallelogram A CDB into two equal parts. QED PROPOSITION XXXV. THEOREM. Parallelograms upon the...base, and between the same parallels, are equal to one anuther. ( Let the parallelograms AB CD, -E-BCFbeuponthe same base 2? C, . and between the same parallels... | |
 | Euclides - 1864 - 262 pages
...EFGH. (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 - 368 pages
...z. III. 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.... | |
 | Woolwich roy. military acad - 1864 - 588 pages
...fractional or negative, and find the coefficient of x* in the expansion of (1 +#•+ £2)~5. 9. Triangles upon the same base and between the same parallels are equal to one another. ABC is an isoceles triangle, vertex A ; D and E are the points of bisection of AB and AC respectively,... | |
 | Architecture - 1865 - 276 pages
...the base shall be equal. Given the vertical angle, and a side to construct the triangle. 3. Prop. 35. Theorem. Parallelograms upon the same base and between the same parallels are equal to one another. Shew this is equally true of triangles. 4. Prop. 44. — Problem. To a given straight line to apply... | |
 | Thomas Squire Barrett - Causation - 1871 - 252 pages
...but be ' true ; as that 1 9 and 1 1 are 30 ; — Exam, of Antitheos, part i. §§ 64 — 65. ' that parallelograms upon the same ' base and between the same parallels ' are equal ; — that all the angles in ' the same segment of a circle are ' equal. The latter are truths which... | |
 | William Kennedy Maxwell - 1871 - 148 pages
...ft. 13. Here, as 4-1 : 65 : : 5 : 79-26, the height of the pole. Ans. 14. Now, triangles that stand upon the same base, and between the same parallels are equal to each other ; therefore, this question will, as shown in the figure, admit of two answers. Here, the... | |
 | Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...they are on the same base EH and between the same IIs ; QED PROPOSITION XXXVII. THEOREM. Triangles upon the same base, and between the same parallels, are equal to one another. Let A s ABC, DBC be on same base BC and between same IIs AD, BC. Then must &ABC= A DBC. From B draw BE... | |
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PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another... 
