| War office - 1861
...— 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 an equilateral... | |
| Euclides - 1862
...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, be... | |
| University of Oxford - Education, Higher - 1863
...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
...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
...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
...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.... | |
| Euclides - 1864
...the diameter BC divides 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** anuther. ( Let the parallelograms AB CD, -E-BCFbeuponthe same base 2? C, . and between the same parallels... | |
| Hugo Reid - Mathematics - 1872 - 124 pages
...produced. 142. If ote. — This illustrates the important geometrical truth, that — Parallelograms on the **same base and between the same parallels are equal to one another;** that is, equal in area. Fic.34 AEFD and ABCD are on the same base AD and between the same parallels... | |
| Thomas Squire Barrett - Causation - 1872 - 213 pages
...former kind ' are truths which cannot but be ' true ; as that 1 9 and 1 1 are 30 ; — NOTE XIX. 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 it... | |
| Euclid, Charles Peter MASON - Geometry - 1872
...a parallelogram is divided into two equal parts by either of its diagonals. (Prop. XXXIV.) 2. That **parallelograms upon the same base and between the same parallels are equal.** (Prop. XXXV.) 3. That the halves of equals are equal. (Ax. VIII.) Let ABC and ABD be two As upon the... | |
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