| War office - 1861
...less than — — . MATHEMATICS. REV. CANON HEAVISIDE, MA Voluntary Paper, No. II. 1. Parallelograms **upon the same base and between the same parallels are equal to one another.** 2. If a straight line be divided into two equal and also into two unequal parts, the rectangle contained... | |
| Euclides - 1862
...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... | |
| Euclides - 1863
...2ioo r on Al a Y % a h + ± ft" _± ± ± 1 ± t -I f 1 [ / <' -T ' it 9 \ l)s 8 a Cl .PROP. 37. — **THEOR. Triangles upon the same base and between the same parallels are equal to one another.** consequently, half the product of the base ana altitude gives the area of a triangle. PROP. 38. —... | |
| University of Oxford - 1863
...equal to three given straight lines, any two of these being greater than the third. 5. Parallelograms **upon the same base, and between the same parallels, are equal to one another.** 6. To a given straight line apply a parallelogram which shall be equal to a given triangle, and have... | |
| Euclides - 1864
...parallelogram 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 ABC shall be... | |
| Woolwich roy. military acad - 1864
...is 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,... | |
| 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
...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... | |
| William Kennedy Maxwell - 1871
...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 - 1872 - 349 Seiten
...CJEFGH, i. 35. v 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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