| Euclides - 1863 - 74 pages
...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 - Education, Higher - 1863 - 316 pages
...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 - 262 pages
...parallelogram ABCD is equal to the parallelogram EFGH. (ax. 1.) Therefore, parallelograms upon equal, &c. QED **PROPOSITION XXXVII. THEOREM. Triangles upon 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 - 588 pages
...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 - 370 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.... | |
| Euclides - 1864 - 448 pages
...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... | |
| Robert Potts - 1865 - 528 pages
...ABCD is equal to the parallelogram. EFGH. (ax. 1.) Therefore, parallelograms upon equal, &e. QE u. **PROPOSITION XXXVII. THEOREM. Triangles upon the same...parallels, are equal to one another. Let the triangles ABC,** DBC\lQ upon the same base BC, and between the same parallels AD, BC. Then the triangle ABC shall be... | |
| J. F. H. de Rheims - Geometrical drawing - 1865 - 336 pages
...Parallelograms upon the same base and between the same parallels are equal to one another. Prop. 37. — **Theorem. Triangles upon the same base and between the same parallels are equal to one another.** Prop. 47. — Theorem. In any right angled trinngle, the square which is described upon the side subtending... | |
| Euclides - 1865 - 80 pages
...the same thing are equal to one another; therefore the parallelograms ABCD and EBCF are equal. Cor. **Triangles upon the same base and between the same parallels are equal to one another;** for the triangle ABC is (40) half the parallelogram ABCD, and the triangle FCB is half the parallelogram... | |
| William Harris Johnston - 1865 - 478 pages
...respects oblique parallelograms abo. By Euclid, Book I, Prop. 35, it is established that «parallelograms **upon the same base and between the same parallels are equal to one another."** Now, the perpendicular distance, D С, between the sides, DF and В С, of the oblique parallelogram... | |
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