| Euclides - 1870
...points. P. 31. Through a given point to draw a st. line parallel to a given st. line. DEM. — P. 37. **Triangles upon the same base and between the same parallels are equal.** Ax. 1. Magnitudes equal to the same magnitude are equal. EXP. 1 HypConcl. Let the AS ABC, DEC, A be... | |
| Euclides - 1871
...[3EBCH= EJEFGH, i. 35. V they are on the same base EH and between the same IIs ; .-. O ABCD =o EFGH. **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 lis AD. BC. Then must &ABC= &DBC. From B draw... | |
| Henry William Watson - 1871 - 285 páginas
...proved equal to the area of AF, therefore the area of AF is equal to the area of GD. PROPOSITION 6. **Triangles upon the same base and between the same parallels are equal to one another** in area. Fig. 14. j) AD P Let the triangles ABC and DBC be upon the same base BC, and between the same... | |
| 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 páginas
...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... | |
| Euclid, Charles Peter MASON - 1872
...ABCD and EFGH, being each equal to the parallelogram ABGH, Are equal to each other. PBOPOSITION XXXVU. **Triangles upon the same base and between the same parallels are equal to** each other. For the construction in this proposition we must be ableto draw a straight line from a... | |
| Hugo Reid - 1872 - 124 páginas
...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... | |
| Lewis Sergeant - 1873
...decimals. (10.) 21 41 21 228 2000 _1824 1~7G, <fcc. (See Arith., § 61.) * 3. Show that parallelograms and **triangles upon the same base and between the same parallels are equal to one another.** (10.) (This appears to mean that parallelograms on the same base and between the same parallels are... | |
| Edward Atkins - 1874
...Therefore the parallelogram ABCD is equal to the parallelogram EFGH (Ax. 1). Proposition 37. — Theorem. **Triangles upon the same base, and between the same parallels, are equal to one another.** Let the triangles ABC, DEC be on the same base BC, and between the same parallels AD, BC ; The triangle... | |
| Euclides - 1874
...divides the parallelogram ACDB into two equal parts. ~ QED PROPOSITION 35. — Theorem. Parallelograms **upon the same base, and between the same parallels, are equal to one another.** Let the parallelograms ABCD, EBCF be upon the same base BC, and between the same parallels AF, BC.... | |
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