| Joseph Hughes - 1883
...Inspector. Euclid. MALES. [All generally understood abbreviations for -sards may be used.] 1. Parallelograms **upon the same base, and between the same parallels, are equal to one another.** Prop. XXXV., Bk. I. 2. To describe a parallelogram equal to a given rectilineal nre, and having an... | |
| Euclid, Isaac Todhunter - 1883 - 400 páginas
...divides the parallelogram AGDB into two equal parts. PROPOSITION 85. THEOREM. Parallelograms on the **same base, and between the same parallels, are equal to one another.** Let the parallelograms ABCD, EBCF be on the same base BC, and between the sameparallels AF, BG: the... | |
| Euclides - 1883 - 96 páginas
...area of the first is the same multiple of the area of the other. PROP. 37. THEOR. Triangles on the **same base and between the same parallels are equal to one another.** Given ABC, DBC, two triangles on the base BC, and between the parallels BC, AD. To prove A ABC = A... | |
| John Robertson (LL.D., of Upton Park sch.) - 1884
...more together 1. Distinguish between a quadrilateral, a parallelogram, a rhombus, and a square. 2. **Triangles upon the same base and between the same parallels, are equal to one another.** 3. In every triangle, the square of the side subtending either of the acute angles, is less than the... | |
| Stewart W. and co - 1884
...is eqaal to the same EBCH ; therefore, also the parallelogram ABCJ) is equal to EFGH. JLX.XVJI. — **Triangles upon the same base, and between the same parallels, are equal to one another.** Let the triangles be ABC, DBC. Produce AD both ways to the points E, F, and through B draw BE parallel... | |
| Euclides - 1884
...EFG and EBCaxo halves of equal things ; also draw the inference. 85. PROPOSITION XXXVII. — THEOREM. **Triangles upon the same base and between the same parallels are equal to one another.** Let the triangles ABC, DBC be upon the same base BC, and between the same parallels AD, BC. Then ABC... | |
| Woolwich roy. military acad - 1884
...this proposition. How many of the exterior angles of any triangle must be obtuse ? 4. Parallelograms **upon the same base, and between the same parallels, are equal to one another.** 5. Describe a square that shall be equal to a given rectilineal figure. Divide a given straight line... | |
| 1884
...circles of given unequal radii so as to touch each other and a given straight line. 6. Parallelograms **upon the same base, and between the same parallels, are equal to one another.** 7. In obtuse.angled triangles, if a perpendicular be drawn from any one of the acute angles to the... | |
| Stewart W. and co - 1884
...respectively, then PR and liV are respectively parallel to straight lines KM. and MN. QED SliCTION III. 1. (a) **Triangles upon the same base and between the same parallels are equal.** (b.) Construct a triangle equal to a given triangle and having a base three times as great (a) See... | |
| Euclides - 1884
...Therefore, the opposite sides &c. Proved. I. 4. E. r. PROPOSITION XXXV. THEOREM. Parallelograms on the **same base, and between the same parallels, are equal to one another.** GIVEN that the parallelograms ABCD and EBCF are on the same base BC, and between the same parallels... | |
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