| Euclid, Robert Simson - Geometry - 1838 - 416 pages
...BCD, and the diameter BC divides the parallelogram ACDB into two equal parts. QED PROP. XXXV. THEOR. **PARALLELOGRAMS upon the same base, and between the...to one another.* Let the parallelograms ABCD, EBCF** be upon the same base BC, and between the same parallels AF, BC ; the parallelogram ABCD shall be equal... | |
| Thomas Holliday - Surveying - 1838 - 80 pages
...quadrilateral figure be equal, they will alto be parallel, and the figure will be a parallelogram. 3. **Parallelograms upon the same base and between the same parallels are equal to one another.** 4. A parallelogram is double the area of a triangle of the same base and altitude. See fig. 22, plate... | |
| Euclides - 1838
...rectangle AB • BC to the rectangle DE • EF. Draw AG, DH perpendicular to BC, EF respectively. Because **parallelograms upon the same base and between the same parallels are equal,** the parallelogram AC is equal to the rectangle AG-BC and the parallelogram DF to the rectangle DH-EF.... | |
| Euclides - 1840
...parallelogram are equal, and it is bisected or divided into two equal parts by a diagonal. PROP. XXXV. THEOR. **Parallelograms upon the same base and between the same parallels are equal.** c ED p PROP. XXXVI. THEOR. Parallelograms on equal bases and between the. same parallels, are equal.... | |
| Euclides - Geometry - 1841 - 351 pages
...parallelogram ABCD is equal to EFGH. Wherefore parallelograms, &c. QED PROP. XXXVII. THEOR. Triangles **upon the same base, and between the same parallels, are equal to one another.** BC, and between the same parallels AD, BC: the triangle ABC shall be equal to the triangle DBC. Produce... | |
| Caricatures and cartoons - 1862
...Nasty pig you are. You learn those ways at school, and nothing else. Master Bob. Don't I, Miss. Hee ! **Parallelograms upon the same base and between the same parallels are equal to** 9ne another, and equal triangles upon equal bases in the same straight lines, and towards the same... | |
| John Playfair - Euclid's Elements - 1842 - 317 pages
...sum of any two adjacent angles of a parallelogram is equal to two right angles. PROP. XXXV. THEOR. **Parallelograms upon the same base and between the same parallels, are equal to one another.** (SEE THE 2d AND 3d FIGUREs.) Let the parallelograms ABCD, EBCF be upon the same base BC, and between... | |
| Chambers W. and R., ltd - 1842
...whole number of square feet coutaiiied in the table, namely, 16. It is demonstrated by Euclid, that **parallelograms upon the same base and between the same parallels are equal to** each other ; from this it follows that the area of a rhombus and a rhomboid can be ascertained by the... | |
| Euclides - 1842
...BCD, and the diameter вc divides the parallelogram ACDB into two equal parts. QED PROP. XXXV. THEOR. **PARALLELOGRAMS upon the same base, and between the same parallels, are equal** or equivalent to one another. Let the parallelograms ABCD, EBCF be upon the same base вc, and between... | |
| Education - 1843
...angles, or are together equal to two right angles. 2. Define a parallelogram. Parallelograms on the **same base and between the same parallels are equal to one another.** Shew that if any quadrilateral figure be bisected by both its diagonals it is a parallelogram. 3. To... | |
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