| Caricatures and cartoons - 1862 - 556 pages
...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 - 332 pages
...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... | |
| William Chambers, Robert Chambers - Encyclopedias and dictionaries - 1842
...to each other ; in proposition 37, the same fact is affirmed with respect to triangles, namely, that **triangles upon the same base and between the same parallels, are equal.** Propositions 36 and 38 are the converse of the preceding. The most celebrated, however, of the succeeding... | |
| Education - 1843 - 570 pages
...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... | |
| Education - 1844 - 688 pages
...MODERATOR AND SENIOR EXAMINER. [The Differential Calculut it not to be wed.] 1 . Parallelograms on the **same base and between the same parallels are equal to one another.** 2. From a given circle to cut off a segment containing an angle equal to a given rectilineal angle.... | |
| Euclid - Geometry - 1845 - 218 pages
...ACDB into two equal parts. QED BOOK I. PROP. XXXV. XXXVI. PROPOSITION XXXV. THEOR. — Parallelograms **upon the same base, and between the same parallels, are equal to one another. Let the** parallelograms ABCD, EBCF be upon the same See the 2nd base BC, and between the same parallels AF,... | |
| Euclides - 1845 - 544 pages
...divides the parallelogram ACDB into two equal parts. QED PROPOSITION XXXV. 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. Then the... | |
| Euclid, James Thomson - Geometry - 1845 - 380 pages
...parallelogram AC is equal (I. ax. 1) to EG. Wherefore parallelograms, &c. PROP. XXXVII. TnEOR.t — **Triangles upon the same base, and between the same parallels, are equal to one another.** * lt will appear, from this proposition, that the perimeters of two equal parallelograms on the same... | |
| Euclides - 1846 - 292 pages
...also the 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. Let the triangles ABC,** DBC be upon the same base BC, and between the same parallels AD, BC : the triangle ABC shall be equal... | |
| W. PEASE - 1846 - 86 pages
...form the isosceles triangle required. The reason of this is (Prob. XXXVII. Bk. I. Euclid,) because **triangles upon the same base, and between the same parallels, are equal to one another** : ie the triangles ACB and AE B, being upon the base, AB, to which the line EC is parallel, therefore... | |
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