 | W. PEASE - 1846 - 86 pages
...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... | |
 | Thomas Gaskin - Geometry, Analytic - 1847 - 301 pages
...Geometry. TG CAMBRIDGE, Nov. 1847. GEOMETRICAL PROBLEMS. ST JOHN'S COLLEGE. DEC. 1830. (No. I.) 1. PARALLELOGRAMS upon the same base and between the same parallels are equal to one another. 2. Of unequal magnitudes,, the greater has a greater ratio to the same than the less. 3. If the diameter... | |
 | Euclides - 1847 - 128 pages
...from the rt. L to the pt. of bisection is = to half the hypothenuse. PROP. XXXV. THEOR. GEN. ENUN. — .Parallelograms upon the same base, and between the same parallels, are equal to one another. PART. ENUN. — Let the a ms ABCD, EBCF (Fig. 2 and 3) be upon the same base BC, and between the same... | |
 | William Whewell - Science - 1847 - 756 pages
...contingent truths. The former kind are Truths which cannot but be true; as that 19 and 11 make 30 ; — that parallelograms upon the same base and between the same parallels are equal: — that all the angles in the same segment of a circle are equal. The latter are Truths which it happens... | |
 | Euclides - 1848 - 52 pages
...equal to one another, and the diameter bisects them, that is, divides them into two equal parts. PROP. XXXV. THEOREM. Parallelograms upon the same base,...between the same parallels, are equal to one another. PROP. XXXVI. THEOREM. PROP. XXXVII. THEOREM. Triangles upon the same base anti between the same parallels,... | |
 | Great Britain. Council on Education - Education - 1848 - 596 pages
...lines ; and point out how the construction fails when that condition is not fulfilled. 2. Prove that parallelograms upon the same base and between the same parallels are equal to one another. Shew hence that the area of a parallelogram is properly measured by the product of the numbers that... | |
 | Great Britain. Committee on Education - 1848 - 606 pages
...lines ; and point out how the construction fails when that condition is not fulfilled. 2. Prove that parallelograms upon the same base and between the same parallels are equal to one another. Shew hence that the area of a parallelogram is properly measured by the product of the numbers that... | |
 | J. Goodall, W. Hammond - 1848 - 390 pages
...lines ; and point out how the construction fails when that condition is not fulfilled. 2. Prove that parallelograms upon the same base and between the same parallels are equal to one another. Show hence that the area of a parallelogram is properly measured by the product of the numbers that... | |
 | Euclid, Thomas Tate - 1849 - 120 pages
...the parallelogram ABCD is equal to EFGH. Wherefore parallelograms, &c. PHOP. 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 EADF triangle... | |
 | Cambridge Philosophical Society - Science - 1849 - 764 pages
...understood, and the proof being gone through, the truth of the proposition must be assented to. That parallelograms upon the same base and between the same parallels are equal; — that angles in the same segment are equal ; — these are propositions which we learn to be true... | |
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PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another... 
