 | William Whewell - Knowledge, Theory of - 1858 - 412 pages
...contingent truths. The former kind are Truths which cannot but be true; as that 19 and n 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... | |
 | Sandhurst roy. military coll - 1859 - 672 pages
...the greater angle shall be greater than the base of the other. 2. Define a parallelogram ; prove that parallelograms upon the same base and between the same parallels are equal to one another. 3. If a straight line be divided into any two parts, the squares of the whole line and of one of the... | |
 | Robert Potts - Geometry, Plane - 1860 - 380 pages
...EFGH. (ax. 1.) Therefore, parallelograms upon equal, &c. QED PROPOSITION XXXVII. THEOREM. T•iangles upon the same base and between the same parallels, are equal to one another. Let the triangles ABC, D-BCbe upon the same base BC, and between the same parallels AD, BC. Then the triangle... | |
 | Royal college of surgeons of England - 1860 - 332 pages
...lines make the alternate angles equal to each other, these two straight lines shall be parallel. 5. Parallelograms upon the same base and between the same parallels are equal to one another. The perimeter of a square is less than that of any other parallelogram of equal area. 6. If a straight... | |
 | Henry William Watson, Edward John Routh - Mathematics - 1860 - 240 pages
...and for the rectangle contained by AB and CD, the rect. AB, CD. 1. DEFINE parallel straight lines. Parallelograms upon the same base, and between the same parallels, are equal to one another. If a straight line DME be drawn through the middle point M of the base BC of a triangle ABC, so as... | |
 | Euclides - 1860 - 288 pages
...; therefore (Ax. 1) the parallelogram ABCD is equal to EFGH. PROPOSITION XXXVII. THEOREM. Triangles upon the same base, and between the same parallels, are equal to one another. Given the triangles ABC and DEC upon the same base BC, and between the same parallels AD and BC ; to... | |
 | John Playfair - Geometry - 1860 - 334 pages
...same EBCH : Therefore also the parallelogram ABOI? it «qual to EFGH. PROP. XXXVII. THEOR. Trim gles upon the same base, and between the same parallels, are equal to ont another. Let the triangles ABC, DBC be upon the same base BC, and between the same parallels, AD,... | |
 | William Whewell - Philosophy - 1860 - 604 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... | |
 | War office - 1861 - 260 pages
...— ax — bx (a — b)(x — a) (b — a)(x—b] Solve the equation x + y = 9^ a? + 2y* = 66 J 7. Parallelograms upon the same base and between the same parallels are equal to one another. 8. The angles in the same segment of a circle are equal to one another. 9. Inscribe an equilateral... | |
 | Euclides - 1862 - 172 pages
...BCD ; therefore the triangle ABC is equal to the triangle BCD ; (l. 4) 44 THE SCHOOL EUCLID. PROP. XXXV.— THEOREM. Parallelograms upon the same base, and between the same parallels, are equal to each other. (References— Prop. i. 4, 29, 34 ; ax. 1, 3, 6.) Let the parallelograms ABCD, EBCF, be... | |
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PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another... 
