 | Euclides - 1862 - 172 pages
...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... | |
 | University of Oxford - Education, Higher - 1863 - 316 pages
...equal to three given straight lines, any two of these being greater than the third. 5. Parallelograms upon the same base, and between the same parallels, are equal to one another. 6. To a given straight line apply a parallelogram which shall be equal to a given triangle, and have... | |
 | Euclides - 1863 - 74 pages
...a h + ± ft" _± ± ± 1 ± t -I f 1 [ / <' -T ' it 9 \ l)s 8 a Cl .PROP. 37. — THEOR. Triangles upon the same base and between the same parallels are equal to one another. consequently, half the product of the base ana altitude gives the area of a triangle. PROP. 38. —... | |
 | Euclides - 1864 - 262 pages
...EFGH. (ax. 1.) Therefore, parallelograms upon equal, &c. QED PROPOSITION XXXVII. THEOREM. Triangles upon the same base and between the same parallels, are equal to one another. Let the triangles ABC, DBCbe upon the same base BC, and between the same parallels AD, BC. Then the triangle ABC shall be... | |
 | 1864 - 370 pages
...z. III. Find the limits of a hyperbola when it is produced by an Irish member. IV. Similar figures upon the same base, and between the same parallels, are equal to one another. Apply this theorem to show the base similarity of certain persons who cut similar figures in Parliament.... | |
 | Euclides - 1864 - 448 pages
...divides the parallelogram A CDB into two equal parts. QED PROPOSITION XXXV. THEOREM. Parallelograms upon the same base, and between the same parallels, are equal to one anuther. ( Let the parallelograms AB CD, -E-BCFbeuponthe same base 2? C, . and between the same parallels... | |
 | Robert Potts - 1865 - 528 pages
...EFGH. (ax. 1.) Therefore, parallelograms upon equal, &e. QE u. PROPOSITION XXXVII. THEOREM. Triangles upon the same base and between the same parallels, are equal to one another. Let the triangles ABC, DBC\lQ upon the same base BC, and between the same parallels AD, BC. Then the triangle ABC shall be... | |
 | Euclides - 1865 - 80 pages
...thing are equal to one another; therefore the parallelograms ABCD and EBCF are equal. Cor. Triangles upon the same base and between the same parallels are equal to one another; for the triangle ABC is (40) half the parallelogram ABCD, and the triangle FCB is half the parallelogram... | |
 | Architecture - 1865 - 276 pages
...Given the vertical angle, and a side to construct the triangle. 3. Prop. 35. Theorem. Parallelograms upon the same base and between the same parallels are equal to one another. Shew this is equally true of triangles. 4. Prop. 44. — Problem. To a given straight line to apply... | |
 | J. F. H. de Rheims - Geometrical drawing - 1865 - 336 pages
...same base and between the same parallels are equal to one another. Prop. 37. — Theorem. Triangles upon the same base and between the same parallels are equal to one another. Prop. 47. — Theorem. In any right angled trinngle, the square which is described upon the side subtending... | |
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Parallelograms upon the same base and between the same parallels, are equal to one another. 
