 | 1867 - 964 pagina’s
...proceed to show. The reader will remember that in Problem XXIV (page 308) it was shown that triangles on the same base and between the same parallels are equal to one another, and that triangles on equal bases and between the same parallels are also equal to one another. Now... | |
 | Robert Simson - 1806 - 546 pagina’s
...paralkio c 4. 1. gram ACDB into two equal parts. QED PROP. XXXV. THEOR. See N. PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another. Sue OH- Let the parallelograms ABCD, EBCF be upon the same base 2dand3d BC, and between the same parallels... | |
 | John Playfair - 1806 - 320 pagina’s
...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, DEC be upon the same base BC, and between the same parallels AD, BC; the triangle... | |
 | Charles Hutton - 1812 - 620 pagina’s
...BC, and also parallel ioit(th. 12). q. ED THEOREM XXV. PARALLELOGRAMS, as also Triangles, standing on the Same Base, and between the Same Parallels, are equal to each other. Let E Let ABCD, ABEP, be two parallelograms, and ABC, ABF, two triangles, standing on the... | |
 | John Mason Good - 1813 - 714 pagina’s
...basis, and between the same parallels, are equal to one another. Prop. XXXVII. Theor. Triangles npon the same base, and between the same parallels, are equal to one another. Prop. XXXVIII. Theor. Triangles upon equal bases, and between the same parallels, are equal to one... | |
 | Euclides - 1816 - 588 pagina’s
...divides the parallelogram ACDB into two equal" parts. PROP. XXXV. THEOR. , s«eN. PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another. See the ad Let the parallelograms ABCD, EBCF be upon the same and 3d fi. base BC, and between the same... | |
 | John Playfair - 1819 - 354 pagina’s
...parallelogram ACDB into two equal parts. Therefore, &c. Q, ED PROP. XXXV. THEOR. Parallelogram* upon the same base and between the same parallels, are equal to one another. vi^(sEE THE 2d AND 3d FIGURDS.) Let the parallelograms ABCD, EBCF be upon the same base BC> and between... | |
 | William Hawney - 1820 - 336 pagina’s
...of the wedge be perpendicular to its base ABFB, or inclined as ABI, since parallelopipedons standing on the same base and between the same parallels are equal to each other (Euclid, XI. and 29.) But when the edge CD of the wedge is longer or shorter than the base,... | |
 | Pierre Simon de Marquis Laplace, Thomas Young - 1821 - 372 pagina’s
...DCB (105), and A BC is common, therefore they are equal (102), and AB=CD, and AC=BD. 115. THEOREM. Parallelograms on the same base, and between the same parallels, are equal. ABC __ T> Since AB=CD, botli being cqnal to EF, AC=BD (15, or 16), and the triangle AEC is equiangular... | |
 | Cambridge Philosophical Society - 1842 - 458 pagina’s
...with the first twenty-six propositions of Euclid, and not till then, it becomes evident to him, that parallelograms on the same base and between the same parallels are equal ; and he cannot even conceive the contrary. When he has a little further cultivated his geometrical... | |
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Parallelograms on the same base and between the same parallels are equal to one another. 
