 | 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,... | |
 | Euclid, Robert Simson - 1821 - 514 pagina’s
...divides the parallelogram ACDB into two equal parts. QED PROP. XXXV. THEOR. PARALLELOGRAMS upon the same base, and between the same parallels, are equal...one another.* "Let the parallelograms ABCD, EBCF be upon the same base BC, and between the same parallels AF, BC; the parallelogram ABCD shall be equal... | |
 | Pierre Simon de Marquis Laplace, Thomas Young - 1821 - 372 pagina’s
...equiangular with 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... | |
 | Charles Hutton - 1822 - 616 pagina’s
...BC, and also parallel to it (th. 12). 4. ED THEOREM XXV. PARALLELOGRAMS, as also Triangles, standing on the Same Base, and between the Same Parallels, are equal to each other. Let £98 Let ABCD, ABEF, be two parallelograms, and ABC, ABF, two triangles, standing on... | |
 | Peter Nicholson - 1825 - 1046 pagina’s
...triangle DBC. Wherefore triangles, &c. QED Propoíiíion XXXVIII. Theorem. Triangles upon equal bases, and between the same parallels, are equal to one another. Let the triangles ABC, DEF be upon equal bases BC, EF, and between the same parallels BF, AD : The triangle... | |
 | Euclid - 1826 - 234 pagina’s
...two trapeziums be equal to one another. PROPOSITION XXXVII. THEOREM. Triangles constituted upon the same base, and between the same parallels, are equal to one another. Let the triangles ABC, DBC, be constituted upon the same base вс, and between the same parallels AD, вс.... | |
 | Euclides - 1826 - 226 pagina’s
...two trapeziums be equal to one another. PROPOSITION XXXVII. THEOREM. Triangles constituted upon the same base, and between the same parallels, are equal to one another. » 3i. i. parallel to сл, " and through c draw CF, parallel to в D. Therefore each of them EBCA,... | |
 | Robert Simson - 1827 - 546 pagina’s
...divides the parallelogram ACDB into two equal parts.' ei. ED PROP. XXXV. THEOR. Parallelograms upon the same base, and between the same parallels, are equal to one another. Let the parnllelograms ABCD, EBCF be upon the same base BC, and between the same parallels AF, BC : the parallelogram... | |
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Triangles upon the same base, and between the same parallels, are equal to one another. 
