 | Dugald Stewart - Logic - 1814 - 582 pages
...only appeal to the thirty-seventh proposition of the first book, in which it is proved that triangles on the same base, and between the same parallels, are equal ; a theorem which appears, from a very simple construction, to be only a few steps removed from the fourth... | |
 | Dugald Stewart - Psychology - 1821 - 348 pages
...appeal to the thirty-seventh proposition of the first book, .' in which it is proved that triangles on the same base, and between the same parallels, are equal ; a theorem which appears, from a very simple construction, to be only a few steps removed from the fourth... | |
 | Pierre Simon de Marquis Laplace, Thomas Young - Celestial mechanics - 1821 - 372 pages
...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 - Philosophy - 1842 - 458 pages
...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... | |
 | Dugald Stewart - 1829 - 418 pages
...only appeal to the thirty-seventh proposition of the first book, in which it is proved that triangles on the same base, and between the same parallels, are equal ; a theorem which appears, from a very simple construction, to be only a few steps removed from the fourth... | |
 | John Playfair - Geometry - 1829 - 210 pages
...the figure is a parallelogram, therefore the opposite angles are equal. PROPOSITION XXXV. THEOREM. Parallelograms on the same base, and between the same parallels, are equal to one another; that is, their surfaces are equal. Let the parallelograms ABCD, DBCF be on the same... | |
 | Dugald Stewart - 1829 - 442 pages
...only appeal to the thirty-seventh proposition of the first book, in which it is proved that triangles on the same base, and between the same parallels, are equal ; a theorem which appears, from a very simple construction, to be only a few steps removed from the fourth... | |
 | Euclides - 1833 - 304 pages
...other, as being together with these equal angles = to two right angles (prop. 29.) PROP. 35, THEOR. Parallelograms on the same base and between the same parallels are equal. Connect the sides opposite the base, (if necessary,) then there are two triangles formed (viz. the... | |
 | Alexander Smith (M.A.) - 1835 - 750 pages
...the mathematicians teach us that the three angles of a triangle are equal to two right angles ; that parallelograms on the same base, and between the same parallels, are equal, and the like ; and they likewise teach us why this is true ; ie they shew how these truths necessarily... | |
 | Alexander Smith - Ethics - 1835 - 350 pages
...the mathematicians teach us that the three angles of a triangle are equal to two right angles ; that parallelograms on the same base, and between the same parallels, are equal, and the like ; and they likewise teach us why this is true ; ie they shew how these truths necessarily... | |
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Prove that parallelograms on the same base and between the same parallels are equal in area. 
