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The elements of Euclid : viz, the first six books, together with the eleventh and twelfth : the errors, by which Theon, or others, have long ago vitiated these books, are corrected, and some of Euclid's demonstrations are restored : also, The book of Euclid's data, in like manner corrected (1834)

Euclid, Euclid, Simson, Robert, 1687-1768 · Philadelphia : Desilver & Thomas · leaf 364

An illustration from The elements of Euclid : viz, the first six books, together with the eleventh and twelfth : the errors, by which Theon, or others, have long ago vitiated these books, are corrected, and some of Euclid's demonstrations are restored : also, The book of Euclid's data, in like manner corrected, 1834, leaf 364
he given space to which the sum of the squares wasrequired to be equal. But if twice the given rectangle be not equal to the given sumof the squares of the sides, it must be less than it, as has beenshown. Let ABCD be the rectangle; join AC and draw BEperpendicular to it, and complete the rectangle… … Euclids data. 361 AC, BE is equal to AB, BCj and the rectangle AB, BC is given,wherefore AC, BE is given: and because the sum of the squaresof AB, BC is given, the square of AC which is equal (47. 1.) tothat sum is given; and AC itself is therefore given in magnitude:let AC be likewise given in…

Mathematics, Greek · Geometry · Trigonometry

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