The Connexion of Number And Magnitude An Attempt to Explain the Fifth book of E
The Connexion of Number And Magnitude An Attempt to Explain the Fifth book of E
De Morgan Augustus
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The defect may be remedied (we take the square as an instance) in two ways. 1. Write all definitions in the following manner. To define a square, for example, " If it be possible to construct a plane figure having four equal sides and one right angle, let that figure be called a square. " 2. Omit the definition of a square, head the 46th proposition of the first book as follows. " Theorem. On a given straight line, a four-sided figure can be constructed which shall have all its sides equal to t...he given straight line, and all its angles right angles. " Having demonstrated this, add the following definition : Let the figure so constructed be called a square. We have shewn that all sets of four magnitudes, A and B of one kind, P and Q both of the same kind with the first, or both of one other kind, can be divided into three classes. 1. Those in which simultaneous assertions on wA and w B, and on mP and nQ, are all (for all values of m and n) either ascending or stationary. 2. Those in which they are all stationary.
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