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quered every prejudice which can arise from reasoning upon a particular figure.

The reader is also carefully to observe the different methods of comparison made use of in the first six books. In the first book, the magnitudes are coinpared either; as exactly agreeing together ; or as being equal to the same magnitude ; or as being radius's of the same circle, which are all common and familiar notions. But in the second book; the method of comparison is by the rectangle, which is by no means a common notion, either as to its name or nature ; and therefore should be made familar; as well as perfe&ly understood. In some part of the third book, the method of comparison is by similar segments, which is also an artificial idea, and ought for the same reason to be made familiar. But the most artificial and therefore the most difficult of all, is that method of comparison founded upon a consideration of quantities as parts and multiples. It will be particularly useful for the student, who has fạiled in his first attempt to understand this fifth book, after reading carefully what I have said in explanation of the two first definitions, to take care to have the suppositions given him by another and then carefully to perform every construction himself. And indeed the reader who would take the easiest way of making himself master of this subject, should have the ruler and compasses in his hand, through the first fix books, only taking care not to forget, that he is handling a ruler and compasses.

THE END OF THE FIRST VOLUME.

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