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Rh English mile south of Augsburg. Tycho tells us in his principal work, Astronomiæ Instauratæ Progymnasmata, at some length, that he was in the act of making out how large an instrument would have to be in order to have the single minutes marked on the graduated arc, when Paul Hainzel came in and a discussion arose between them on the subject. Tycho was convinced that no good would result to science from using "those puerile tools" with which astronomers then observed, and he concluded that it was necessary to construct a very large quadrant, so large that every minute could readily be distinguished, and fractions of a minute estimated; "for he did not then know the method of subdividing by transversals." This last remark is curious, as we have already seen that he attributed his acquaintance with the method to Scultetus, but he evidently means that it had not yet occurred to him to use this plan on an arc as well as on a rectilinear scale. He spoke in favour of constructing a quadrant, as he had already made several of three or four cubits radius (this is the only evidence we have of this fact), and was sufficiently familiar with the cross-staff to know that no accurate results were to be expected from it. The outcome of this discussion was that Paul Hainzel undertook to defray the expense of a quadrant with a radius of 14 cubits (or about 19 feet). The most skilful workmen were engaged, and within one month the huge instrument was completed. Twenty men were scarcely able to erect it on a hill in Hainzel's garden at Göggingen; it was made of well-seasoned oak; the two radii and the arc were joined together by a framework of wood, and a slip of brass along the arc had the divisions marked on it. Unlike all Tycho's later quadrants, it was suspended by the centre,