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Rh The first to suggest a method of subdividing an arc of moderate dimensions was Pedro Nunez, whose work, De Crepusculis, was published in 1542. He proposed inside the graduated arc of a quadrant to draw 44 concentric arcs, and divide them respectively into 89, 88, 87. . . 46 equal parts, so that the alidade in any position would (more or less accurately) touch a division mark on one of the 45 circles. The indication of this mark was multiplied by $90°⁄n$ where n is the number of divisions on the arc on which the mark touched by the alidade is. But however ingenious this proposal was, it was anything but a practical one, as it is not easy to divide an arc into 87 or 71 equal parts, and the observer would generally be in doubt which division was nearest the alidade. Tycho Brahe tried this plan on three of the instruments first constructed at Hveen (the two smallest quadrants and a sextant), but abandoned it again as far inferior to the one he subsequently adopted. By a strange misunderstanding, the name of Nonius is even at the present day often applied to the beautiful and practical invention of Vernier (1631), with which it has nothing whatever in common. A step towards the idea of Vernier was made by Christopher Clavius and the Vice-Chancellor Curtius, and the latter communicated this plan to Tycho in 1590, but it was not much more practical than that of Nunez, and was probably never carried out in practice.

We have seen that Tycho Brahe in his youth followed the example of the Arabians by constructing a large quadrant at Augsburg, with a radius of 19 feet. But already