The eighth Figure represents a Quadrant made of Brass or any solid Matter, of a bigness at pleasure, having the Limb divided into 90 Degrees. The Use of this Quadrant may be to find the Lengths of Tangents, and by this means to divide a right Line into Degrees, as we did the Meridian of the horizontal Dial (Fig. 7.) we may find likewise thereon the Divisions of the Equinoctial Line thro’ which the Hour-Lines must pass, in regular Dials; as also in declining Dials, if the Substyle falls exactly upon a compleat Hour-Line, by laying off the Length of the Radius of the Equinoctial Circle, from the Center A to H or L, and drawing a right Line, as HI or LM, parallel to the Radius of the Quadrant AC. For example, the Length L1 or n, answering to 15 Deg. of the Quadrant, shall be the Tangent of the first Hour-Line’s distance from the Meridian or Substyle of the Dial, which being laid off upon the Equinoctial Line, whose Radius is supposed equal to AL, will determine a Point therein thro’ which the said Hour-Line must be drawn. L12, answering to 30 Deg. of the Limb of the Quadrant, will be the Tangent of the second Hour-Line's distance from the Meridian or Substyle. L3, the Tangent of 45 Deg. will be that of the third, and so on. Now if by this means you draw the Hour-Lines of three Hours successively on each side the Meridian or Substyle, which in all make six Hours successively; these are sufficient for finding the Hour Lines of the other Hours, according to the Method before explained in speaking of declining Dials, and which may be even applied to all regular Dials. For example, If the Hour-Lines of six Hours successive be drawn upon an horizontal Dial, as, from 9 in the Morning to 3 in the Afternoon, you may draw all the other Hour-Lines of the Dial by the aforesaid Method; as the Hour-Lines of 7 and 8 in the Morning, and 4 and 5 in the Afternoon, whose Points in the Equinoctial Line are sometimes troublesome to be pricked down, and principally the Points of the Hour-Lines of 5 and 7, because of the Lengths of their Tangents.
The Hour-Lines found by the abovesaid Method, which we shall not here repeat, will serve for finding of others; and these which are last found being produced beyond the Center, will give the opposite ones.
The said Quadrant will serve moreover as a portable Dial, since the Hour-Lines may be drawn upon it by means of a Table of the Sun’s Altitude above the Horizon of the Place for which the Dial is to be made. See more of this in the next Chapter.