Mathematical Instruments
Book I. Ch. II.

Of the Construction and Use of the Square.

A Square is an Instrument serving to raise Perpendiculars, and to know whether one Line be perpendicular to another.

Fig. D

It is made of two Rulers of Brass, or other Metal, joined Fig. D. in such manner as to make a right Angle with each other. There are some Squares, whole two Rulers, or Branches, are firmly fixed; and others that open and fruit by help of a Joint, that ought to be well fitted to hinder the Square from shaking; and that it may preserve it’s right Angle. To do which, there is adjusted in a small Gutter made at the Angle (which is 45 Degrees) of one of the Branches of the Square, three Knuckles proportionable in Length and Breadth, to the Length and Breadth of the Square. These Knuckles ought to be so far distant from each other, that they may exactly receive between them two other Knuckles, which are adjusted to the other Branch of the Square. The Knuckles being thus placed, are soldered to the Branches, and afterwards are united to one another by means of a Pin, which must exactly fill the Cavity of the Knuckles, that thereby the Motion of the Branches may be steady.

Note. There are some Squares to which a Thread and Plummet is hung, which serves for levelling; that is, to make horizontal Planes: also upon one of the Sides of the Square are sometimes sundry Lines and Scales placed; and upon the other, half a Foot divided into 6 Inches, every one of which is subdivided into 12 Lines: moreover, there are sometimes added to it other Country Measures compared with the Paris Foot.

Use I. To let fall from a given Point, a Perpendicular upon a given Line.

Fig. 45

Let the Line given be AB, and C the given Point, either in or without the Line.

Apply one of the Sides of the Square to the given Line, in such manner that the other Side touches the given Point; then draw the lane CD, which will be a Perpendicular. Note, If the Square be turned about, and that Side which before was applied to the Line, is made to pass thro’ the Point C, and, as before, another Line be drawn, as CD: by this means you may know whether the Square be true. For when it is true, the two Lines drawn thro’ the Point C, will make but one Line.

Use II. To know if one Line be perpendicular to another; that is, whether they make right Angles with each other.

Apply one of the Sides of the Square to one of the Lines, and see if the other Side exactly agrees with the other Line. All this is so extreme easy, there needs but a few words to explain it.

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