Problem 2.

To erect a Perpendicular on any Point in a Right Line given.

Suppose upon the Point C on the Right Line A B.

Construction. First open your Compasses any Wideness, and fetting one Foot in the Point C, with the other make two Dashes at E and F; then opening your Compaffes any Distance greater than the former, set one Foot in E, and with the other describe the Arch bh; with the fame Extent, setting one Foot in F, with the other describe the Archgg interfecting the former at D. Lastly, through the Points Dand C draw the Line DC, and it will be the Perpendicular required.

This Probleın is not only useful to Mathematicians, but also almost to all Artificers, especially those who are obliged to make use of true Squares.

Problem 3.

To erect a Perpendicular on the End of a Right Line.

Let AB be the Line given; and let B be the Point on which the Perpendicular is to be erected.

Construction. First open your Compasses to any small Distance, and fetting one Foot in the Point B, describe the Arch bed. The Compasses remaining at the same Wideness, set one Foot in c, and describe the Arch fd; with the other in d, describe the Arch eg, intersecting the former in E. Lastly, from E draw the Line E B, which will be the Perpendicular required.

Surveying, Dialling, &c. cannot be carried on without the continual Ufe of this Problem.

Problem 4.

To let fall a Perpendicular upon a Right Line given from a Point at any Distance above it.

Let A Bbe the given Line; and let C be a Point above

it, from whence the Perpendicular is to fall.

Construction. First, with the Compasses opened fomething wider than the Distance which the Perpendicular is to fall, set one Foot in the Point C, and with the other defcribe the Arch EDF, interfecting the given Line at E and F. Then, from the Points E and F strike the cross Dafhes at G. Lastly, draw the Line CD, and it is the Perper.dicular required.

The greatest Part of the Practice of Mechanics confifts in the Knowledge of drawing (both upward and downward) Perpendicular Lines.

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Problem 5.

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To draw a Line parallel to another Line given, at any Distance proposed.

Let the Line given be A B, and the Distance of the Parallels equal to the Line E.

Construction. First, open your Compafles to the Length of the Line E, the Distance required. Set one Foot in the Point A, and describe an Arch on the Side you are to draw the Parallel on, as at C. Do the like from B to D. Lastly, by the Convexity of these two Arches draw the Line CD, which will be the Parallel required.

The Use of Parallel Lines is very great in Naviga

tion, and the Construction of fome Kinds of Dials.

Problem 6.

To protract, or lay down an Angle of any Number of Degrees.

Let the Angle to be protracted or delineated confift of 40 Degrees.

Construction. First, with any Radius, or Opening of the Compaffes upon the Point C, defcribe a Circle, which divide into 360 equal Parts, called Degrees; then from the Center C draw two Lines, one through the Beginning of the Degrees, and the other through 40, and it is done: Because all Angles are estimated or measured by the Number of Degrees contained in the Arch of the Circle intercepted between the Legs that form that Angle.

Note. If the Angle contains lefs than 90 Degrees, it is faid to be Acute. If exactly 90 Degrees, it is a Right Angle. If more than 90, it is Obtuje; and so continues to 180, at which Place the Angle vanishes; the Legs becoming a Right Line.