Pantometria — A Geometrical Treatize of Measuring (1591) - Page 14

Example.

A geometric diagram showing a horizontal line BC, a vertical line AD on the left, and a vertical line CF on the right. A diagonal line AE is drawn. Within the diagram, the word "Paralleles." is printed between two horizontal lines.

Admit A is the assigned point, BC the line, and AD the perpendicular dropped from A. If CF is the perpendicular created from C, I open my compass to the width of AD, set one foot in C, and mark point E on CF. Then, applying my ruler, I draw the line AE, which is a parallel to BC.

The 4th Chapter.

To divide any limited straight line into as many equal parts as you wish.

Because the division of lines into many equal parts is required for making plots and measuring ground by instrument, I thought it good to give instruction thereof before I treat of those matters. Upon either end or limit of the divisible line, create a perpendicular—one upward and the other downward. Opening your compass at random, measure out as many parts on either perpendicular as you would make divisions in your line. By drawing straight lines from the points on one perpendicular to the points on the other (beginning from the first of the one to the last of the other), you shall divide the given line into as many equal parts as there are divisions in your perpendiculars.

Example.

Admit line AB, which I would divide into seven equal portions. I create perpendiculars AC and BD upon A and B, as you may behold in the figure. Opening my compass at random, I measure out seven parts, ending at E and F. Then, by drawing lines from the divisions in one to the other (beginning from the last in one perpendicular to the first in the other), as you may behold in the figure, the line AB is parted into seven equal portions. In this manner, you may proceed infinitely to divide it into as many portions as you list.

A diagram showing a horizontal line AB being divided into seven equal segments. This is achieved by drawing two perpendicular lines (AC going up and BD going down) and connecting points on these perpendiculars with parallel slanted lines that intersect AB.