The English academy, or, A brief introduction to the seven liberal arts grammar, arithmetick, geometrie, musick, astronomie, rhetorick & logic : to which is added the necessary arts and mysteries of navigation, dyaling, surveying, mensuration, gauging & fortification, practically laid down in all their material points and particulars, highly approved to be known by the ingenious, and as such are desirous to profit, or render themselves accomplished : chiefly intended for the instruction of young scholars, who are acquainted with no other than their native language, but may also be very useful to other persons that have made some progress in the studies of the said arts / by John Newton.

Proposition I. Vpon a Right Line given, to erect a Perpen∣dicular, from any Point assigned.

Let it be required to erect a Perpendicu∣lar to the line DG, from the Point B, in Fig. 2. take two equidistant Points, as D and G, open your Compasses to a convenient distance, and setting one Foot of your Com∣passes in B, draw the Arch EC, and keep∣ing your Compasses at the same distance, set one Foot in G, and with the other draw the Arch HIF, and through the Intersections of these two Arches draw a right line, as BL, which shall be perpendicular to the Point B.

But if it were required to erect a Perpen∣dicular from the end of a line, do thus, your Compasses being opened to any convenient distance, set one Foot in the Point given, as at A, in the line AB, and the other at D, or where you please, and making D the Cen∣tre, draw the Arch CAE, and from the points C and D, draw the right line CDE, then draw the line AC, which shall be Per∣pendicular to the line AB, from the point A, as was required.