Only with compasses

Although recently it has been almost completely superseded by the computer, the drawing board was, for several centuries, one of the main work tools of the architect and of the project manager. On the drawing board, the difference in precision between ruler and compasses is still quite noticeable, since neither Peaucellier's mechanism, nor the even less accurate mechanisms of by Watt and his followers, could be used to draw.

Thence derives the problem of using the ruler as little as possible, or even of eliminating it completely, and to execute the drawing with just the compasses. Of course we are not speaking of the actual drawings, since no compass could ever trace a straight line, but to the construction preliminary to the drawing, when it's time, for example, to find two points through which a straight line must pass. In these constructions, the use of the ruler entails a much lower precision than that of the compasses.

t the end of the Eighteenth century, the problem of ruler-less constructions was solved by Lorenzo Mascheroni, who demonstrated that all the constructions that can be effected with ruler and compasses can also be effected with only the compass. In particular, Mascheroni applies his method to the division of circumference in equal parts, an essential operation in building astronomy apparatuses.

Later it was discovered that Mascheroni had been preceded by a Seventeenth century Danish mathematician, Georg Mohr, whose work, since it had no applications at the time, had remained virtually unknown.

n the computer, we can see some of the main geometric constructions, executed with the compass only.