Baldassare Lanci's surveying instrument may be operated as a theodolite, a geometric square, or a perspective machine. For the first two applications, the surveyor employs its compass, scale of degrees, and shadow square. The sliding bar supporting the two folding arms is shifted to the right in order to position the right arm in the center of the instrument, where it functions as an alidade for measuring the horizontal angles.

Topographic surveying

A topographic survey can be made by triangulating from two stations where the distance between them is known. Let us consider the surveying of the course of a river from a hilltop. The instrument is positioned at the first station, and its sliding bar aligned with the second. We know that the distance between these two station points will be proportional to the distance between the two folding arms on the sliding bar. The surveyor, standing at the first station, sights a point on the river's bank through the sighting device on the arm at the left end of the sliding bar. This arm is blocked before moving the instrument to the second station. From this new station, the surveyor aligns the sliding bar with the first station, and sights the same point on the bank through the sighting device on the right arm. The triangle formed by the arms and the sliding bar will be proportional to the imaginary triangle whose base is the distance between the two stations, and whose vertex is the point on the bank. The surveyor thus obtains a direct representation in scale of the landscape's topographic features. The distance of this point from the station may be measured on the basis of the two similar triangles formed. All other significant points may be measured from the two stations. If a drawing sheet is placed on the disk, the surveyor may draw the position of each feature, thus visualizing the triangulations, determine the distances between positions and, finally, sketch a rudimentary, but nonetheless precise, topographic map.

Measuring the height of a tower

The instrument also serves to measure the heights of buildings and mountains. Let us take the case of a tower. The disk is set in an upright position so that the sliding bar is parallel to the ground line. The distance of the instrument from the tower is known. The surveyor, looking through the sighting device of the right arm, aligns it with the top of the tower. The left arm is fixed in an upright position, parallel to the tower. The triangle formed by the arms and the sliding bar will be proportional to that formed by the tower and the distance of observation. Given the resulting similar triangles, the surveyor may estimate the height of the tower on the basis of a simple proportional ratio, where the unknown measurement is proportional to the segment bc on the vertical arm. The height of the instrument must be added to the resulting measurement.

Perspective drawing

The perspective operation of the instrument was principally conceived for military purposes, whereby the surveyor's perspective drawing of the likes of a fortress was used to render the building's plan. For this operation, the instrument was originally equipped with two other accessories: a curved panel with a drawing sheet, and a sighting device with an ocular tube and a metal stylus. The ocular tube and the stylus are parallel to one another and can be moved in any direction. Looking at the fortress through the ocular tube, the surveyor traces its outline point by point with the stylus onto the drawing sheet. The points marked on the paper may then be joined to reveal a perspective drawing of the fortress.

In order to obtain the plan of the fortress, the surveyor must project the perspective drawing by rotating the projecting rays onto the horizontal plane. For this operation, the drawing is laid flat beside a circle representing the instrument's disk in plan. The surveyor draws a vertical line from point A of the perspective drawing, and marks its distance from the central axis on the edge of the circle. Through this point, he then draws a line from the centre of the circle and a line tangent to the circle resulting from the rotation of the vertical line traced on the perspective drawing. The height of point A is marked on the tangent. The projecting ray derived from the rotation of the point of view passes through this new point. The intersection between the projecting ray and the straight line passing through the centre of the circle determines the position of point A on the plan. The operation must be repeated for each point of the perspective drawing in order to obtain a series of points that, once joined, will outline the plan of the fortress.