The greatest development took place after the introduction of artillery in the methods and instruments used for trigonometrical surveying or range-finding. Every principle which is to-day known and applied in the construction and use of modern trigonometrical surveying instruments can be traced in a modified form to the construction and application of the instruments of the sixteenth and seventeenth centuries.
In the practice of artillery, the first important question is the distance or range of the enemy. As in war it was clearly impossible to obtain the same by direct linear measurement, instruments were devised for measuring the range trigonometrically, all based on the calculation of a single triangle, the base and two angles of which could be measured. These instruments were simply modified to the extent of furnishing in the instrument itself a constant base or angle so that only one or at most two measurements were necessary.
The one instrument that has received the greatest development in the modern type is the quadrant, a simple graduated arc from whose center was suspended a plumb-line, or which carried a movable arm with raised sights for measuring horizontal or inclined angles. This arm has retained the name alhidada derived from the Arabic.
Such was the trigonometrical instrument used by the earliest navigators and astronomers for determining latitudes, and by surveyors and artillerists for finding ranges.
In the latter part of the 16th century Thomas Digges, surveyor and author, conceived the idea of combining two such graduated arcs in one instrument, the one placed horizontally and the other in a vertical plane, the whole supported on a rigid stand or tripod, and he called the same his Theodolitus, which is said by DeMorgan to have been the origin of the name of the modern instrument.
In the earliest books in the practice of artillery and of surveying, the crescent of the dreaded Moor appears in the woodcuts illustrating range finding or trigonometrical surveying generally floating over the tower of some captured castle or town, which it is desired to bombard. This clearly demonstrated that the chief use of trigonometrical instruments was for military purposes.
Among the instruments of surveying of this period which became practically obsolete in England in the present century, but which is most widely used elsewhere, is the plane-table, unquestionably one of the earliest instruments invented for measuring or recording angles.
At the period 1570, when the Germans claim that it was invented by Pretorius, a professor of the University of Nuremburg, it was unquestionably in use in England, and it is mentioned by Thomas Digges, in his Pantometria, published in 1590, as a platting instrument for such as are ignorant of arithmetical calculations. On the relative merits of the theodolite and plane table authorities still differ.
Throughout Europe great activity in the development of the practical applications of geometry soon followed the exchange of ideas brought about by the introduction of printing.
Side by side with the important geographical discoveries of the age came the minor improvements in scientific instruments which rendered national surveys and geodetic operations possible at a later period.