It should always be understood that expensive apparatus is not necessary for such illustrative work. The telescope used on the transit is only three hundred years old, and the world got along very well with its trigonometry before that was invented. So a little ingenuity will enable any one to make from cheap protractors about as satisfactory instruments as the world used before 1600. In order that this may be the more fully appreciated, a few illustrations are here given, showing the old instruments and methods used in practical surveying before the eighteenth century. [Illustration: A QUADRANT OF THE SEVENTEENTH CENTURY] The illustration on page 236 shows a simple form of the quadrant, an instrument easily made by a pupil who may be interested in outdoor work. It was the common surveying instrument of the early days. A more elaborate example is seen in the illustration, on page 237, of a seventeenth-century brass specimen in the author's collection.[77] [Illustration: A QUADRANT OF THE SEVENTEENTH CENTURY Bartoli's "Del modo di misurare," Venice, 1689] Another type, easily made by pupils, is shown in the above illustration from Bartoli, 1689. Such instruments were usually made of wood, brass, or ivory.[78] Instruments for the running of lines perpendicular to other lines were formerly common, and are easily made. They suffice, as the following illustration shows, for surveying an ordinary field. [Illustration: SURVEYING INSTRUMENT OF THE EIGHTEENTH CENTURY N. Bion's "Traite de la construction ... des instrumens de mathematique," The Hague, 1723] [Illustration: THE QUADRANT USED FOR ALTITUDES Finaeus's "De re et praxi geometrica," Paris, 1556] The quadrant was practically used for all sorts of outdoor measuring. For example, the illustration from Finaeus, on this page, shows how it was used for altitudes, and the one reproduced on page 240 shows how it was used for measuring depths. A similar instrument from the work of Bettinus is given on page 241, the distance of a ship being found by constructing an isosceles triangle. A more elaborate form, with a pendulum attachment, is seen in the illustration from De Judaeis, which also appears on page 241. [Illustration: THE QUADRANT USED FOR DEPTHS Finaeus's "Protomathesis," Paris, 1532] [Illustration: A QUADRANT OF THE SIXTEENTH CENTURY De Judaeis's "De quadrante geometrico," Nuernberg, 1594] [Illustration: THE QUADRANT USED FOR DISTANCES Bettinus's "Apiaria universae philosophiae mathematicae," Bologna, 1645] The quadrant finally developed into the octant, as shown in the following illustration from Hoffmann, and this in turn developed into the sextant, which is now used by all navigators. [Illustration: THE OCTANT Hoffmann's "De Octantis," Jena, 1612]