Ever since the Hellenistic period, instruments were built based on the principle of a rod (known as a style) casting a shadow on a quadrant. Such instruments, called sundials, combined two notions: first, the Sun as a time-keeper revolving around the immobile Earth in a uniform daily motion; second, the geometrical analysis of the projection of the style's shadow on surfaces inclined at different angles.

In the simplest sundial model, a vertical style is set in a horizontal quadrant. Three curves indicate the daily paths of the edge of the shadow on specific days of the year. The curve farthest from the style denotes the path at the winter solstice, when the Sun moves at the lowest altitude above the horizon. The intermediate curve shows the path at the spring equinox and fall equinox, when day and night are of equal length. The curve nearest the style marks the path at the summer solstice, when the Sun travels highest above the horizon.

A second series of lines divides the three curves into sections that, while uneven, are covered by the edge of the shadow in one hour each. On the morning of any given day, the shadow appears to tilt westward. For the first six hours of the day, the shadow steadily shortens, reaching its minimum length at midday. It then lengthens in the following six hours until disappearing eastward at sunset.

From a careful observation of the shadow cast on a sundial quadrant, we can therefore determine not only the time of day, but also the time of year.