How do navigators use the stars, including our sun, the moon, and planets to find their way? Well, for at least two millennia, navigators have known how to determine their latitude — their position north or south of the equator. At the North Pole, which is 90 degrees latitude, Polaris (the North Star) is directly overhead at an altitude of 90 degrees. At the equator, which is zero degrees latitude, Polaris is on the horizon with zero degrees altitude. Between the equator and the North Pole, the angle of Polaris above the horizon is a direct measure of terrestrial latitude. If we were to go outside tonight and look in the northern sky, we would find Polaris at about 40 degrees 13 minutes altitude – the latitude of Coimbra.
In ancient times, the navigator who was planning to sail out of sight of land would simply measure the altitude of Polaris as he left homeport, in today’s terms measuring the latitude of home port. To return after a long voyage, he needed only to sail north or south, as appropriate, to bring Polaris to the altitude of home port, then turn left or right as as appropriate and “sail down the latitude,” keeping Polaris at a constant angle.
The Arabs knew all about this technique. In early days, they used one or two fingers width, a thumb and little finger on an outstretched arm or an arrow held at arms length to sight the horizon at the lower end and Polaris at the upper.
The critical development was made independently and almost simultaneously by John Hadley in England and by Thomas Godfrey, a Philadelphia glazier, about 1731. The fundamental idea is to use of two mirrors to make a doubly reflecting instrument—the forerunner of the modern sextant.

How does such an instrument work? How many of you have ever held a sextant in your hand? Hold the instrument vertically and point it toward the celestial body. Sight the horizon through an unsilvered portion of the horizon mirror. Adjust the index arm until the image of the sun or star, which has been reflected first by the index mirror and second by the silvered portion of the horizon mirror, appears to rest on the horizon. The altitude of the heavenly body can be read from the scale on the arc of the instrument’s frame.
Hadley’s first doubly reflecting octants were made from solid sheets of brass. They were heavy and had a lot of wind resistance. Lighter wooden instruments that could be made larger, with scales easier to divide accurately and with less wind resistance quickly replaced them.

Hadley’ octant of 1731 was a major advancement over all previous designs and is still the basic design of the modern sextant. It was truly a “point and shoot” device. The observer looked at one place – the straight line of the horizon sighted through the horizon glass alongside the reflected image of the star. The sight was easy to align because the horizon and the star seemed to move together as the ship pitched and rolled.
We have seen how navigators could find their latitude for many centuries but ships, crews and valuable cargo were lost in shipwrecks because it was impossible to determine longitude. Throughout the seventeenth century and well into the eighteenth century, there was an ongoing press to develop techniques for determining longitude. The missing element was a way to measure time accurately. The clock makers were busy inventing ingenious mechanical devices while the astronomers were promoting a celestial method called “lunar distances”. Think of the moon as the hand of a clock moving across a clock face represented by the other celestial bodies. Early in the 18th century, the astronomers had developed a method for predicting the angular distance between the moon and the sun, the planets or selected stars. Using this technique, the navigator at sea could measure the angle between the moon and a celestial body, calculate the time at which the moon and the celestial body would be precisely at that angular distance and then compare the ship’s chronometer to the time back at the national observatory. Knowing the correct time, the navigator could now determine longitude. When the sun passes through the meridian here at Coimbra, the local solar time is 1200 noon and at that instant it is 1233 PM Greenwich Mean Time. Remembering that 15 degrees of longitude is equivalent to one hour of time gives us the longitude of 8 degrees, 15 minutes West of Greenwich. The lunar distance method of telling time was still being used into the early 1900’s when it was replaced by time by radio telegraph.
An octant measures angles up to 90 degrees and is ideally suited for observations of celestial bodies above the horizon. But greater angle range is needed for lunar distance observations. It was a simple matter to enlarge Hadley’s octant, an eighth of a circle, to the sextant, a sixth of a circle, that could measure up to 120 degrees.
In the first half of the eighteenth century there was a trend back to wooden frame octants and sextants to produce lighter instruments compared to those made of brass.

Probably the finest 18th century instrument maker was the Englishman Jesse Ramsden. His specialty was accurate scale division. Here’s a small brass sextant that Ramsden made shortly before his death in 1800. Ramsden’s major achievement was to invent a highly accurate “dividing engine”—the apparatus used to divide the scale into degrees and fractions of degrees. His design was considered so ingenious that the British Board of Longitude awarded Ramsden a prize of 615 pounds—in 18th century terms, a small fortune. His “dividing engine” now resides in the Smithsonian Institution in Washington.
The development of more precise scale division was a milestone in instrument development. Certainly, it permitted more accurate observations but it also permitted smaller, lighter, more easily handled instruments.

Source(s);

http://www.mat.uc.pt/~helios/Mestre/Novemb00/H61iflan.htm