Aristarchus of Samos (ca 310 BC) in his book "On the Sizes and Distances of the Sun and Moon" tried to determine the relative distance between the Earth and the Sun by noting from simple geometry that the Earth-Moon-Sun formed a right triangle with the 90 degree angle's vertex at the position of the Moon when the moon was at quarter phase ( 1/2 of its disk illuminated by the Sun). This means that if you could measure the Moon-Earth-Sun angle, you could work out what the relative length of the hypotenuse of this triangle was between the Earth and the Sun, in terms of the length of the Earth-Moon distance. The problem is that this angle is very close to 90 degrees and in fact is about 89 degrees. Even a 1 degree error on such a skinny triangle creates a sizeable error. So how did Aristarchus measure this angle?
He attempted to measure the time interval between the first and third quarter Moons, and computed their difference which by the geometry of the situation would give you twice the angle of Moon-Earth-Sun. The problem is that although this works in principle, the Moon's orbit is not circular and the Moon does not travel at constant speed. These factors caused Aristotle to get a distance of 18 - 20 times the Earth-Moon distance as the distance to the Sun rather than (93 million/240,000) = 3900.