Distance to the Sun
Aristarchus argued that the Sun, Moon, and Earth form a near right triangle at the moment of first or last quarter moon. He estimated that the angle was 87°. Using correct geometry, but inaccurate observational data, Aristarchus concluded that the Sun was 20 times farther away than the Moon. The Sun is actually about 390 times farther away. He pointed out that the Moon and Sun have nearly equal apparent angular sizes and therefore their diameters must be in proportion to their distances from Earth. He thus concluded that the Sun was 20 times larger than the Moon. This is also incorrect, although logical.
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