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This same spot Galileo is referring to a specific large dark area on the Moon, likely the Mare Tranquillitatis or a similar basin is seen to be surrounded by certain darker boundaries before the second quadrature The "quadrature" refers to the Moon's first or last quarter phase, when it is 90 degrees from the Sun; these appear darker on the side turned away from the Sun, like the highest ridges of mountains, but where they face the Sun they stand out brighter. The opposite occurs in the cavities term: cavities (cavitates) - Galileo's word for what we now call lunar craters, of which the part turned away from the Sun appears bright, while the part situated toward the Sun is dark and shadowy. Then, as the luminous surface is diminished, as soon as almost the entire said spot is covered in darkness, the brighter ridges of the mountains prominently climb above the shadows. The following figures demonstrate this double appearance.
The following image from the original 1610 edition of Sidereus Nuncius shows the "terminator" line—the division between day and night on the Moon—revealing the rugged texture of the lunar landscape.