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I looked all over for a date and got everything from "early 1800s" to "late 1800s" but nothing exact, so I had to make an educated guess. The first cameras practical enough to take such a photo were developed around 1840 and the excavations began in 1867.
Imagine being so furious and pathetic to destroy the nose of a statue 3+ thousand years old.
Indeed. However, somehow one can understand his furor, without condoning the destruction, as the people were worshipping the Sphinx as a god.
As well, similar things still happen even today:
In 2001, we could see in TV as the Taliban were destroying the Buddha statues in Bamiyan, which were about 1500 years old or in 2015, as the barbarians of Daesh were demolishing the ruins in Palmyra, a remainders of a city almost 2000 years old. These rages happened despite nobody was actually worshipping the statues, just because they did exist.