Why was the Celsius scale initially inverted (0 degrees representing water's boiling point and 100 degrees representing its melting/freezing point)?
There are two reasons why the Celsius scale was originally inverted from our day by day Celsius scale (0 degree the boiling point of water at normal pressure and 100 degree the melting point of ice). The main reason is that in around 1740 when it was invented people used the thermometer to measure the temperature of the air outside or the temperature of the human body (not for doing scientific experiments). Thus, because the temperature of the boiling water is so high, usually in the day by day use only positive temperatures were reported by the original inverted scale. In other words, Celsius did not want to mix positive and negative temperatures in usual applications of his thermometer scale.
The second reason of having now an inverted Celsius scale is that at the time the Celsius scale was invented, the Kelvin scale did not exist. Only about 100 years later it was invented, by taking a more precise point for 273.16 degree Kelvin (0 degree Celsius) as being the triple point of the water (not of the ice that melts). Although only 10 years after the Celsius scale invention, some scientists began to use it upside down (reversed) , the reversed scale was adopted as a standard scale only after the Kelvin scale was invented. This was done because of the necessity that both scales show the same temperature only with a difference of 273.16 degrees Celsius.