By the beginning of the 18th century, life in the city of Edinburgh (today's Old Town) was overcrowded and unsanitary.
Edinburgh was overcrowded and dirty in the 18th century. 
mnli hypothesis: Edinburgh was overcrowded and dirty in the 18th century.  premise: By the beginning of the 18th century, life in the city of Edinburgh (today's Old Town) was overcrowded and unsanitary.