Terwesten was born in
The Hague of parents of German origin. His father, Hans Jacob Terwesten or Zurwesten, was originally from
Augsburg while his mother Catharina came from Berlin. They had married in The Hague in 1648, where Hans Jacob worked as a goldsmith. The marriage produced ten children, of whom three sons and two daughters survived.
Augustinus was the oldest son. In his father's workshop Augustinus learned the art of engraving, goldsmithing and wax modelling. This was followed by two years of apprenticeship with the history painter
Nicolaes Willingh, who became court painter to the Great Elector in Berlin in 1667.
Ezaias, the middle son of the family, also worked temporarily in his father's workshop and settled later in Rome as a flower and fruit painter. He initially studied under his 21 years older brother Augustin. He further received training from
Willem Doudyns and
Daniel Mijtens the Younger. He also became professor at the Academy of Berlin. He returned to The Hague in 1710. He married that same year Thedora van Rheenen with whom he had five children. Two of them—Augustinus the Younger and Pieter—also became painters. His pupils were Herman Diederik Cuipers, Pieter van Cuyck (I),
Jan van Gool,
Johan Graham, Hendrik van Hulst, Jacob van Nachenius, Andries Storck, as well as his two sons Augustinus the Younger and Pieter. He was active in the drawing academy of The Hague throughout his professional life. He worked until old age. As late as 1751, at the age of 81, he was commissioned to decorate a courtroom and executed it. After two strokes he died in The Hague on 11 June 1757. ==Work==