Question: Princess Frederica Dorothea "Louise" Philippine of Prussia, was a member of the House of Hohenzollern, and was a niece of which King of Prussia from 1740 until 1786, the longest reign of any Hohenzollern king?

William I, or in German Wilhelm I (full name: "William Frederick Louis of Hohenzollern", German: "Wilhelm Friedrich Ludwig von Hohenzollern" , 22 March 1797 – 9 March 1888), of the House of Hohenzollern was King of Prussia from 2 January 1861 and the first German Emperor from 1 January 1871 to his death, the first Head of State of a united Germany.  Under the leadership of William and his Minister President Otto von Bismarck, Prussia achieved the unification of Germany and the establishment of the German Empire.  Despite his long support of Otto von Bismarck as Minister President, William held strong reservations about some of Bismarck's more reactionary policies, including his anti-Catholicism and tough handling of subordinates.  Contrary to the domineering Bismarck, William was described as polite, gentlemanly and, while a staunch conservative, more open to certain classical liberal ideas than his grandson Wilhelm II. <SEP>  She was a niece of Frederick the Great, being the second daughter and third child of Prince Augustus Ferdinand of Prussia by his wife Margravine Elisabeth Louise of Brandenburg-Schwedt. Princess Frederica Dorothea "Louise" Philippine of Prussia (24 May 1770 - 7 December 1836) was a member of the House of Hohenzollern. <SEP>  His most significant accomplishments during his reign included his military victories, his reorganization of Prussian armies, his patronage of the arts and the Enlightenment in Prussia, and his final success against great odds in the Seven Years' War.  Frederick was the last titled King in Prussia and declared himself King of Prussia after achieving full sovereignty for all historical Prussian lands. Frederick II (German: "Friedrich" ; 24 January 171217 August 1786) was King of Prussia from 1740 until 1786, the longest reign of any Hohenzollern king.  Prussia had greatly increased its territories and became a leading military power in Europe under his rule.  He became known as Frederick the Great ("Friedrich der Große ") and was affectionately nicknamed "Der Alte Fritz " ("Old Fritz") by the Prussian and later by all German people. <SEP> The monarchs of Prussia were members of the House of Hohenzollern who were the hereditary rulers of the former German state of Prussia from its founding in 1525 as the Duchy of Prussia.  The Duchy had evolved out of the Teutonic Order, a Roman Catholic crusader state and theocracy located along the eastern coast of the Baltic Sea.  The Teutonic Knights were under the leadership of a Grand Master, the last of whom, Albert, converted to Protestantism and secularized the lands, which then became the Duchy of Prussia.  The Duchy was initially a vassal of the Kingdom of Poland, as a result of the terms of the Prussian Homage whereby Albert was granted the Duchy as part of the terms of peace following the Prussian War.  When the main line of Prussian Hohenzollerns died out in 1618, the Duchy passed to a different branch of the family, who also reigned as Electors of Brandenburg in the Holy Roman Empire.  While still nominally two different territories, Prussia under the suzerainty of Poland and Brandenburg under the suzerainty of the Holy Roman Empire, the two states are known together historiographically as Brandenburg-Prussia.  Following the Second Northern War, a series of treaties freed the Duchy of Prussia from any vassalage to any other state, making it a fully sovereign Duchy in its own right.  This complex situation (where the Hohenzollern ruler of the independent Duchy of Prussia was also a subject of the Holy Roman Emperor as Elector of Brandenburg) laid the eventual groundwork for the establishment of the Kingdom of Prussia in 1701.  For diplomatic reasons, the rulers of the state were known as the King in Prussia from 1701 to 1772; largely because they still owed fealty to the Emperor as Electors of Brandenburg, the "King in Prussia" title (as opposed to "King of Prussia") avoided offending the Emperor.  As the Prussian state grew through several wars and diplomatic moves throughout the 18th century, it became apparent that Prussia had become a Great Power that did not need to submit meekly to the Holy Roman Empire.  By 1772, the pretense was dropped, and the style "King of Prussia" was adopted.  Thus it remained until 1871, when in the aftermath of the Franco-Prussian War, the King of Prussia Wilhelm I was crowned German Emperor.  From that point forward, though the Kingdom of Prussia retained its status as a constituent state of the German Empire, all remaining Kings of Prussia also served as German Emperor, and that title took precedence.