One of the problems posed by the Marquis de l Hospital in his calculus textbook Analyse des

Question:

One of the problems posed by the Marquis de l€™ Hospital in his calculus textbook Analyse des Infiniment Petits concerns a pulley that is attached to the ceiling of a room at a point C by a rope of length ℓ. At another point B on the ceiling, at a distance from c (where d > r), a rope of length θ is attached and passed through the pulley at F and connected to a weight ℓ. The weight is released and comes to rest at its equilibrium position ℓ. As l€™ Hospital argued, this happens when the distance | ED |is maximized. Show that when the system reaches equilibrium, the value of is