Collection of early modern swords (17th to 18th centuries) at the George F. Harding Collection of Arms and Armor, The Art Institute of Chicago (artic.edu/aic). From the left: five rapiers, two broadswords (a claymore(?) and a schiavona), another rapier (with cup-hilt), and a parrying dagger (main-gauche). Visible on the right edge: the balde of another rapier, and part of another parrying dagger. Visible at the bottom edge: part of two elaborate decorative short swords, probably from Mughal India[1].

Original description from flickr.com (the item marked "1" is the cup-hilted rapier on the right (8th from the left), "2" is the schiavona on the right (7th from the left)):

Rapiers

Or are those sabers? I'm terrible at this.

1: Blade: Italian Hilt: Spanish Cup-hilted rapier in the Spanish manner 1650/60 Steel, iron, wood Length: 50 in. Blade length: 42 3/4 in. Weight: 2 lbs. 11 oz. Item number: George F. Harding Collection, 1982.2147

2: Hilt by Master VG Italian, Venice, active 1790/1800 Schiavona, 1790/1800 Steel, silver, wood, stone Overall length: 42 3/8 in. Blade length: 36 1/2 in. Weight: 2 lbs. 14 oz. Item number: George F. Harding Collection, 1982.2144