Understanding the Rigging
-or-
"What in the heck are all these ropes for?"
The first time ye comes aboard a ship, the vast number of lines may be overwhelmin'.  A crowded harbor can look like the winter home of colossal spiders.  However, there be order underlyin' this seamin' chaos, fer each line has a purpose. 

A sailing vessel be a complex machine, but once ye know the parts and see how they work together, ye can see the order and logic of the thing.

All lines on ship do one of two basic jobs - they keep the masts from fallin', or they control the sails.  The lines what support the masts be called
standing rigging.  Those what be put in motion to sail a vessel be called running rigging.
Ropes vs. Lines
All lines are made of rope.  A line is just a rope with a job.  The only place on a ship where you�ll find rope is in the forecastle where it be stored.
    An 18th century full-rigger, like the one shown here, typically has 70-80 lines of standin' riggin' and 110-120 lines of runnin' riggin'.  This need not be as dauntin' to larn as it seems, fer the way to eat an elephant be one bite at time.  So allow me to cut it down to bite-sized pieces. 

Firstly, instead of trying to figger out 14 sails at once, let us look at just one.  Since six of those sails be square sails, we will start there.
That be better, but 'tis still a mighty big bite.  So allow me to break it down further by function, starting with the standin' riggin'.
Standing Rigging
Ratlines - The lightweight lines, running horizontally across and secured to the shrouds, that seamen stand on to climb aloft.
Shrouds - The lines or cables, running aloft from the deck to points on the masts, used to support a mast from side to side (port to starboard).
Stays - Lines or cables used to support the masts fore-and-aft.  Backstays run from a mast to aft.  Forestays run from a mast to forward.
Now that we have a steady mast, let us begin the runnin' riggin' by riggin' a yard.
Brace - One of two lines per yard, one attached to each yardarm; these are used to pivot the yards around the mast.
Halyard - Evolved from "haul yard."  Line by means of which a sail, yard, gaff, flag, etc. is hoisted.
Lift -  A rope or tackle, going from the yardarms to the masthead, to support and move the yard.
Parral -  The rope by which a yard is confined to a mast at its center.
Now we can bend a sail to our yard, so let us discuss the lines what be used to tie-up the sail
Gaskets - The lines used to secure a furled sail to its yard.  Shown here coiled as they would be once the sail is unfurled.  When furlin' the sail the gaskets are uncoiled and spiraled around the sail and yardarm from outboard to the mast.
Reef-points - Short lengths of line passing through eyelets in a sail in one or two rows.  These be tied around the yard when high winds make shortenin' the sail adviseable.
Robands
-  Small pieces of line, used to hold the head of the sail to the yard or gaff.
Now we be ready fer the lines which trim and furl the sail.
Bowline - (Pronounced bo-lin.)  A rope leading forward from the leech of a square sail, to keep the leech well out when sailing close-hauled in order to keep the wind on the back of the sail.
Buntlines - The lines attached to the middle of the foot of the sail used to haul the bunt up to the center of the yard.
Clewlines - The lines  attached to the clews and used to haul those corners upward to the yard fer furlin'.  The clewlines should run behind the sail, but if'n I drew 'em that way ye'd not be able see what I be talkin' about.
Leechlines - The lines attached to the leech and used to haul that edge upward to the yard for furling.
Sheet - The line connected to the clew of a sail that hauls it out when set, either to the yard below it or (on a loose-footed sail) to a point aft on the deck.  On a loose-footed sail, the sheet on the windward side be slack and thus called the lazy sheet, while the sheet on the leeward side be taught and called the active sheet.
Tack - A line connected to the clew of a loose-footed sail that pulls it forward.  Properly trimmed, the tack on the leeward side be slack and thus called the lazy tack, while the tack on the windward side be taught and called the active tack.
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