Ok it still doesn't work. It must be something to do with my VS project.
I went into VS 2012 (Pro). File -> New -> Project. Picked "HTML Application with TypeScript" from the Visual C# category and gave it a name.
I then added the BaseCircle.ts file (via Add Existing) and just threw this into the app.ts file that it creates you by default (the one with the Greeter class in):
var test:BaseCircle = new BaseCircle(100,100,100);
I also made sure I had the reference path set and added the BaseCircle.js script tag to the default.html file.
Hit F5 and nothing but the compiler error "error code 1".
Comment out the test var line above and it compiles and runs just fine.
Have I missed something in the project set-up perhaps?