partial.js

function partial(fn) { // `fn` is the original function
    // `args_a` are the arguments (barring `fn`) of the first call.
    var args_a = Array.prototype.slice.call(arguments, 1);

    // Now, we return a new function, with the first set of arguments already applied.
    return function partialApplicator() {
        // `args_b` are the arguments applied at the second call
        var args_b = Array.prototype.slice.call(arguments);

        // Now, concatenate both Arrays and apply them to the original function
        return fn.apply(undefined, args_a.concat(args_b));
    };
}

simple.js

function simpleAddition(a, b) {
    return a + b;
}

var add20to = partial(simpleAddition, 20);

add20to(100); // -> 120
add20to(230); // -> 250