Downcasting base-class objects to a derived-class

In my AP Comp. class, we wrote a Symbolic Algebra program in Java that
is completely based on one interface: IExpression.
I want to port my Java code to C++, for experience, and I'm having a
few issues.

C++ doesn't (to my knowledge) have an equivalent of an Interface, so
I;

class IExpression {
public:
        IExpression() {};
        virtual bool hasVar() ;
        virtual double eval(double);
        virtual string getStr();
        virtual string getSmart();
        virtual bool equals(IExpression&);
        virtual IExpression simplify();
        virtual IExpression derivative();
};

Once the "interface" or base-class was done, I wanted to implement it
with a simple class from my project: Number;

class Number : public virtual IExpression {
    private:
        double value;
        void init();
    public:
        Number(double);
        bool equals(Number &that);

        bool hasVar();
        double eval(double);
        string getStr();
        string getSmart();
        bool equals(IExpression&);
        IExpression simplify();
        IExpression derivative();
};

I wrote the implementation of Number's methods in the header, and I
wont bother posting (most of) them.
The one that's giving me hell is;

bool Number::equals(IExpression &that) {
    if (typeid(this) == typeid(that)) {
        return this->equals(reinterpret_cast<Number&> (that));
    } else {
        return false;
    }
}

bool Number::equals(Number &that) {
    return this->value == that.value;
}

C++ has given me arcane error messages, and I don't know what I'm
doing that's so horribly incorrect.
I think it's a down-casting problem in equals(), but it's also telling
me that I have an "undefined reference to vtable".

How can I fix this?