No. A single SSL certificate covers every page within your domain. If your SSL certificate is issued for www.mydomain.com, then your SSL certificate will work for https://www.mydomain.com/index.html; https://www.mydomain.com/support/about_us.html and so on.
However, if you want to secure subdomains (e.g. something.mydomain.com, jobs.mydomain.com), then you may need to purchase a wildcard certificate instead.