Julia Quinn's 'The Duke and I' is a book you can definitely find for online reading without any downloads on several official platforms. The simplest route is through a public library's digital service, like Libby or OverDrive, if you have a membership; you can check it out as an ebook and read it right in your browser, no app or file needed. Some subscription services also offer browser-based reading—I know that Scribd (now Everand) often has it in its romance catalog, and you can read it online through their website once you're logged in.
For a completely free, no-sign-up-required option, you's less straightforward but still possible through publisher or author-sponsored samples. For instance, HarperCollins, the publisher, frequently provides extended excerpts of their popular titles directly on their website. You won't get the whole book this way, but you can often read a substantial chunk of the first few chapters legally, which is a great way to see if the writing style grabs you. I'd also recommend keeping an eye on platforms like Google Books Preview, which sometimes allows for a generous 'preview' length that you can read online.
Remember, reading via an official site's browser window means you're supporting the author and publisher in a small way, and you avoid the security risks that can come with some unofficial download hubs. The experience is usually seamless, with proper formatting and no pop-up ads disrupting your flow. My last read-through of a Julia Quinn novel was actually on my library's browser reader, and it felt just as comfortable as holding a physical copy, with the added convenience of picking up right where I left off on any device.