For that browser to be able to preview the PDF document, you need to be using the compatible browser, the browser which supports previewing the PDF documents, either by a thir-party plugin or right out of the box; built-in support.
If the browser doesn't support a file, instead of opening it... It will download and save the file on the machine for the user to preview (open) it using any of the software application installed on their machine.
To preview PDFs, you need to be reading the PDF yourself; using a library. And then streaming those bytes down to the client and rendering them as HTML content. There are quite multiple libraries which allow you to convert the PDF data to HTML data. Read the following threads.
http://stackoverflow.com/questions/2295555/how-to-convert-pdf-into-html-using-c-sharp[
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PDF to HTML conversion in asp.net(c#)[
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http://forums.asp.net/t/1417395.aspx?convert+pdf+to+html+in+c+[
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