Over a period of time, I've found links to many electronic resources about early slide rules. I'm putting them here because finding the best keywords to search with can be quite time-consuming if you happen to be interested. The way I'm going to approach this is to see if I can't include a link to an electronic source with some commentary.
Cajori, Florian
Cajori was a well-known historian of math who among his wide variety of interests, devoted attention to early slide rules
I have a hard copy of a book published by Astragal Press, with the introduction of Oughtred Society's Bob Otnes. It contains "A history of the logarithmic slide rule and Allied Instruments", along with his "History of Gunter's scale and the slide rule in the seventeenth century".
The first book "history of the logarithmic slide rule" can be found in the international slide rule museum
The second book "History of Gunter's scale" is available on gutenberg.org in scanned text form.
Many of Cajori's other works can be found on archive.org.
I've located two papers of interest to Oughtred's Circles of Proportions:
Bryden, D.J, Scotland's Earliest Surviving Calculating Device: Robert Davenport's Circles of Proportion of c. 1650
I have read this excellent paper a few times, as it pertains to the instrument I selected for my replica scales.
The paper is available from JSTOR. JSTOR is a fee-based service, and you'd have to pay for a subscription to download it. At the time I'm writing this, you can sign up for free access that allows you to read up to 100 articles per month.
Turner, A.J, William Oughtred, Richard Delamain, and the Horizontal Instrument in Seventeenth-Century England.
This paper is super interesting. It does touch on the Oughted/Delamain debate but is more about instrument making and the horizontal instrument.
Fred Sawyer, John Schilke, and Nicola Severino, Andreas Schoner's Stereographic Sundial Design. This article (Compendium vol. 16, number 4, December 2009) identifies instances of the use of a stereographic projection in a sundial long before Oughtred,
Schoner, Andreas
Archive.org has a work by Schoner, Gnomonice (1562), which shows a clear representation of the stereographic projection featured in Oughtred's horizontal dial (page 186 in the PDF file). They cite a couple of earlier examples as well.
Oughtred, William
A downloadable facsimile of Oughtred's original Circles of Proportion can be found here on Google Books. I'm grateful to whoever scanned them as the copy is very clean. This is actually a compendium of a few related books, including the original 'Circles of Proportion', Oughtred's 'Juste Apology' where he defends his priority for the invention against Richard Delamain, and a tract on navigation that includes a revision to the Circles of Proportion, and a description of a linear slide rule.
You can also find an OCR version of the text on Early English Books Online. I've been finding it useful to have both in hand. The EEBO OCR algorithm is pretty good at figuring out what the text is, in cases where the original scanned document is hard to read whereas the scanned document has all the figures, which don't feature in the OCR text..
That said, the Google Book copy is actually quite clean. The scanned images of the text are important as that is where diagrams and equations might be visible.
Richard Delamain's Grammalogea is likewise available on Early English Books Online. I'm not certain which of the 4 versions of the book are available on EEBO.
On Archive.org, you can find Edmund Gunter's book: The works of Edmund Gunter: containing the description and use of the sector, cross-staff, bow, quadrant, and other instruments.
Also from Archive.org and/or google books.
Richard Delamain's: The making description and principal uses of a small portable instrument....called a Horizontal Quadrant
The features an invention that I gather is one of the items that Delamain and Oughtred were arguing about priority. It's kind of a folded version of the Horizontal Instrument. Delamain claimed he was inspired by something Edmund Gunter wrote, probably in the work by Gunter cited above.
Coggeshal's sliding rule [manuscript]: the description and use of the sliding rule
Measuring made easy or the description of the Coggeshall sliding rule, 1744 (Good) and
The Art of Practical Measuring by the Sliding Rule, 1785 (Ham)
I'll have to spend some time with these, currently, I suppose them all to be a composition of a pamphlet by Coggeshall with each edition/author contributing additional information. One other book I've found may have been written by Coggeshall, or if not he contributed a preface.
Thomas Everard Stereometry: Or, The Art of Gauging Made Easie, by the Help of the Sliding-rule , 1721
This is the eighth edition of a book that dates back to ca. 1685.
Nicolas Bion: The construction and principal uses of mathematical instruments ca 1758
This is probably the best resource on scientific instrument making from the 18th century. Since it is the English version, this should be the translation by Edmond Stone, ca. 1758.