Tom and Lu Wetmore
I appreciate the work you have done searching through the original documents. We both seem to have that need. I have copies of most of the sources and reread them every year or so, and then ponder once again what was happening in the 1620s and 30s. Not just Oughtred and Delamain, but Briggs and Gunter too. In my opinion Gunter is the unsung hero of the whole bunch. He was the true discoverer and father of the three main slide rule scales. Only his name has stood the test of four centuries and is still found today in Gunter's Rules. As for Oughted and Delamain you and I have opposite conclusions. I am in the Oughtred camp. But I don't feel there is enough evidence to justify a serious argument, or at least I don't want to engage in one.
Yes, Oughtred was the author of the Latin version of the "Circles of Proportion and Horizontal Instrument", with Forster the translator. Did you know that in Taylor's book about the mathematical practitioners of Tudor and Stuart England, he did list Oughtred as the author and Forster as translator?
I also believe that the dedication in that book is the earliest good written account that mentions a true linear slide rule. It refers to two rulers with Gunter's scales on them that are used together without compasses. It was written in 1632 based on an eyewitness account that happened in 1630 based on devices that Oughtred had made years earlier. For me it is the key source in understanding the invention of the linear slide rule.
You say we cannot fully understand what Oughtred's 1638 letter is about. Here I disagre. It is instructions to Allen about design details for the cross staff Allen is making. The only thing that brings that letter out of the ordinary and calls it to our attention is the fact that Oughtred wants Allen to put Gunter's three scales on the cross staff. It isn't clear whether Oughtred wanted only one set to be used with compasses, or two sets, one on each part, to be used as a slide rule.
I have read the two tirades that Oughted and Delamain wrote against one another. It is very nasty stuff, difficult to read, and frankly depressing. Delamain's tirade is pretty much all vitriol, while Oughtred's, though also very nasty, has lots of mathematical examples of Delamain's failings that back up his arguments. I score that battle for Oughtred.
Yesterday I wrote another email to post to this group, but held it back because I believe I can get pretty thick-headed and obtuse in the stuff I write. It contains a copy of the part of the Forster's dedication that mentions Oughtred's linear and circular slide rules. Since it is so germain to this discussion, I'll dust it off and send it a little later.