Alexander Hamilton wrote in The Federalist #29:

"But though the scheme of disciplining the whole nation must be abandoned as mischievous or impracticable; yet it is a matter of the utmost importance that a well digested plan should as soon as possible be adopted for the proper establishment of the militia. The attention of the government ought particularly to be directed to the formation of a select corps of moderate size upon such principles as will really fit it for service in case of need. By thus circumscribing the plan it will be possible to have an excellent body of well trained militia ready to take the field whenever the defence of the State shall require it. This will not only lessen the call for military establishments; but if circumstances should at any time oblige the government to form an army of any magnitude, that army can never be formidable to the liberties of the people, while there is a large body of citizens little if at all inferior to them in discipline and the use of arms, who stand ready to defend their own rights and those of their fellow citizens. This appears to me the only substitute that can be devised for a standing army; the best possible security against it, if it should exist.” - https://founders.archives.gov/documents/Hamilton/01-04-02-0186

If he believed the people are to be "little if at all inferior to [a standing army] in discipline and the use of arms", it also stands to reason he believed they should have arms little if at all inferior to said army. This was one of our founding fathers' greatest fears - that the government should turn on the people.

Joseph Story, a Supreme Court Justice from 1811 - 1845 (while some of the founders yet lived) in "A Familiar Exposition of the Constitution" wrote of the Second Amendment:

"One of the ordinary modes, by which tyrants accomplish their purposes without resistance, is, by disarming the people, and making it an offence (sic) to keep arms, and by substituting a regular army in the stead of a resort to the militia....The militia is the natural defence (sic) of a free country against sudden foreign invasions, domestic insurrections, and domestic usurpations of power by rulers.... The right of the citizens to keep and bear arms had justly been considered, as the palladium of the liberties of a republic; since it offers a strong moral check against the usurpations and arbitrary powers of rulers; and it will generally, even if these are successful in the first instance, enable the people to resist and triumph over them."