I'm currently working through selected portions of Newton's Principia, but I'm already stuck in trying to understand his explanation for the first corollary (i.e., Corollary I) to the laws of motion. Here's a link for quick reference: https://en.wikisource.org/wiki/The_Mathematical_Principles_of_Natural_Philosophy_(1846)/Axioms,_or_Laws_of_Motion
While I believe I understand the corollary as a whole, I'm primarily baffled by his last sentence in his explanation, namely, "...Therefore it will be found in the point D, where both lines meet. But it will move in a right line from A to D, by Law I."
As many of you might recognize, Law I states the law of inertia: "Every body preserves in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed thereon." In other words, objects experiencing no external forces either remain at rest or continue their motion in a straight line.
With Corollary I considering motion for a body under two simultaneous forces while Law I considers motion in absence of forces, I don't see how Law I is even relevant for drawing that conclusion in that last sentence. Maybe one of you might know?
On a further note, in the Scholium following the corollaries, Newton credits Galileo for the first two Laws and the first two Corollaries; however, I'm unable to find anything direct from Galileo regarding the first corollary.