Explosive Based Weapons
  
The modern history of weapons begins with cannons, introduced to the history of Europe at the battle of Crecy during the hundred years war.   Both Newton and Galileo lived in an age of rapid improvements in cannons, and were probably affected by the technology.  Galileo used perfectly round metal balls for timing of acceleration.  Newton used the metaphor of a very powerful cannon in his explanation of the Earth being orbited by a body under the influence of a large velocity and the power of gravity.  Newton also had a theory of projectile penetration into a medium which is in the Principia.  It stated that "that the distance a projectile will travel through a medium (air, water, etc.) stands in the same ratio to the length of the projectile as the density of the projectile's material to the density of the medium."   > Detail from Source >
   
Terminology
 Three of our modern terms have their origin in the artillery of the middle age.  A cannon was a weapon which was comparatively mobile, it moved with the maneuver forces.  It was loaded from the muzzle end and was bored out to a single diameter.  It was aimed at enemy soldiers or ships (firing line of sight).   They often fired a collection of scrap metal, rocks, chains etc to kill people or damage wooden ships.
  
A mortar was, and still is,  a weapon that solves the recoil problem by directing the recoil into the earth.  Early mortars could only be fired at a 45 degree angle.  They altered the powder charge to control range.  The mortar had to be reinvented in its modern form (an infantry weapon) during WWI by a British engineer named Stokes.  The War Office ignored him for 6 months.
  
Early howitzers could be fired at a wider choice of angles.  Both weapons were bored out  to two different diameters so that the very heavy cannon balls did not crush the gunpowder charge (possibly exploding it).  The section that held the charge was smaller in diameter.         >  See Diagram >
  
These weapons were difficult to move and traveled with the "siege train" when castles or walled cities had to be reduced.          
Two types of projectiles were known  in the armies of Europe by the 1500s.  A solid ball cast to be as round as possible is the ancestor of all shot, whereas a hollow projectile filled with explosive and a fuze is the ancestor of all shell.  

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