Add spaces: ThistheoryallowedCavalieritofindsimplyandrapidlytheareaandvolumeofvariousgeometricfigures.

Answer: This theory allowed Cavalieri to find simply and rapidly the area and volume of various geometric figures.

Add spaces: HoltecAutomatichasmanyyearsofexperiencewithdesigningandprogrammingservotechnology.

Answer: Holtec Automatic has many years of experience with designing and programming servo technology.

Add spaces: TheVidenskabernesSocietyhadawardedhimtheirGoldMedalin1884beforehebecameamember,butin1888hewashonouredwithelectiontotheSociety.

Answer:
The Videnskabernes Society had awarded him their Gold Medal in 1884 before he became a member, but in 1888 he was honoured with election to the Society.