Add spaces: ...Theidealofmathematicsshouldbetoerectacalculustofacilitatereasoninginconnectionwitheveryprovidenceofthought,orexternalexperience,inwhichthesuccessionofthoughts,orofeventscanbedefinitelyascertainedandpreciselystated.

Answer: ... The ideal of mathematics should be to erect a calculus to facilitate reasoning in connection with every providence of thought, or external experience, in which the succession of thoughts, or of events can be definitely ascertained and precisely stated.

Add spaces: HeavydutyFixedcasterfromWeldedsteelhousing,platefitting,VulcanizedPolyurethanetread,precisionballbearing,Wheel-100mm,300KG

Answer: Heavy duty Fixed caster from Welded steel housing, plate fitting, Vulcanized Polyurethane tread, precision ball bearing, Wheel- 100mm, 300KG

Add spaces: andtherehaveweseengiants--thesonsofAnakareofthegiants--andwewereinoursightasgrasshoppers,andsowewerealsointheirsight.

Answer:
and there have we seen giants -- the sons of Anak are of the giants -- and we were in our sight as grasshoppers, and so we were also in their sight.