Page:The Analyst; or, a Discourse Addressed to an Infidel Mathematician.djvu/54

44 the equal Quantities qo and o being detroyed by contrary Signs.

XXVII. As on the one hand it were aburd to get rid of o by aying, let me contradict my elf: Let me ubvert my own Hypotheis: Let me take it for granted that there is no Increment, at the ame time that I retain a Quantity, which I could never have got at but by auming an Increment: So on the other hand it would be equally wrong to imagine, that in a geometrical Demontration we may be allowed to admit any Error, though ever o mall, or that it is poible, in the nature of Things, an accurate Concluion hould be derived from inaccurate Principles. Therefore o cannot be thrown out as an Infiniteimal, or upon the Principle that Infiniteimals may be afely neglected. But only becaue it is detroyed by an equal Quantity with a negative Sign, whence o - qo is equal to nothing. And as it is illegitimate to reduce an Equation, by ubducting from one Side a Quantity when it is not to be detroyed, or when an equal Quantity is not ubducted from the