the equal Quantities qo and o being deſtroyed by contrary Signs.
XXVII. As on the one hand it were abſurd to get rid of o by ſaying, let me contradict my ſelf: Let me ſubvert my own Hypotheſis: Let me take it for granted that there is no Increment, at the ſame time that I retain a Quantity, which I could never have got at but by aſſuming an Increment: So on the other hand it would be equally wrong to imagine, that in a geometrical Demonſtration we may be allowed to admit any Error, though ever ſo ſmall, or that it is poſſible, in the nature of Things, an accurate Concluſion ſhould be derived from inaccurate Principles. Therefore o cannot be thrown out as an Infiniteſimal, or upon the Principle that Infiniteſimals may be ſafely neglected. But only becauſe it is deſtroyed 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 ſubducting from one Side a Quantity when it is not to be deſtroyed, or when an equal Quantity is not ſubducted from
