Now I Will Have Less Distraction.

To Those Who Ask What The Infinitely Small Quantity In Mathematics Is, We Answer That It Is Actually Zero. Hence There Are Not So Many Mysteries Hidden In This Concept As They Are Usually Believed To Be.

In The Meantime, Most Noble Sir, You Have Assigned This Question To The Geometry Of Position, But I Am Ignorant As To What This New Discipline Involves, And As To Which Types Of Problem Leibniz And Wolff Expected To See Expressed In This Way.

Although To Penetrate Into The Intimate Mysteries Of Nature And Thence To Learn The True Causes Of Phenomena Is Not Allowed To Us, Nevertheless It Can Happen That A Certain Fictive Hypothesis May Suffice For Explaining Many Phenomena.

The Kind Of Knowledge Which Is Supported Only By Observations And Is Not Yet Proved Must Be Carefully Distinguished From The Truth; It Is Gained By Induction, As We Usually Say. Yet We Have Seen Cases In Which Mere Induction Led To Error. Therefore, We Should Take Great Care Not To Accept As True Such Properties Of The Numbers Which We Have Discovered By Observation And Which Are Supported By Induction Alone. Indeed, We Should Use Such A Discovery As An Opportunity To Investigate More Exactly The Properties Discovered And To Prove Or Disprove Them; In Both Cases We May Learn Something Useful.

If A Nonnegative Quantity Was So Small That It Is Smaller Than Any Given One, Then It Certainly Could Not Be Anything But Zero. To Those Who Ask What The Infinitely Small Quantity In Mathematics Is, We Answer That It Is Actually Zero. Hence There Are Not So Many Mysteries Hidden In This Concept As They Are Usually Believed To Be. These Supposed Mysteries Have Rendered The Calculus Of The Infinitely Small Quite Suspect To Many People. Those Doubts That Remain We Shall Thoroughly Remove In The Following Pages, Where We Shall Explain This Calculus.