"What Science can be more accurate than Geometry? What Science can afford Principles more evident, more certain, yea I will add, more simple than Geometrical Axioms, or exercises a more strictly accurate Logic in drawing its Conclusions? But Aristotle and ' affirm that Unity (they had more rightly said Numbers) the Principle of Arithmetic, is more simple than a Point which is the Principle of Geometry, or rather of Magnitude. Because a Point implies Position, but Unity does not. A Point, says Aristotle, and Unity are not to be divided, as Quantity: Unity requires no Position, a Point does. But this Comparison of a Point in Geometry with Unity in Arithmetic is of all the most unsufferable, and derives the worst Consequences upon Mathematical Learning. For Unity answers really to some Part of every Magnitude, but not to a Point: Thus if a Line be divided into six equal Parts, as the whole Line answers to the Number six, so every sixth Part answers to Unity, but not to a Point which is no Part of this Right Line. A Point is rightly termed Indivisible, not Unity. (For how ex. gr. can \frac{2}{6} + \frac{4}{6} equal Unity, if Unity be indivisible, and incomposed, and represent a Point) but rather only Unity is properly divisible, and Numbers arise from the Division of Unity. A Geometrical Point is much better compared to a Cypher or Arithmetical Nothing, which is really the Bound of every Number, coming between it and the Numbers next following, but not as a Part. A Cypher being added to or taken from a Number does neither encrease nor diminish it; from it is taken the Beginning of Computation, while itself is not computed; and it bears a manifest Relation to the principal Properties of a Geometrical Point. Nor is that altogether unexceptionable, which is said of Position; for a Point taken universally is not less indeterminate, and void of Position, than Unity taken the same Way: But Unity taken particularly implies a definite Position, and all other particular Circumstances, as well as a particular Point. Lastly, the Accuracy of Arithmetic and Geometry is so far from being different that it is altogether the same, drawn from the same Principles, and employed about the same Things. I might here annex many Observations and Consequences drawn from hence; but Not to be too tedious and prolix, I judge it will appear plain enough to every one who duly weighs what I have suggested, that, in reality, Number (at least that treated of by Mathematicians) differs nothing from continued Magnitude it self, nor seems to have any other Properties (Composition, Division, Proportion, and the like) than either from, or in respect to it, as it represents, or supplies its Place; nor consequently that it is any Species of Quantity distinct from Magnitude, or the Object of any Science but Geometry (which is conversant about Magnitude in general): In sum, that Number includes in it every Consideration pertaining to Geometry. Therefore the Element Writer (whatsoever Ramus can object, who taunts him with that Name) did not unadvisedly, in inserting Arithmetical Speculations among the Elements of Geometry, nay rather he did great Service to the Mathematics, and merited highly in not permitting these Sciences to be separated from one another, as if they were separate in Nature, but assigning to Arithmetic a suitable Place in Geometry."