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SECT. II.
BEsides the manifest Allusion of Reason,* 1.1 we have the assent of all Phi∣losophers, who have declared their opinions concerning the Com∣position of a Continuum, to assure a necessity, that it must consist either (1) of Mathematical Points; or (2) of Parts and Mathematical points, uni∣ted; or (3) of a simple Entity, before actual division, indistinct; or (4) of Individuals, i. e. Atoms.
(1) Not of Mathematical Points; because 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉, Punctum,* 1.2 in the sense of Euclid, is Cujus nulla sit pars, in respect it wants all Dimensions, and consequently all Figure: which is the ground of Aristotles Axiom, Punctum puncto additum non potest facere majus. To render the absurdity of this opinion yet more conspicuous, let us remember, that the Authors and Defendants of it have divided themselves into three distinct Factions. (1) Some have admitted in a Continuum, points Finite simpliciter & deter∣minatè; (2) Others allow points also Finite, but not simpliciter, sed 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉 secundum quid; (3) And others contend for points Infinite, simpliciter▪ & absolutè. The First and Second endeavour to stagger the former Axiom of Aristotle, by an illegal transition from Quantity Continued, to Discrete, alledging this instance, that one Unity added to another makes a greater quantity. The Last recur to Plato's Authority, who concedeth two Infi∣nites, •• Greater and Less, commemorated by Aristotle (3. phys. 27.) Now, for a joint redargution of all, we demand, how they can divide a Line con∣sisting of 5 insectiles into two equal segments? For, either they must cast off the intermediate insectile, or annex it to one division: if the first, they split themselves upon that rock, our supposition; if the last, they clash with the 9. proposit. 1. lib. Euclid. To evade the force of this Dilemma, they have invented many subter••uges: but how unsuccessfully, may be enquired of Aristotle (in 6. physicor.) who there convicts them all of either Falsity, or Impossibility; where, having praemised an excellent enunciation of the Analogy between Motion, Time, and Place, He apodictically concludes, that, if a Continuum did consist of points Mathematical, all Motions would be equally swift. Not∣withstanding this, such was the contumacy of Arriaga, that in hopes to elude this insoluble Difficulty, He praetends to discover a new kind of Motion, distinguished by certain Respites, or Pau∣ses intercedent•• thereupon inferring that all things are moved, du∣ring their motion, with equal Celerity, but because the motion of one thing is intercepted with many pauses, and the motion of another with few, therefore doth the motion of this seem swift, and the mo∣tion of that slow; as if the degrees of Celerity and Tardity did re∣spond to the Frequency and Rarity of Respites interceding. If this be true, then must a Pismire move flower then an Eagle only be∣cause this dist••nguisheth its motion by shorter pauses, and that by longer: nor can a Faulcon overtake a Partridge, since our eyes as∣sure, that a P••rtridge strike•• six strooks at least with his wings▪ while its 〈◊〉〈◊〉 strikes one. Mar••gravius (in histor. Animal.