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A97051 Due correction for Mr Hobbes· Or Schoole discipline, for not saying his lessons right. In answer to his Six lessons, directed to the professors of mathematicks. / By the professor of geometry. Wallis, John, 1616-1703. 1656 (1656) Wing W576; Thomason E1577_1; ESTC R204165 114,934 142

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Due Correction FOR M R HOBBES OR Schoole Discipline for not saying his Lessons right In Answer To His Six Lessons directed to the Professors of Mathematicks By the Professor of GEOMETRY Hobs Leviathan part 1. chap. 5. pag. 21. Who is so stupid as both to mistake in Geometry and allso to persist in it when another detects his error to him OXFORD Printed by Leonard Lichfield Printer to the University for Tho Robinson 1656. TO THE Right Honourable HENRY Lord Marquesse of Dorchester Earle of Kingston Vicount Newark Lord Pierrepoint and Manvers c. MY LORD YOUR Honour may perhaps think it strange that a person so wholly a stranger as I should tender you such a peece as this Yet will I doubt not acquit me of rudenesse and incivility in so doing when you consider That the adverse party whom it takes to taske hath made his appeale hither and finding himselfe foiled in Latine hath here put in his English Bill for some reliefe And it is but reason that Bill and Answer be filed in the same Court He had the confidence to tender his book first to another honorable Person the Earle of Devonshire with this presumption That though things were not so fully demonstrated as to satisfie every Reader yet 't was good enough to satisfie his Lordship he did not doubt Which presumption of his was then the more tolerable because he then thought his demonst●a●io●s good But when he had been so fully convinced what weake stuffe it was that now the utmost of his hopes is for so I understand from his friends that though he be mistaken in the Mathematicks yet he hopes to prove himselfe an honest man which yet is more I suppose than by his principles he need to be To make the world believe that your Lordship doth approve of his Principles Method and Manners in those writing and that this is the only cause of the favours you have expressed towards him is so high an affront as had he not a great confidence of your Lorships Magnanimity to despise it or Clemency to pardon it he would not have offered to a person of so much honour and worth Since therefore he hath brought it before you as a controversy wherein he desires your Lordship to consider and judge whether he have said his six Lessons aright I shall not at all demurre to the jurisdiction of the court but as readily admit his Umpar as allow him the choise of his own Weapon and so tender your Lordship an English Answer to his English Appeale from my Latine Confutation of his treatise in Latine That when in the judgement of this own Umpar he sees himselfe foiled at his own weapons he may hereafter make choise of French or Dutch or some other Language which he may hope to be more favourable to him than Latine or English hath yet been He tells your Lordship what great feates he hath done in his book and your Lordship knows as well by this and my former answer how they have been defeated And then he reckons up certaine positions some of them absurd enough and would have you believe them to be our Principles at Oxford But doth not tell your Lordship where they are to be found in any writings of ours Now that your Lordship may not seek them there in vaine where they are not to be found I shall briefely shew where the rise of all these accusations lye in his own writings not in ours First He had taught us Cap. 13. § 16. Si ratio detur minoris ad majus rationesque aliquot addantur ipso aequales non multiplicari proprie sed submultiplicari dicitur itaque quando additur primae rationi altera ratio primae quantitatis ad tertiam ●emissis est rationis primae ad secundam That is in plaine English If there be any proportion assigned of a lesse quantity to a greater and to that proportion be added another proportion equall to it that proportion that doth result by this addition is not the double but the halfe of that assigned proportion Now because this is very absurd and I had told him so He would have your Lordship believe that it was I had said not he that Two equall proportions are not double to one of the same proportions Which is his first Charge Secondly He had sayd farther in the same place Cap. 13. § 16. Ratio 2 ad 1 vocatur dupla 3 ad 1 tripla c. and he saith true But then forgetting that these were his own words he would have it thought Less 5. p. 42. absurd to say that the proportion of two to one is double and asks is not every double proportion the double of some proportion And doth here intepret that phrase of his own the proportion of two to one is called double to be all one as to say That a proportion is double triple c. of a number but not of a proportion Which is his second charge Thirdly he had Cap. 8. § 13 14. without any necessity layd ●he whole stresse of Geometry upon this supposition That It is not possible for the same body to possesse at one time a greater at another time a lesser place For if this be possible the same body is by his definition at the same time equall to a bigger and to a lesse body than it selfe as I there shewed by a consequence so cleare that he cannot himselfe deny it Which he there first attempts to prove as simply as a man would wish but then presently flyes off againe and say● that a thing in it selfe so manifest needs no demonstration But sayd I without declaring my own opinion in the case which what it is he knowe● not An assertion of such huge consequence to his doctrine as this is and being as he well knows generally denyed whatever he or I think of it by all those who maintaine Condensation Rarification in a proper sense without either vacuum or the admission and extrusion of a forraigne body ought to be well proved by him that builds so much upon it and not be assumed gratis Now because of this it is that he tells you in his third charge That 't is one of our principles That the same body without adding to it or taking from it is sometimes greater and sometimes lesse So hainous a matter is it to require a proofe from him of what he doth affirme though of never so great consequence Fourthly He tells us Cap. 14. § 19. and 't is true enough that an Hyperbolick line and its Asymptote doe still come nearer and nearer till they approach to a distance lesse then any assignable quantity And consequently if infinitely produced must be supposed to meet or to have no distance at all and so the distance of that hyperbola so produced from a line parallel to the Asymptote to be the same with the distance of that Asymptote from the said parallell that i● equall to a given quantity And that this is a