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A25363 Dary's miscellanies examined and some of his fundamental errors detected by authority of ancient and modern mathematicians ... : to which is added a task for Mr. Dary of his own setting / by Robert Anderson. Anderson, Robert, fl. 1668-1696. 1670 (1670) Wing A3102; ESTC R9335 6,859 16

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the fourth page our gunner hath more fire-works to wit his note for progressions is invalid and of no force For saith he there is no need of unity for the first terme of this progression My answer is that note for progression is of force and truth and unity of use thus the question it self requires whole numbers the seventh of the fifth of Dioph. finds whole numbers therefore greathan an unit therefore well limited The second part in defence of the Art of Practicall gaging and it begins in the fifth page and there he telleth his Reader how he hath been commended by divers artists in this City Here he appeals to men as ignorant as himself is vain glorious In the 6 pag. he flingeth dirt in the face of the printer thus in which I see there are many press-faults that is false they are the segment makers faults for the segments are the complement of one to the other to 100000 c. therefore no printers faults In the sixth and seventh pages he sheweth how to calculate a table of segments and here his understanding mends a little for he works pretty well since the last time I taught him so then as one mends in his Rules so I hope the other will mend in his calculation with that instruction I formerly gave him so we may expect a better table of segments some time or other In the 8. page he again dwindles and would fain insinuate into the affection of his Reader and make him believe that I did not know that there was a third c. differences in the table of segments to speak the truth that table of segments was calculated so falsly that the first differences did manifestly shew it further If Mr. Dary had known that way or any other way better to examine Tables by before he published those segments more shame to him to publish such false tables without examination In the 9 and 10. pa. the Gunner has fire and gun-powder viz. know ye not that the Table for wine ale and beer are capable but only of the first and second differences If so more shame to the Calculator that they have more diff and they so much confusedly put As for that Book entituled A guide to the young gager I knew not the man nor heard of the Book untill a great part of it was printed neither did I see one line of that part of it till it was publickly exposed to sale Thus have I passed through this fiery conflict and have not heard the bounce of one gun nor received any harme which makes me conclude our gunner and his crew are as bad marks men as they are segment makers for he promi●ed at the beginning of his preface to charge his guns and pepper me Thus have I considered him as a Gunner with his Crew now will I consider him as a Geometer with his famous Companions These famous men whose true descent doth run From aged Neptune and the glorious Sun AN EXAMINATION OF Dary's Miscellanies IN the first page of the Preface he saith Most whereof have lain by me many years If so I hope very true 1 In the second page of the Preface saith he For although the sides thereof be continued they would never be included or terminated in one point as the Pyramide is that is the sides of a Pyramide are included in one point which I deny thus a point hath no part by 1 def 1 Euclid A Superfices for such are the sides of a Pyramide have length and breadth 5 def 1 Euclid That which hath no part to include that which hath length and breadth is absurd that 's a lumping point for an able Anylist 2 In the fourteenth page saith he The 3 Angles of any Spherical Triangle being given there are likewise three sides of another Spherical Triangle given whose Angles are equal to the sides of the former Triangle Here the Gentlemen forgot to complement and I presume in the next they will forget all good manners Further the sum of the sides of any spherical triangle are less then two semi-circles Reg. 39 of 3. The sum of the three angles of any spherical triangle are greater then two right angles but less then six Reg. 49 of 3. therefore the Rule is false except the sum of the three sides be greater then two right angles but the Rule is set down general therefore a general error 3 In page 21. we have it thus If a sphere be by a plain touch'd and the eye be placed at the center of the sphere then a right line infinitely extended from the eye to any assigned point in the spherical surface shall project the assigned point upon the plain Here the Radius of the Sphere is taken to be infinite for saith he then a right line infinitely extended from the eye to any assigned point in the spherical surface but the plain is without the sphere therefore beyond infiniteness it self which is absurd however this proves them to be infinite Projectors 4 In page 29. at the 18th it is thus If a sphere be inclosed in a cylinder and that cylinder be cut with plains parallel to its base then the intercepted rings of the cylinder are equal to the intercepted surfaces of the respective segments of the sphere that is false For Hemisphaerii superficies aequalis est superficiei curvae cylindri eadem ipsi basim eadem altitudinem habentis saith Torricellius at the 18. Prop. de sphaera solidis sphaeralibus lib. prim and as the whole so the parts by the 19. Prop. of the same Here we have a combat betwixt Torricellius and our Geometers First they say the intercepted rings of the cylinder are equal to the intercepted surfaces of the respective segments of the sphere Torricellius proves that the intercepted superfices of the cylinder are equal to the intercepted superfices of the respective segments of the sphere 2. These Geometers say if a sphere be inclosed in a cylinder here we may make the Diameters of the base of the cylinder of any magnitude greater then the diameter of the sphere and yet the sphere be inclosed Torricellius proves that the cylinder and hemisphere must have the same base 3. These Geometers regard it not whether the sphere and cylinder are upright or inclining Torricellius by construction makes them upright Thus do these Geometers make solid superfices for a ring is solid 5 In page 33. they set down a rule for the sphere and conclude it will hold in the spheroid this rule will also hold if it were the Frustum of a Spheroid putting d●d equal to the fact of the right angled conjugates in the base That is false by 21 of 1 of Apollonius and 31 and 33 of Archimedes of conoid and spheroid for the diameter of the base one way or the right angled conjugates of the base the other with the height of either will not limit a spheroid as the diameter of the base and the height doth a sphere This