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we know iis proportion to gi ven quantitiest And whether this proportion can be linoKn, but by expressions or exponenis, either geometricat, algebraicat, or arithmetical t And whether expressions in lines or speciescan be useful, but so far fortii as they are reduci ble to numbers tau. et s. Whether the finding out proper expressions or notations os quantity be not the most generat character and tenden cy of the mathematichst And arithmetical operation that whicli limits and desines thcir
au. 26. Whether mathematicians have lassiciently considerod the analogy and use of signf t And hois far the specific limited nature of things corresponds thereto lsu. 27. Whether hecause, in stating a generat case of pure Algebra, me are at fuit liberty to mahe a character denote, either a positive or a negative quantity, or nothing at all, We may, there re, in a geometricalcase, limited by hypotheses and reasonings stom particular properties and relations os figures, claim the fame license istu. 28. Whether the misting of the hypothesis, or as we may callit) the fallacia suppostionis bo not a sophism, that far and wide insedis themodern rea nings, both in the mechanical philosophy and in the abstruseand sine geometry tau. 29. Whether we can form an idea or notion os velocity distinctfrom and exclusive of iis mea res, as we can of heat distinet from and exclusi ve of the degrees on the thermometer, by whicli it is meast red tAnd whether this he not supposed in the rea nings of modern analysis t
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Qu. 3O. Whether motion can be conceived in a potnt of space t Andis motion cannot, whether velocity can t And is not, whether a first ortast veloci ty can he conceived in a mere limit , either initial or final, of the described space tou. 3I. Where there a re no increments, whether there can be any
ratio os increments t Whether nothings can be considered as proportionalto reat quantiti est Or whether to talk of their proportions he not totalli nonsenset Also in What sense we are to understand the proportion ofa sursace to a line, of an area to an ordinate 8 And whether species ornumbers, though pro perly expressing quantities Whicli are not homogen ous, may yet be said to express their proportion to each other tru. 32. Whether is ali assignable circles may be squared, the circle is not, to ali intenis and purposes, squared a s weli as the parabola t Orwhether a parabolicat area can in fact be measu red more accurately thana circulari Qu. 33. Whether it Would not be righter to approximate Dirly, thanto endea vOUr at accuracy by sophisinsts u. 3 . Whether it would not be more decent to proceed by trials and inductions, than to pretend to demonstrate by false principieststu. 33. Whether there be not a Way of arri ving at truth, althoughthe principies a re not scienti fio, nor the rea soning just y And whether such a way ought to be called a linach or a science ρβα 36. Whether there can be science of the conclusion, where thereis not evidence of the principiest And whether a man can have evidence
of the principies, without understanding themt And there re, Whether the
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the mathematicians of the present age act like men os science, in takingso much more palns to apply their principies, than to understand themisu. 37. Whether the greatest genius wreflling with false principies maynot be solled i And whether accurate quadratures can he obtained without new psulata or assumptions t And is not, whether those whicli are intelligibie and consistent ought not to be preferred to the contrary t See Sect. XXVIII. and XXIX. Qu. 38. Whether tedious calculations in algebra and fluxions he theliheltest method to improve the mind t And whether mens heing accustomed to reason altogether about mathematical signs and figures, dothnoi mahe them at a tost ho to rea n without them tau. 39. Whether Whatever readinest analysts acquire in stating a problem, or finding api expressions sor mathematical quantities, the fame doth necessarily inser a proportionable ability in conceiving and expressingother matters tetu. o. Whether it be not a generat case or rute, that one and the fame coefficient dividing equat products gives eques quotienis i And yet whether such coefficient can be interpreted by o or nothing t Or whether any one Will say, that is the equation et X o α 5 κ o, be divided by o, the quotient on both sides are equat i Whether there re a cate may notbe generat with respect to ali quantities, and yet not extend to nothings,or include the case of nothingi And whether the bringing nothing under the notion os quantity may not have betrayed men into false re
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in such demonstrations, they are not obliged to the same strict rea ningas in geometry t And whether such their rea nings are not deducedfrom the sanae axioms with those in geometry t Whether there re algebra be not as truly a science as geometry tetu. 42. Whether men may not reason in species as weli as in wordsi Whether the fame rules of logic do not obtain in both cases t And whether we have not a right to expect and demand the same evidence in
both pou. 3. Whether an algebraist, fluxionist, geometrician or demonstrator of any kind can expect indulgence sor obscure principies or inco rect reasonings ' And whether an algebraical note, or species can at theend of a process be interpreted in a sense, which could not have been substitu ted for it at the beginningi or whether any particular supposition can come under a generat case whicli doth not consist with the re soning thereost Ou. ψέ. Whether the disserence bet een a mere computer and a manos science be not, that the orae computes on principies clearly conceived, and by rules evidently demonstrated, whereas the other doth not tetu. s. Whether, although geometry be a science, and algebra allo ed to he a science, and the analytical a most excellent method, in the application neverthelese of the analysis to geometry, men may not have admitted false principies and wrong methods of rea ning testu. 46. Whether, although algebraical rea nings are admitted to bfever se just, When confined to sigias or species as generat representatives of quantity, you may not neverthelest fati into error, is, when you limitthem to stand sor Particular things, you do not limit yourself to rea nconsistently
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au. 7. Whether the view of modem mathematicians doth not ra-ther feem to be the coming at an expression by artifice, than the comingat science by demonstration t 8. Whether there may not be found metaphysios as Heli as un-seundi Sound as weli as un und logic t And whether the modern analyties may not be brought under one of these denominations, and whichtau. 9. Whether there be not reatly a philosophia prima, a certain
transcendental science superior to and more extensive than mathematics, whicli it might bellove our modern analysis rather to learn than despise tetu. so. Whether ever since the recovery of mathematical learning, there have not been perpetuat disputes and controversies among the mathematicians t And whether this doth not disparage the evidelice of their methods tau. 5 I. Whether any thing but metaphystcs and logic can open the CyeS Os mathematicians and extricate them out of their dissiculties tam 32. Whether Upon the received principies a quantity can by any division or subdivision, though carried e ver so far, be reduced to nothingtsa. Whether is the end of geometry be practice, and this practice he mea ring, and we measure only assignable extensions, it Willnot sollo that unlimited approximations completely ansNer the intention os geometry t
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m. 3 . Wh. ther the fame things whicli are no v done by infinites may not be done by finite quantitiest And whether this would not he agreat relies to the imaginations and understandings of mathematical mentetu. 5s. Whether those philomathematical physicians, anatomists, and dealers in the animal oeconomy, who admit the doctrine os fluxions withan implicit Dith, can with a good grace insuli other men sor belle ving vhat they do not comprehend 's6. Whether the corpuscularian, experimental, and mathema
etu. 57. Whether Dom this, and other concurring causes, the mindsos speculative men have not been born downward, to the debasing and stupisting of the higher faculties t And whether we may not hence account for that prevat ling narrownesi and bigotry among many Who Passsor men os science, their incapaci ty for things morat, intellectuat, or theo' logical, their pronenesis to mea ire ali trullis by sense and experience of
animal liktau 58. Whether it be reatly an effect of thinhing, that the same menadmire the great author for his fluxions, and deride him sor his religion tetu. 39. Is certain philosophical virtuosi of the present age have noreligion, whether it can be said to he want of faith Z qu. 6o. Whether it be not a juster way of rea ning, to recommendpoints of faith from their essedis, than to demonstrate mathematical principies by their conclusion st
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61. Whether it be not lese exceptionabie to admit potnis abovereason than contrary to reason toti. 62. Whether mysteries may not with better right be allowed os in divine Dith, than in human science t u. 63. Whether such mathematicians as cry out against mysteries, have ever examined their own principies 'su. 6 . Whether mathematicians, who are so delicate in religiouspoinis, are strictly scrupulous in their own sciencet Whether they do notsubmit to authority, talie things upon trust, belleve potnis inconceiva-hlet Whether they have not their mysteries, and what is more, their repugnancies and contradictions isti. 63. Whether it might not hecome men, Who are puggled and perplexed a ut their own principies, to judge warily, candidly, and modestly concerning other matterstau. 66. Whethor the modern analytics do not surnim a strong argumentum ad hominem, against the philomathematical in fideis of these timestati. 67. Whether it follows stom the abovementioned remariis, that
accurate and just rea ning is the peculiar character of the present age tAnd whether the modern gro th of infidelity can he ascribed to a distin tion se truly valvabiet