386 FLUXIONS. 
Hotery. The new caleulus was not at first cultivated with that L'Hdpital; thie was when he came to Paris in the year History. 
—y—" attention which its importance deserved ; and, therefore, 1692. These are curious, as the earliest essays inthis =" 
in order to rouse the attention of mathematicians, Leib- branch . we wre Seay pe ae rote 
nits, in 1687, proposed the following problem: “| To merit. w ave an it 
determine the curve a heavy body ought to describe, to L'Hopital’s work, but they were not published un- _ 
in order to descend equally.in equal times.” Huy, til 1742, when they appeared pre hgmmeshnu ae 
sas: the’ fret cheb uhomredkquhab wnaidhe Manaieten the Bernoulli's works. . 2 : 
curve, but he did not indicate his method of solution. It is to be that Newton did not a 
James Bernoulli also resolved the problem by the dif- a design he had formed in 1671, of i _ 
ferential calculus, and published his analysis in the thod of fluxions, and its 3 for, 
Leipsic Acts of 1690. About the same time, John ception of what he done, herdiy'any. thing 
Laboars of Bernoulli, a younger brother of James, began his ca- ihe cevury. "Dund ‘Gregory explained same ts 
tbe Ber. reer as a mathematician: he studied the science, aided 
coulis by his brother's instructions, and he contracted a friend- principles pod applications; ana ¢iatinag dhe 
ship for Leibnitz, which continued until the death of /igurarum, printed in 1684. John: 
the latter, in 1716. He made the calculus known in __ treatise, De curcarum quadraturis, ist 1698,- which he 
oe ah ee RRR Sa ee prema irscn oo Byres res “s 1 in 1718, with 
de l'Hopital. Leibnitz and the lis resolved the title De calculo fluentium. oivre and Fatio 
many new and difficult problems, which they gave solutions in the Philosophical sl Teanseotions of the 
as challenges to the geometers of that hey also ama voomoerasitiy: tite S008 efi teat Galatea the 
2 Lek CORE aa 
achain or cord which hangs freely, but is fas- In the year 1703, George Cheyne, ss )Gledilicls seme Cheyne 
cmnoll andes easton), and the curve of swiftest de- thematician and physician, published his Methodus 
scent, which had proved too difficult for Galileo, and Fluxionum inversa, Edin, 1703. ‘The author committed 
the mathematical theories known in his time. A spirit some mistakes which were pointed out by De Moivre: 
na He had also been wanting or a rane the. — 
w a war of problems, each endeavouri maticians on the continent, and exposed to 
re eo etn i map dpe heir the animadversions of John Bernoulli. In the year 
degree of animosity on the part of John not at all be- 170¢, a treatise of fluxions was published by «Charles 
coming, was yet of advantage to the science, as it pro- Hayes Gent. This, we believe, a Hayes. 
duced the celebrated rical problems, a class prota han, pear tthr or fpervatitncnit ac yo 
more difficult than any that had previously engaged guage. 
the attention of mathematicians ; iho, indeed, _—_ It is remarkable that Newton himself should:have Newton. 
Newton had resolved a problem ‘of this kind in his been so slow in publishing any be considered athe 
Principia, when treating of the solid of least resistance. calculus. The 1699 must be 
The calculus went on, improving continually ; it was epoch at which his numerous 
tothe theory of evolutes, one of the most beau- env dest: nierle qpantelipaietesig bmanationndanties 
iful discoveries made by H ; but, with the ex- second volume of the works of Wallis. At length, 
ception of some pieces in the Leipsic Acts, there was however, in the 1704, when he printed his Optics, 
as yet no work Mulisbed his nad ror a he added to it, 4 acai Quadeaténs Curbarsenysin 
i pad 
dentially to Leibnitz in ier lifetime, ie ya a and rome Ki ee with rrp 
‘ . a L - 
differential equations, by se- Mensurarum, published in 1722, by his friend Dr 
the v: quantities an far back ae 1694, In Smith. The inventions of Cotes were extended and 
Manfredi. 1707, Gabriel Manfredi, an Italian, gave an entire eted by De Moivre, in his Miscellanea Analytica, Moivre. 
work, entitled, De Constructione poe at ere feos published in 1730, Dr Brook ‘Taylor also holds a dis- 7... 
tialium primi gradus, which all that tinguished place in the higher: wwhovexs 7 
Se Rows dine ‘Ainab uchening (SerRariategeel tel eee re me aterm 
inted in 1715, contains in second man 
Jobn Bere oe = a a series of lectures on the Piicaions of fuxions 40 ph ea al problems: 
noulli. integral calculus, for the use of his scholar and patron, theorem forthe developement of any function of 
