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I
THE NATURE AND INVESTIGATION OF FLUXIONS. 11
*nd fo of others. But, in the folution of problems, it will be
convenient to make the firft fluxion of fome one of the fimple
quantities (x or y) invariable, not only to avoid trouble, but
that it may ferve as a ftandard to which the variable fluxions
of tire other quantities, depending thereon, maybe always referred. The reader is alfo defired here (once for all) to take
particular notice, that the fluxions of all kinds and orders zvhat-
ever are contemporaneous, or fuch as may be generated together, with their refpeclive celerities, in one and the fame
time.
SECTION II.
Of the Application of Fluxions to the Solution of Problems
De Maximis et Minimis.
22. IF a quantity conceived to be generated by motion
increafes or decreafes till it arrives at a certain magnitude or
pofition, and then, on the contrary, grows leifer or greater,
and it be required to determine the faid magnitude or pofition, the queftion is called a problem de Maximis fy Minimis.
GENERAL ILLUSTRATION.
Let a point m move uniformly in a right line, from A towards B, and let another point n move after it, with a velocity either increafing or decreafing, but fo that it may, at a
certain pofition, D, become equal to that of the former point
m, moving uniformly.
This being premifed, let the motion of n be firft confidered
Ah
D C
<B
as an increafing one; in which cafe the
diftance of n behind m will continually in- n m
creafe, till the two points arrive at the cotemporary pofitions
C and D; but afterwards it will again decreafe, for the motion of n, till then, being flower than at D, it is alfo flower
than that of the preceding points (by hypothefis), hut becoming quicker, afterwards, than that of m, the diftance mn
(as has been already faid) will again decreafe; and therefore
is a maximum, or the greateft of all, when the celerities of the
two points are equal to each other.
But if n arrives at D with a decreafing celerity, then its
motion being firft fwifter, and afterwards flower, than that of
m, the diftance mn will firft decreafe and then increafe ; and
C2
| Title | Doctrine and application of fluxions. |
| Alternative Title | The doctrine and application of fluxions containing (besides what is common on the subject) a number of new improvements in the theory, and the solutions of a variety of new and very interesting problems in different branches of the mathematics... To which is prefixed an account of his life. The whole revised and carefully corrected by William Davis. |
| Reference Title | Simpson, Thomas, 1805, The doctrine and application of fluxions. |
| Creator |
Simpson, Thomas, 1710-1761. Davis, William, 1771-1807 . |
| Subject | Calculus. |
| Publisher | London. |
| DateOriginal | 1805 |
| Format | JP2 |
| Extent | 31 cm. |
| Identifier | 138 |
| Call Number | QA303.S45 1805 |
| Language | English |
| Collection | History of Mathematics |
| Rights | http://www.lindahall.org/imagerepro/ |
| Data contributor | Linda Hall Library, LHL Digital Collections. |
| Type | Image |
| Title | Page 11. |
| Format | tiff |
| Identifier | 1138_039 |
| Relation-Is part of | Is part of: The doctrine and application of fluxions containing (besides what is common on the subject) a number of new improvements in the theory, and the solutions of a variety of new and very interesting problems in different branches of the mathematics... To which is prefixed an account of his life. The whole revised and carefully corrected by William Davis. |
| Rights | http://www.lindahall.org/imagerepro/ |
| Type | Image |
| OCR transcript | I THE NATURE AND INVESTIGATION OF FLUXIONS. 11 *nd fo of others. But, in the folution of problems, it will be convenient to make the firft fluxion of fome one of the fimple quantities (x or y) invariable, not only to avoid trouble, but that it may ferve as a ftandard to which the variable fluxions of tire other quantities, depending thereon, maybe always referred. The reader is alfo defired here (once for all) to take particular notice, that the fluxions of all kinds and orders zvhat- ever are contemporaneous, or fuch as may be generated together, with their refpeclive celerities, in one and the fame time. SECTION II. Of the Application of Fluxions to the Solution of Problems De Maximis et Minimis. 22. IF a quantity conceived to be generated by motion increafes or decreafes till it arrives at a certain magnitude or pofition, and then, on the contrary, grows leifer or greater, and it be required to determine the faid magnitude or pofition, the queftion is called a problem de Maximis fy Minimis. GENERAL ILLUSTRATION. Let a point m move uniformly in a right line, from A towards B, and let another point n move after it, with a velocity either increafing or decreafing, but fo that it may, at a certain pofition, D, become equal to that of the former point m, moving uniformly. This being premifed, let the motion of n be firft confidered Ah D C |
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