Page 64. |
Previous | 92 of 474 | Next |
|
|
small (250x250 max)
medium (500x500 max)
Large
Extra Large
large ( > 500x500)
Full Resolution
|
This page
All
|
Il
64
THE MANNER OF FINDING FLUENTS.
;1
And that of a 4- z X z
. m rn\n4^
fi -X- y
-- : for here
z
m x n 4- t
the root, Or the quantity under the general index n, being
to
a
4- z , and its fluxion
ra
mi
z (art. f4), we fliall, by di-
! -\«
am 4- zm>
viding by the laft of thefe quantities,have -—; whence,
m
increafing the index by unity, and dividing by (u 4- 1) the in*
• S«4-1
dex fo increafed, there comes out
m X n 4- 1
After the very fame manner the fluents of other expreflion»
may be deduced, when the quantity or multiplicator, without the vinculum, is either equal, or in a confiant ratio, to
the fluxion of the quantity under the vinculum: as in the ex-
—n m n — *
preffion a 4- cznl X az «; where the number of dimensions of 2 under the vinculum (or general index) being equal
to thofe of 2 without the vinculum 4- 1, the fluent may therefore be had, as in the preceding examples; and will come out
m4-l
ft -4- c 7^ ' y //
-: and that this (or any other expreflion derived
ne x m 4- l
in like manner) is the true fluent will evidently appear, by
n
fuppofing x equal to a 4- cz , the quantity under the vinculum; for then (equal quantities having equal fluxions) x will
n— *
be rr nez z (art. 8) ; and confequently a 4- czn X dz z
7 • 7 m ■ J W4-X
. m ax-. ax x . . . r ax
(rr x x —) rr ; whole fluent is therefore -:■■■ ■ ■■-
ncJ nc nc xw+1
/ , _-,v d X a 4- cz \ j r
(art. 77) rr — —, as before.
ne X m 4- I
78. In afligning the fluents of given fluxions there is another particular that ought to be attended to not yet taken
notice of; and that is, whether the flowing quantity, found
by the common rule above delivered, does not require the
addition or fubtraction of fome confiant quantity to render it
y^-?iw
■s*
| 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 64. |
| Format | tiff |
| Identifier | 1138_092 |
| 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 | Il 64 THE MANNER OF FINDING FLUENTS. ;1 And that of a 4- z X z . m rn\n4^ fi -X- y -- : for here z m x n 4- t the root, Or the quantity under the general index n, being to a 4- z , and its fluxion ra mi z (art. f4), we fliall, by di- ! -\« am 4- zm> viding by the laft of thefe quantities,have -—; whence, m increafing the index by unity, and dividing by (u 4- 1) the in* • S«4-1 dex fo increafed, there comes out m X n 4- 1 After the very fame manner the fluents of other expreflion» may be deduced, when the quantity or multiplicator, without the vinculum, is either equal, or in a confiant ratio, to the fluxion of the quantity under the vinculum: as in the ex- —n m n — * preffion a 4- cznl X az «; where the number of dimensions of 2 under the vinculum (or general index) being equal to thofe of 2 without the vinculum 4- 1, the fluent may therefore be had, as in the preceding examples; and will come out m4-l ft -4- c 7^ ' y // -: and that this (or any other expreflion derived ne x m 4- l in like manner) is the true fluent will evidently appear, by n fuppofing x equal to a 4- cz , the quantity under the vinculum; for then (equal quantities having equal fluxions) x will n— * be rr nez z (art. 8) ; and confequently a 4- czn X dz z 7 • 7 m ■ J W4-X . m ax-. ax x . . . r ax (rr x x —) rr ; whole fluent is therefore -:■■■ ■ ■■- ncJ nc nc xw+1 / , _-,v d X a 4- cz \ j r (art. 77) rr — —, as before. ne X m 4- I 78. In afligning the fluents of given fluxions there is another particular that ought to be attended to not yet taken notice of; and that is, whether the flowing quantity, found by the common rule above delivered, does not require the addition or fubtraction of fome confiant quantity to render it y^-?iw ■s* |
|
|
|
|
|
|
| A |
|
| C |
|
| D |
|
| E |
|
| G |
|
| H |
|
| I |
|
| L |
|
| M |
|
| N |
|
| O |
|
| P |
|
| R |
|
| S |
|
| T |
|
|
|
