## A Treatise on Infinitesimal Calculus: Differential calculus. 1857 |

### From inside the book

Results 1-5 of 29

Page xiv

CONSTRUCTION OF RULES FOR DIFFERENTIATION OF FUNCTIONS. Sbction

1. — The differentiation of

differentiating ... Differentiation of a function of two independent variables ... 73 48

.

CONSTRUCTION OF RULES FOR DIFFERENTIATION OF FUNCTIONS. Sbction

1. — The differentiation of

**explicit functions**of one variable. 25-29. Rules fordifferentiating ... Differentiation of a function of two independent variables ... 73 48

.

Page xvi

Extension to implicit functions 162 97- Extension to functions of many series 163

Sbction 7- — The formation of differential equations by means of elimination. 98.

Elimination of constants from an

...

Extension to implicit functions 162 97- Extension to functions of many series 163

Sbction 7- — The formation of differential equations by means of elimination. 98.

Elimination of constants from an

**explicit function**165 99. Elimination of constants...

Page xviii

137- The theorem for functions of two variables analogous to that of Art. 1 1 1 222

138. ... Maxima and minima of

determination of the number of maxima and minima of a given function 247 153.

137- The theorem for functions of two variables analogous to that of Art. 1 1 1 222

138. ... Maxima and minima of

**explicit functions**of one variable. 145. ... Thedetermination of the number of maxima and minima of a given function 247 153.

Page xxii

An

cusps 384 251. The number of double points of a curve of the nth degree . 385

252. The number of cusps of a curve of the nth degree 387 253. The relation of a

...

An

**explicit function**is explained which well exhibits some of the peculiarities ofcusps 384 251. The number of double points of a curve of the nth degree . 385

252. The number of cusps of a curve of the nth degree 387 253. The relation of a

...

Page 26

If one variable is involved in such an expression, it is said to be a

variable ; if two variables are involved, to be a ... must vary also ; and as a similar

variation of any other of the 26 ON

If one variable is involved in such an expression, it is said to be a

**function**of onevariable ; if two variables are involved, to be a ... must vary also ; and as a similar

variation of any other of the 26 ON

**EXPLICIT**AND IMPLICIT**FUNCTIONS**. [13.### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

7 | |

23 | |

30 | |

37 | |

51 | |

60 | |

70 | |

79 | |

356 | |

359 | |

368 | |

374 | |

381 | |

387 | |

393 | |

411 | |

89 | |

99 | |

103 | |

113 | |

114 | |

119 | |

125 | |

135 | |

137 | |

143 | |

149 | |

156 | |

162 | |

169 | |

180 | |

187 | |

198 | |

209 | |

211 | |

215 | |

224 | |

230 | |

232 | |

236 | |

243 | |

250 | |

257 | |

258 | |

259 | |

260 | |

262 | |

263 | |

264 | |

266 | |

270 | |

271 | |

273 | |

274 | |

279 | |

280 | |

282 | |

284 | |

285 | |

287 | |

288 | |

291 | |

292 | |

293 | |

295 | |

298 | |

304 | |

305 | |

311 | |

321 | |

326 | |

330 | |

338 | |

344 | |

350 | |

417 | |

423 | |

432 | |

440 | |

448 | |

454 | |

464 | |

471 | |

480 | |

486 | |

493 | |

494 | |

495 | |

496 | |

497 | |

498 | |

500 | |

501 | |

502 | |

503 | |

504 | |

506 | |

509 | |

511 | |

513 | |

514 | |

516 | |

518 | |

520 | |

521 | |

534 | |

547 | |

553 | |

559 | |

565 | |

571 | |

575 | |

576 | |

579 | |

582 | |

584 | |

586 | |

589 | |

591 | |

593 | |

594 | |

597 | |

598 | |

600 | |

601 | |

603 | |

604 | |

606 | |

607 | |

608 | |

609 | |

610 | |

1 | |

17 | |

### Other editions - View all

### Common terms and phrases

algebraic curves algebraical angle asymptote axis becomes Calculus change of sign changes sign circle coefficients conic constant coordinates corresponding critical values curvature cycloid decreases determine direction double point drawn dy _ elimination ellipse epitrochoid equa equal equicrescent equivalent explicit function expression factors finite quantity geometrical given point Hence homogeneous homogeneous function hyperbola hypocycloid hypotrochoid imaginary increases infinitesimal Infinitesimal Calculus infinity involving l)th let us suppose logarithmic maxima and minima maximum or minimum minimum value negative normal nth degree number of points observed ordinate parabola parallel partial derived-functions pass perpendicular plane curve plane of reference point of inflexion points of intersection polar positive properties radius real roots right-hand member roots of f(x shewn Similarly singular value straight line substituting symbol tangent Theorem tion Tractory triangle vanish whence Witch of Agnesi zero

### Popular passages

Page 19 - Burke. Four Letters on the Proposals for Peace with the Regicide Directory of France. Edited, with Introduction and Notes, by EJ Payne, MA Extra fcap. 8vo. cloth, 5s.