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

### From inside the book

Results 1-5 of 55

Page vi

... is capable of gradual growth and of infinitesimal

aspect is what Infinitesimal Calculus contemplates : and investigates the new

properties of it, the new symbols required to express them, and the new laws to

which ...

... is capable of gradual growth and of infinitesimal

**increase**Number under thisaspect is what Infinitesimal Calculus contemplates : and investigates the new

properties of it, the new symbols required to express them, and the new laws to

which ...

Page xvi

...

188 111. The proof that * (*n) - » fco) = (x„ — v {x0 + 6 (xn — x0) } , f (x) being

finite and continuous for all values of x between x„ and xo 190 1 1 2. The proof

that ...

...

**increase**and diminish with x, or as x**increases**, f(x) decreases, and vice versd188 111. The proof that * (*n) - » fco) = (x„ — v {x0 + 6 (xn — x0) } , f (x) being

finite and continuous for all values of x between x„ and xo 190 1 1 2. The proof

that ...

Page 15

But continuous

another only by going through all the intermediate numbers, whereby the

successive increments or augments which the numbers receive are infinitesimal ;

thus, ...

But continuous

**increase**is when number grows, that is, passes from one value toanother only by going through all the intermediate numbers, whereby the

successive increments or augments which the numbers receive are infinitesimal ;

thus, ...

Page 16

... and so on to any finite number of divisions, the

the number of divisions be iufinite, and ... the greater number by receiving at each

successive step an infinitesimal

... and so on to any finite number of divisions, the

**increase**is discontinuous; but ifthe number of divisions be iufinite, and ... the greater number by receiving at each

successive step an infinitesimal

**increase**, the mode of**increase**is continuous. Page 17

Thus the inferior limit of j~T# *8 * » though f°r every value of x greater than 0 the

quantity is less than 1, yet the nearer x approaches to 0, the less becomes the

difference between y~ — and 1 ; and the superior limit is 0 ; for as x

the ...

Thus the inferior limit of j~T# *8 * » though f°r every value of x greater than 0 the

quantity is less than 1, yet the nearer x approaches to 0, the less becomes the

difference between y~ — and 1 ; and the superior limit is 0 ; for as x

**increases**,the ...

### 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.