A Treatise on Infinitesimal Calculus: Differential calculus. 1857University Press, 1857 - Calculus |
From inside the book
Results 1-5 of 65
Page xxii
... factors of the general equation of the curve 364 SECTION 3. - Direction of curvature and points of inflexion . 240. Direct proof that a curve is convex or concave downwards 12y dx2 according as is positive or negative ... 367 241 ...
... factors of the general equation of the curve 364 SECTION 3. - Direction of curvature and points of inflexion . 240. Direct proof that a curve is convex or concave downwards 12y dx2 according as is positive or negative ... 367 241 ...
Page 11
... factors , is a number also : and thus they may be added , and the whole expression is homogeneous and correct . Whereas , did such symbols re- present concrete quantities , as , for example , geometrical lines , the first three terms ...
... factors , is a number also : and thus they may be added , and the whole expression is homogeneous and correct . Whereas , did such symbols re- present concrete quantities , as , for example , geometrical lines , the first three terms ...
Page 21
... depends on the difference of the orders of the component factors . a Thus x3 x = ax2 ; x " × x a хт a = axn − m = xm - n the former or latter form being taken according as n is greater or 9. ] 21 THEOREMS ON INFINITIES AND INFINITESIMALS .
... depends on the difference of the orders of the component factors . a Thus x3 x = ax2 ; x " × x a хт a = axn − m = xm - n the former or latter form being taken according as n is greater or 9. ] 21 THEOREMS ON INFINITIES AND INFINITESIMALS .
Page 32
... factor of it . But the only infinitesimal that it in- volves is da , therefore we may reasonably presume that de will be the factor ; the presumption however must be verified by sub- sequent investigations . Dividing both sides by dx ...
... factor of it . But the only infinitesimal that it in- volves is da , therefore we may reasonably presume that de will be the factor ; the presumption however must be verified by sub- sequent investigations . Dividing both sides by dx ...
Page 34
... factor in the numerators of the several terms of the series is less than 1 ; and therefore , no term being negative , the whole series is greater than its first two terms , that is , is greater than 2. Also since 3 = 1+ ( 1 − 1 ) ̄ ...
... factor in the numerators of the several terms of the series is less than 1 ; and therefore , no term being negative , the whole series is greater than its first two terms , that is , is greater than 2. Also since 3 = 1+ ( 1 − 1 ) ̄ ...
Contents
1 | |
2 | |
3 | |
4 | |
5 | |
6 | |
7 | |
8 | |
320 | |
326 | |
331 | |
334 | |
338 | |
344 | |
350 | |
356 | |
9 | |
10 | |
11 | |
12 | |
13 | |
15 | |
16 | |
30 | |
31 | |
32 | |
34 | |
37 | |
57 | |
58 | |
71 | |
85 | |
93 | |
94 | |
101 | |
113 | |
114 | |
119 | |
120 | |
125 | |
137 | |
143 | |
149 | |
156 | |
172 | |
180 | |
185 | |
202 | |
212 | |
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 | |
297 | |
301 | |
303 | |
307 | |
311 | |
359 | |
367 | |
373 | |
381 | |
388 | |
393 | |
411 | |
417 | |
423 | |
433 | |
439 | |
447 | |
454 | |
461 | |
468 | |
475 | |
481 | |
491 | |
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 | |
574 | |
575 | |
576 | |
579 | |
582 | |
584 | |
586 | |
589 | |
591 | |
593 | |
594 | |
597 | |
598 | |
600 | |
601 | |
603 | |
604 | |
606 | |
607 | |
608 | |
609 | |
610 | |
Other editions - View all
Common terms and phrases
a₁ algebraical angles b₁ becomes Calculus change of sign changes sign circle coefficients constant cosec curve d2F d2F d²u d²x d²y d³u d³y derived function determine differential equation dr dr dr dy dx dx dx dy dx² dy dx dy dy dy dz dy² dz dx equal equicrescent explicit function expression F(xo F(xo+h factor finite quantity fraction func given Hence homogeneous function increases increments indeterminate form infinite infinitesimal Infinitesimal Calculus infinity involved logarithms loge Maclaurin's maxima and minima maximum or minimum minimum value negative partial derived-functions positive primitive equation radius replaced result right-hand member roots Similarly sin x singular value Sturm's Theorem substituting suppose symbols Theorem tion vanish variables variation versin whence zero