A Treatise on Infinitesimal Calculus: Differential calculus. 1857University Press, 1857 - Calculus |
From inside the book
Results 6-10 of 100
Page 9
... equal parts respectively , or into 3n and 7n equal parts respectively , the unit would have been only one - half or one - nth part of what it was in the pre- vious resolution ; and yet the ratio of the lines , or of the num- bers which ...
... equal parts respectively , or into 3n and 7n equal parts respectively , the unit would have been only one - half or one - nth part of what it was in the pre- vious resolution ; and yet the ratio of the lines , or of the num- bers which ...
Page 18
... equal or unequal parts , as the case may be , the larger the number of parts is , the smaller is each part ; and if the number of parts be infinitely great , each part is an infini- tesimal : and the less the difference is between the ...
... equal or unequal parts , as the case may be , the larger the number of parts is , the smaller is each part ; and if the number of parts be infinitely great , each part is an infini- tesimal : and the less the difference is between the ...
Page 19
... equal to , and a2 is the number of parts into which a α has been divided : thus 2 and severally represent an ... equal parts , then is an infinity , and i is relative to the infinitesimal i . And again , suppose a to be a a resolved into ...
... equal to , and a2 is the number of parts into which a α has been divided : thus 2 and severally represent an ... equal parts , then is an infinity , and i is relative to the infinitesimal i . And again , suppose a to be a a resolved into ...
Page 23
... equal , in which case it is absolutely zero . Thus ai " + bi " ( a + b ) i " , ai " — bi " — ( a — b ) i " , ai " —ai " = 0 . = = THEOREM VI . - Since an infinitesimal is derived from a FINITE number by the resolution of the finite ...
... equal , in which case it is absolutely zero . Thus ai " + bi " ( a + b ) i " , ai " — bi " — ( a — b ) i " , ai " —ai " = 0 . = = THEOREM VI . - Since an infinitesimal is derived from a FINITE number by the resolution of the finite ...
Page 38
... equal to , and therefore may be used indifferently for , each other . Hence , when x is an infinitesimal , sin x x = tan x ; which proposition is frequently expressed in the form , ( 13 ) The limiting ratio of the sine , the arc , and ...
... equal to , and therefore may be used indifferently for , each other . Hence , when x is an infinitesimal , sin x x = tan x ; which proposition is frequently expressed in the form , ( 13 ) The limiting ratio of the sine , the arc , and ...
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