Customer Reviews (1)

The truth about Berkeley's critique of the calculus
A very widespread myth has it that Berkeley's critique of the infinitesimal calculus constituted a profound challenge that forced MacLaurin to write a thorough treatise reexamining its foundations. The facts of the matter, however, are as follows.

Berkeley was an incompetent dilettante, whose superficial critique did not shake the foundations of the calculus in the least. Berkeley's critique is "groundless" (p. 427) and the alleged flaws that he "pretends to discover" (p. 427) are all due to him having "not understood" (p. 427) the mathematics in question.

The foundations of the calculus were well understood (and Berkeley's trifling arguments preempted), and in need of no revision whatever. "[Newton's] notion of fluxions has nothing obscure, mysterious, unintelligible or absurd in it." (p. 428) "What this writer [Berkeley] advances against the foundations of the methods of Fluxions serves only to shew that he has not considered or understood what its great Author [Newton] said in their defence when he first published them; for if he had, he would have found the most material of his objections prevented & answered there." (p. 425)

MacLaurin did not write his Treatise of Fluxions in reply to Berkeley's critique. "Upon more consideration I did not think it best to write an Ansuer to Dean Berkeley but to write a treatise of fluxions which might ansuer the purpose and be useful to my scholars." (p. 250). In other words, a reply to Berkeley would not have been "useful to scholars."

Although Berkeley's critique was motivated by religious zealotry, the conflict between mathematics and religion is a figment of his imagination. "I am satisfied that the interests of true Science and true Religion are united, & that they do real prejudice to Mankind who endeavour to represent them as opposite in any measure." (p. 427) "I believe it will be easily granted by all who are acquainted with the History of Learning that there is no other order or Class of Learned Men that has produced fewer writers on the side of Infidelity, or fewer adversarys to natural or revealed Religion than that of the Mathematicians. The greatest Men among them have distinguished themselves as firm in the belief, and ornaments to the practice of Christianity, and particularly these men who invented or promoted the parts which this Author has so warmly attack'd." (p. 426) ... Read more

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This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

Product Description
This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

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Purchase of this book includes free trial access to www.million-books.com where you can read more than a million books for free.This is an OCR edition with typos.Excerpt from book:BOOK II.Of the theory of motion or rational mechanics.CHAP. I.Of fpacey time, matter and motion.i. A S we are certain of our own txiftence, and of that /% of our ideas, by internal confcioufnefs ; fo JL A. we are fatisfied, by the fame confcioufnefs, that there are objects, powers, or caufes without us, and that ad: upon us. For in many of our ideas, particularly thofe that are accompanied with pain, the mind muft be paflive, and receive the impreflions (which are involuntary) from external caufes or inftruments, that depend not upon us. We eafily diftinguifh thefe objects into two general clafles. The firft is of thofe which we perceive to have a fpontaneity, or felf- moving power, and feveral properties and affections fimilar to thofe of our own minds, fuch as reafoning, judging, willing, loving, hating, jfc. The fecond general clafs is of thofe in which no fuch affections appear, but which are fo far of a paflive nature, that they never move of themfelves, neither, when they are in motion, do they ever ftop without fome external influence. If one of thefe move out of its place, without the appearance of a mover, we immediately conclude that this is owing to fome invifible agent ; fo much/are we perfuaded of its own inertia. If we lay up one of them in any place, we expec t to find it there at any diftance of time, if no other powers haveO hadhad accefs to it. This paflive nature, or inertia, is what chiefly diftinguifhes the fecond clafs of external objects, which is called body or matter ; as the former is called mind orfpirit.2. How external objects, of cither clafs, act upon the mind, by producing fo great a variety of impreflions or ideas, is not our bufinefs at prefent to enquire : neither is it neceflary for us to determine how exact or perfect... ... Read more

Customer Reviews (1)

Against systematic philosophy
This is a very predictable book which there is little point in reading today. However, on one point I think it differs significantly from standard histories. Today it is often said that Newton's followers quickly forgot the imperfections that Newton had seen in his theory (action at a distance, etc.) and adopted his world view unconditionally. This is no doubt true but its emphasis is somewhat altered by Maclaurin's insistence that the greatness of the Principia is its *imperfection* and the fact that it is *not a system*:

"They who have indulged themselves in inventing systems and compleating them, tho' they have sometimes set out in a manner that has appeared plausible, yet, in pursuing those schemes, such consequences have arisen as could not fail to disgust all but such as were intoxicated with the deceit." (p. 95). "We may also learn ... from the bad success of so many fruitless attempts, to be less fond of perfect and finished schemes of natural philosophy; to be willing to stop when we find we are not in a condition to proceed farther; and to leave to posterity to make greater advances, as time and observation shall enable them." (p. 91).

A historical digression is intended to show how geometry grew only gradually; an example will convey the spirit: "one, we are told, discovered that the three angles of an equilateral triangle were equal to two right ones; another went farther, and shewd the same thing of those that have two sides equal and are called isosceles triangles; and it was a third who found that the theorem was general, and extended it to triangles of all sorts." (p. 92, with reference to Proclus).

"From what we have observed concerning the history of natural philosophy, it may easily be understood why its progress has been so different; and whence it proceeds that we seldom have found in it, as in geometry, that pleasing gradual rise from small beginnings to grater heights. Instead of searching into nature, men retired to contemplate their own thoughts; ... where they ought to have hesitated, they decided; and where there was no difficulty, they doubted." (p. 93). "One ill-grounded maxim was imagined, to support another, and fiction was grafted upon fiction. Hypotheses were invented, nor for reducing facts or observations of a complicated nature to rules and order, (for which purpose they may be of service) but as principles of science. These were of so great authority as not to be overturned by contradictory observations, or by the extravagant consequences that arose from them; but the author, charm'd with his rhapsody, proceeded, without minding these, to the conclusion of his fable. Thus one age or sect could not but destroy, for the most part, the labour of another." (p. 94).

"But it has appeared sufficiently, from the discoveries of ... Sir Isaac Newton, that the fault has lain in the philosophers themselves, and not in philosophy. A compleat system indeed was not to be expected from one man, or one age, or perhaps from the greatest number of ages; could we have expected it from the abilities of any one man, we surely would have had it from Sir Isaac Newton: but he saw too far into nature to attempt it." (p. 96). ... Read more

Product Description
This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

Product Description
This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

Product Description
This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

Product Description
This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

Product Description
This is a reproduction of a book published before 1923.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process.We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide.We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

Product Description
This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

Product Description
This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

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This Book Is In French. ... Read more

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This Book Is In French. ... Read more

Product Description
This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

Product Description
This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

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This book presents important works by the Scottish mathematician Colin MacLaurin (1698-1746), translated in English for the first time. It includes three of the mathematician’s less known and often hard to obtain works. A general introduction puts the works in context and gives an outline of MacLaurin's career. Each translation is also accompanied by an introduction and analyzed both in modern terms and from a historical point of view.

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The 18th century was a wealth of knowledge, exploration and rapidly growing technology and expanding record-keeping made possible by advances in the printing press. In its determination to preserve the century of revolution, Gale initiated a revolution of its own: digitization of epic proportions to preserve these invaluable works in the largest archive of its kind. Now for the first time these high-quality digital copies of original 18th century manuscripts are available in print, making them highly accessible to libraries, undergraduate students, and independent scholars.
Medical theory and practice of the 1700s developed rapidly, as is evidenced by the extensive collection, which includes descriptions of diseases, their conditions, and treatments. Books on science and technology, agriculture, military technology, natural philosophy, even cookbooks, are all contained here.
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The below data was compiled from various identification fields in the bibliographic record of this title. This data is provided as an additional tool in helping to insure edition identification:
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British Library

T093640

With a half-title.Two plates are numbered XXV.

Edinburgh : printed by T. W. and T. Ruddimans, 1742. 2v.([6],vi,763,[1]p.),XL[i.e.XLI]plates ; 4° ... Read more

Product Description
The 18th century was a wealth of knowledge, exploration and rapidly growing technology and expanding record-keeping made possible by advances in the printing press. In its determination to preserve the century of revolution, Gale initiated a revolution of its own: digitization of epic proportions to preserve these invaluable works in the largest archive of its kind. Now for the first time these high-quality digital copies of original 18th century manuscripts are available in print, making them highly accessible to libraries, undergraduate students, and independent scholars.
Medical theory and practice of the 1700s developed rapidly, as is evidenced by the extensive collection, which includes descriptions of diseases, their conditions, and treatments. Books on science and technology, agriculture, military technology, natural philosophy, even cookbooks, are all contained here.
++++
The below data was compiled from various identification fields in the bibliographic record of this title. This data is provided as an additional tool in helping to insure edition identification:
++++
British Library

T093640

With a half-title.Two plates are numbered XXV.

Edinburgh : printed by T. W. and T. Ruddimans, 1742. 2v.([6],vi,763,[1]p.),XL[i.e.XLI]plates ; 4° ... Read more

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Chapters: James Clerk Maxwell, Thomas Reid, Frederick Soddy, Colin Maclaurin, George Gordon, 1st Earl of Aberdeen, Alexander Bain, John Boyd Orr, 1st Baron Boyd-Orr, Antony Flew, Michael Woodruff, Matthew Hay, Iain Torrance, David Daube, Reginald Victor Jones, John Struthers, John Bainbridge Webster, Tom Devine, Andrew Melville, Ian Bradley, Donald M. Mackinnon, Paul Mealor, George Paget Thomson, Hugh Pennington, John Stuart Blackie, Robert Adamson, George Turnbull, Alexander Watt, Peter Clift, Katia Sycara, Christopher Howes, Alexander Ogston, Charles Wyville Thomson, Frederick Baltimore Calvert, Alexander Gray, Neil Walker, Benedict Jones, Alister Hardy, Paul Wilkinson, Roger Williams, James Beattie, John David Brewer, Arthur Robertson Cushny, Andrew Norman Meldrum, Douglas Young, Charles Sanford Terry, Thomas Jamieson, Lewis Macdonald, William Macgillivray, Alexander Arbuthnot, John Sewel, Baron Sewel, Hector Munro Macdonald, Hans Kosterlitz, Matthew Mcdiarmid, Duncan Rice, Robert Morrison Maciver, David Dumville, Francis Grant Ogilvie, Margaret K. Knight, Ewen Maclachlan, Richard Rose, James Nicol, Gordon Rawcliffe, Theo Barker, Alexander Souter, George Adam Smith, W. Douglas Simpson, Roland Robertson, Dugald Baird, Graeme Catto, John Carroll, Robert Hamilton, Walter Hamilton Moberly, John Mallard, William Laurence Brown, Stanley Eveling, Steve Boardman, John Laird, E. M. Wright, William Minto, J. B. Torrance, G.o. Sayles, John Callender, George Dickie, Derek Burke, Peter Noble, George Grub, John Fraser, Lindley M. Fraser, Mark Shucksmith, J. Norman Davidson, Kenneth Norrie, John Bennett Black. Source: Wikipedia. Pages: 330. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: James Clerk Maxwell (13 June 1831 5 November 1879) was a Scottish theoretical physicist and mathematician. His most ...More: http://booksllc.net/?id=16062 ... Read more