Elementary Illustrations of the Differential and Integral Calculus by De Morgan

(1 User reviews)   4187
By Charlotte Girard Posted on Nov 15, 2025
In Category - Philosophy
De Morgan, Augustus, 1806-1871 De Morgan, Augustus, 1806-1871
English
Okay, hear me out. I know 'Elementary Illustrations of the Differential and Integral Calculus' sounds like the opposite of a good time. But this 19th-century book by Augustus De Morgan is a fascinating time capsule. It’s not a dry textbook—it’s a gentle, almost conversational guide written to convince regular people that calculus wasn't just for geniuses. The real story here is De Morgan's mission: to make the intimidating world of changing quantities and areas under curves accessible to anyone curious. Think of it as a patient teacher from 1842, reaching through time to show you that math can be understood, not just memorized.
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the description by accepting the presidency of an Atheistical society. With few exceptions, the heretics of one generation become the revered saints of a period less than twenty generations later. Lord Bacon, in his own age, was charged with Atheism, Sir Isaac Newton with Socinianism, the famous Tillotson was actually charged with Atheism, and Dr. Burnet wrote vigorously against the commonly received traditions of the fall and deluge. There are but few men of the past of whom the church boasts to-day, who have not at some time been pointed at as heretics by orthodox antagonists excited by party rancor. Heresy is in itself neither Atheism nor Theism, neither the rejection of the Church of Rome, nor of Canterbury, nor of Constantinople; heresy is not necessarily of any-ist or-ism. The heretic is one who has selected his own opinions, or whose opinions are the result of some mental effort; and he differs from others who are orthodox in this:--they hold opinions which are often only the bequest of an earlier generation unquestioningly accepted; he has escaped from the customary grooves of conventional acquiescence, and sought truth outside the channels sanctified by habit. Men and women who are orthodox are generally so for the same reason that they are English or French--they were born in England or France, and cannot help the good or ill fortune of their birthplace. Their orthodoxy is no higher virtue than their nationality. Men are good and true of every nation and of every faith; but there are more good and true men in nations where civilisation has made progress, and amongst faiths which have been modified by high humanising influences. Men are good not because of their orthodoxy, but in spite of it; their goodness is the outgrowth of their humanity, not of their orthodoxy. Heresy is necessary to progress; heresy in religion always precedes endeavor for political freedom. You cannot have effectual political progress without wide-spread heretical thought. Every grand political change in which the people have played an important part has been preceded by the popularisation of heresy in the immediately earlier generations. Fortunately, ignorant men cannot be real heretics, so that education must be hand-maiden to heresy. Ignorance and superstition are twin sisters. Belief too often means nothing more than prostration of the intellect on the threshold of the unknown. Heresy is the pioneer, erect and manly, striding over the forbidden line in his search for truth. Heterodoxy develops the intellect, orthodoxy smothers it. Heresy is the star twinkle in the night, orthodoxy the cloud which hides this faint gleam of light from the weary travellers on life’s encumbered pathway. Orthodoxy was well exemplified in the dark middle ages, when the mass of men and women believed much and knew little, when miracles were common and schools were rare, and when the monasteries on the hill tops held the literature of Europe. Heresy speaks for itself in this nineteenth century, with the gas and electric light, with cheap newspapers, with a thousand lecture rooms, with innumerable libraries, and at least a majority of the people able to read the thoughts the dead have left, as well as to listen to the words the living utter. The word heretic ought to be a term of honor; for honest, clearly uttered heresy is always virtuous, and this whether truth or error; yet it is not difficult to understand how the charge of heresy has been generally used as a means of exciting bad feeling. The Greek word [--Greek--] which is in fact our word heresy, signifies simply selection or choice. The heretic philosopher was...

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Let's be clear: this isn't a novel with a plot. The 'story' is De Morgan's journey to explain calculus without all the scary jargon. He starts with simple ideas about things changing—like how fast a stone falls—and slowly builds up the concepts. He uses practical examples and clear diagrams to show how calculus helps us measure curves, find maximum values, and understand motion. The book is structured as a series of lessons, each one tackling a new piece of the puzzle, from basic principles to more complex applications.

Why You Should Read It

You should read it for the unique voice. De Morgan writes like a kindly, enthusiastic professor who genuinely wants you to 'get it.' You can feel his passion for demystifying math. It's a peek into how people learned complex subjects before modern textbooks existed. Reading it today, you appreciate the foundational ideas of calculus presented in their pure, original form, free from the dense notation that often overwhelms students now.

Final Verdict

This is perfect for history of science nerds, math teachers looking for perspective, or a curious reader who wants to understand the 'why' behind calculus without the pressure of a graded course. It's not for someone seeking a quick reference or modern practice problems. But if you enjoy seeing how great ideas were first communicated, De Morgan's patient, illustrative approach is a quiet delight.



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Dorothy Walker
1 year ago

This book was worth my time since the flow of the text seems very fluid. This story will stay with me.

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4 out of 5 (1 User reviews )

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