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117-449: The work is long and seemingly loosely structured, and although there are autobiographical elements, it is not a straightforward or linear autobiography. Its subtitle, 'Biographical Sketches of My Literary Life and Opinions', alludes to The Life and Opinions of Tristram Shandy, Gentleman by Laurence Sterne , suggesting that the formal qualities of the Biographia are intentional. The form

234-612: A Trinitarian God who is the origin of all things. Reid and Perkins argue that in September 1818 Coleridge solved the technical problems he had earlier faced in the Biographia , and that he provides a firmer foundation for the Schelling's two forces in the Opus Maximum , where he offered a critique of the form of logic underlying Schelling's system. In the Opus Maximum the two forces are

351-497: A sphere , the area of an ellipse , the area under a parabola , the volume of a segment of a paraboloid of revolution , the volume of a segment of a hyperboloid of revolution , and the area of a spiral . Archimedes' other mathematical achievements include deriving an approximation of pi ( π ) , defining and investigating the Archimedean spiral , and devising a system using exponentiation for expressing very large numbers . He

468-470: A Circle . The actual value is approximately 1.7320508, making this a very accurate estimate. He introduced this result without offering any explanation of how he had obtained it. This aspect of the work of Archimedes caused John Wallis to remark that he was: "as it were of set purpose to have covered up the traces of his investigation as if he had grudged posterity the secret of his method of inquiry while he wished to extort from them assent to his results." It

585-441: A ball into a container after each mile traveled. As legend has it, Archimedes arranged mirrors as a parabolic reflector to burn ships attacking Syracuse using focused sunlight. While there is no extant contemporary evidence of this feat and modern scholars believe it did not happen, Archimedes may have written a work on mirrors entitled Catoptrica , and Lucian and Galen , writing in the second century AD, mentioned that during

702-408: A careless kind of a civil, nonsensical, good humoured Shandean book..." Strongly influenced by Cervantes' Don Quixote , Sterne's Tristram Shandy also gave rise to the term "cervantic" (which Sterne at the time spelled "cervantick"). In 1766, at the height of the debate about slavery, Ignatius Sancho wrote a letter to Sterne encouraging the writer to use his pen to lobby for the abolition of

819-497: A circle. After four such steps, when the polygons had 96 sides each, he was able to determine that the value of π lay between 3 ⁠ 1 / 7 ⁠ (approx. 3.1429) and 3 ⁠ 10 / 71 ⁠ (approx. 3.1408), consistent with its actual value of approximately 3.1416. He also proved that the area of a circle was equal to π multiplied by the square of the radius of the circle ( π r 2 {\displaystyle \pi r^{2}} ). In On

936-422: A complicated metafictional twist), and starring Steve Coogan , Rob Brydon , Keeley Hawes , Kelly Macdonald , Naomie Harris , and Gillian Anderson . The movie plays with metatextual levels, showing both scenes from the novel itself and fictionalised behind-the-scenes footage of the adaptation process, even employing some of the actors to play themselves. In February 2014, a theatrical adaptation by Callum Hale

1053-508: A crisis he solved by inventing a "letter from a friend" advising him to skip the deduction and move straight to the conclusion. It was a brilliant rhetorical solution, but also a decision which laid him open to charges of philosophical dilettantism and plagiarism, subjects of much controversy. The underlying problem is that Schelling's dialectic does not ever supply a final synthesis in which the two forces find equilibrium (a moment of true self-instantiation), which means that they cannot account for

1170-399: A front view of that marvellous theatre, the soul; the arrangements of lights and the perspective have not failed in their effects, and while we imagined that we were gazing upon the infinite, our own hearts have been exalted with a sense of infinity and poetry." At the start of his novel La Peau de chagrin , Honoré de Balzac includes an image from Tristram Shandy : a curvy line drawn in

1287-562: A graphic novel by cartoonist Martin Rowson . Michael Nyman has worked sporadically on Tristram Shandy as an opera since 1981 . At least five portions of the opera have been publicly performed and one, "Nose-List Song", was recorded in 1985 on the album The Kiss and Other Movements . The book was adapted on film in 2006 as A Cock and Bull Story , directed by Michael Winterbottom , written by Frank Cottrell Boyce (credited as Martin Hardy, in

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1404-414: A head with the following claim: DESCARTES , speaking as a naturalist, and in imitation of Archimedes , said, give me matter and motion and I will construct you the universe.... In the same sense the transcendental philosopher says; grant me a nature having two contrary forces, the one of which tends to expand infinitely, while the other strives to apprehend or find itself in this infinity, and I will cause

1521-408: A line which rotates with constant angular velocity . Equivalently, in modern polar coordinates ( r , θ ), it can be described by the equation r = a + b θ {\displaystyle \,r=a+b\theta } with real numbers a and b . This is an early example of a mechanical curve (a curve traced by a moving point ) considered by a Greek mathematician. This

1638-500: A major if puzzling work in criticism and theory, with George Saintsbury placing Coleridge next to Aristotle and Longinus in his influential History of 1902-04. Recent criticism has been divided between those who think that the Biographia ' s philosophical pretensions were illusory, and those who take the philosophy seriously. While contemporary critics recognize the degree to which Coleridge borrowed from his sources (with passages lifted straight from Schelling), they also see in

1755-435: A mischaracterization. Archimedes was able to use indivisibles (a precursor to infinitesimals ) in a way that is similar to modern integral calculus . Through proof by contradiction ( reductio ad absurdum ), he could give answers to problems to an arbitrary degree of accuracy, while specifying the limits within which the answer lay. This technique is known as the method of exhaustion , and he employed it to approximate

1872-460: A number that was greater than the grains of sand needed to fill the universe. In doing so, he challenged the notion that the number of grains of sand was too large to be counted. He wrote: There are some, King Gelo , who think that the number of the sand is infinite in multitude; and I mean by the sand not only that which exists about Syracuse and the rest of Sicily but also that which is found in every region whether inhabited or uninhabited. To solve

1989-603: A passage in Volume ;V, chapter 3, Petrie observes: "such passage...reveals that Sterne's copying was far from purely mechanical, and that his rearrangements go far beyond what would be necessary for merely stylistic ends". A major influence on Tristram Shandy is Rabelais ' Gargantua and Pantagruel . Rabelais was by far Sterne's favourite author, and in his correspondence he made clear that he considered himself Rabelais's successor in humorous writing. One passage Sterne incorporated pertains to "the length and goodness of

2106-728: A person, and focuses on the war machines that he is said to have built in order to defend the city from the Romans. Polybius remarks how, during the Second Punic War , Syracuse switched allegiances from Rome to Carthage , resulting in a military campaign under the command of Marcus Claudius Marcellus and Appius Claudius Pulcher , who besieged the city from 213 to 212 BC. He notes that the Romans underestimated Syracuse's defenses, and mentions several machines Archimedes designed, including improved catapults , crane-like machines that could be swung around in an arc, and other stone-throwers . Although

2223-603: A reference to the mathematical drawing that he was supposedly studying when disturbed by the Roman soldier. There is no reliable evidence that Archimedes uttered these words and they do not appear in Plutarch's account. A similar quotation is found in the work of Valerius Maximus (fl. 30 AD), who wrote in Memorable Doings and Sayings , " ... sed protecto manibus puluere 'noli' inquit, 'obsecro, istum disturbare' " ("... but protecting

2340-408: A solution that applied the hydrostatics principle known as Archimedes' principle , found in his treatise On Floating Bodies : a body immersed in a fluid experiences a buoyant force equal to the weight of the fluid it displaces. Using this principle, it would have been possible to compare the density of the crown to that of pure gold by balancing it on a scale with a pure gold reference sample of

2457-404: A temple dedicated to the goddess Aphrodite among its facilities. The account also mentions that, in order to remove any potential water leaking through the hull, a device with a revolving screw-shaped blade inside a cylinder was designed by Archimedes. Archimedes' screw was turned by hand, and could also be used to transfer water from a low-lying body of water into irrigation canals. The screw

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2574-494: A tender tale of the sorrows of a friendless poor negro-girl, and my eyes had scarce done smarting with it, when your letter of recommendation in behalf of so many of her brethren and sisters, came to me—but why her brethren?—or yours, Sancho! any more than mine? It is by the finest tints, and most insensible gradations, that nature descends from the fairest face about St James's, to the sootiest complexion in Africa: at which tint of these,

2691-548: A toddler, Tristram suffered an accidental circumcision when Susannah let a window sash fall as he urinated out of the window because his chamberpot was missing. Sterne's presence inside the narrative changed the course of traditional novelistic interpretations as his narrative structure digresses through many jumbled and fragmentary events into a non-traditional, dual overlapping plot. These digressive methods reflect his inability to simply explain each event as it occurs, as he frequently interrupts these events with commentary about how

2808-521: A very successful publicity stunt. Yorick is also the protagonist of Sterne's second work of fiction, A Sentimental Journey Through France and Italy . Most of the action is concerned with domestic upsets or misunderstandings, which find humour in the opposing temperaments of Walter—splenetic, rational, and somewhat sarcastic—and Uncle Toby, who is gentle, uncomplicated, and a lover of his fellow man. In between such events, Tristram as narrator finds himself discoursing at length on sexual practices, insults,

2925-410: Is 4 π r for the sphere, and 6 π r for the cylinder (including its two bases), where r is the radius of the sphere and cylinder. This work of 28 propositions is also addressed to Dositheus. The treatise defines what is now called the Archimedean spiral . It is the locus of points corresponding to the locations over time of a point moving away from a fixed point with a constant speed along

3042-465: Is a novel by Laurence Sterne . It was published in nine volumes, the first two appearing in 1759, and seven others following over the next seven years (vols. 3 and 4, 1761; vols. 5 and 6, 1762; vols. 7 and 8, 1765; vol. 9, 1767). It purports to be a biography of the eponymous character. Its style is marked by digression, double entendre, and graphic devices. The first edition was printed by Ann Ward on Coney Street , York . Sterne had read widely, which

3159-490: Is also meditative . As Kathleen Wheeler shows, the work is playful and acutely aware of the active role of the reader in reading. Critics have reacted strongly to the Biographia Literaria . Some early readers thought it demonstrated Coleridge's opiate-driven decline into ill health, and soon after Coleridge's death he was accused of plagiarising Schelling . By the early twentieth century, however, it had emerged as

3276-461: Is both a unity and something characterised by division (into two forces which foreshadow the subject/object distinction). The division supplies the two forces Coleridge mentioned. Coleridge had clearly hoped to modify Schelling's argument (the transcendental deduction) so as to put it in a conservative, Trinitarian context. However, with half of the Biographia already printed, Coleridge realised that his proposed modifications were not going to work,

3393-794: Is it, that the ties of blood are to cease? and how many shades must we descend lower still in the scale, ere mercy is to vanish with them?—but 'tis no uncommon thing, my good Sancho, for one half of the world to use the other half of it like brutes, & then endeavor to make 'em so. In 2005, BBC Radio 4 broadcast an adaptation by Graham White in ten 15-minute episodes directed by Mary Peate, with Neil Dudgeon as Tristram, Julia Ford as Mother, David Troughton as Father, Adrian Scarborough as Toby, Paul Ritter as Trim, Tony Rohr as Dr Slop, Stephen Hogan as Obadiah, Helen Longworth as Susannah, Ndidi Del Fatti as Great-Grandmother, Stuart McLoughlin as Great-Grandfather/Pontificating Man and Hugh Dickson as Bishop Hall. Tristram Shandy has been adapted as

3510-499: Is possible that he used an iterative procedure to calculate these values. In Quadrature of the Parabola , Archimedes proved that the area enclosed by a parabola and a straight line is ⁠ 4 / 3 ⁠ times the area of a corresponding inscribed triangle as shown in the figure at right. He expressed the solution to the problem as an infinite geometric series with the common ratio ⁠ 1 / 4 ⁠ : If

3627-456: Is present throughout Sterne's novel. The frequent references to Rocinante , the character of Uncle Toby (who resembles Don Quixote in many ways) and Sterne's own description of his characters' " Cervantic humour", along with the genre-defying structure of Tristram Shandy , which owes much to the second part of Cervantes' novel, all demonstrate the influence of Cervantes. The novel also makes use of John Locke 's theories of empiricism , or

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3744-545: Is reflected in Tristram Shandy . Many of his similes, for instance, are reminiscent of the works of the metaphysical poets of the 17th century, and the novel as a whole, with its focus on the problems of language, has constant regard for John Locke 's theories in An Essay Concerning Human Understanding . Arthur Schopenhauer called Tristram Shandy one of "the four immortal romances". While

3861-518: Is still in use today for pumping liquids and granulated solids such as coal and grain. Described by Vitruvius , Archimedes' device may have been an improvement on a screw pump that was used to irrigate the Hanging Gardens of Babylon . The world's first seagoing steamship with a screw propeller was the SS Archimedes , which was launched in 1839 and named in honor of Archimedes and his work on

3978-473: Is that which we use in our everyday perception of things in the world. The later chapters of the book deal with the nature of poetry and with the question of poetic diction raised by Wordsworth. While maintaining a general agreement with Wordsworth's point of view, Coleridge elaborately refutes his principle that the language of poetry should be one taken with due exceptions from the mouths of men in real life, and that there can be no essential difference between

4095-462: Is titled "Tristram Shandy". Archimedes Archimedes of Syracuse ( / ˌ ɑːr k ɪ ˈ m iː d iː z / AR -kim- EE -deez ; c.  287  – c.  212   BC ) was an Ancient Greek mathematician , physicist , engineer , astronomer , and inventor from the ancient city of Syracuse in Sicily . Although few details of his life are known, he is regarded as one of

4212-551: Is under the care of the Laurence Sterne Trust since its acquisition in the 1960s. The gardens, which Sterne tended during his time there, are daily open to visitors. The novel's success has resulted in permanent additions to the English lexicon; within the text of Tristram Shandy Sterne describes the novel as "Shandean", coining a term which still carries the meaning that Sterne originally attached to it when he wrote, "I write

4329-622: Is worth 1,000 Pedants and commonplace-fellows like Dr. J." George Washington enjoyed the book. The young Karl Marx was a devotee of Tristram Shandy , and wrote a still-unpublished short humorous novel, Scorpion and Felix , that was obviously influenced by Sterne's work. Goethe praised Sterne in Wilhelm Meister's Journeyman Years , which in turn influenced Nietzsche . Writing in The Times in January 2021, critic Michael Henderson disparaged

4446-432: Is writing his history of life could never be included in his actual writing. Heinrich Heine (1796–1856) mentioned the book in his writings. "The author of Tristram Shandy reveals to us the profoundest depths of the human soul; he opens, as it were, a crevice of the soul; permits us to take one glance into its abysses, into its paradise and into its filthiest recesses; then quickly lets the curtain fall over it. We have had

4563-559: The Byzantine Greek architect Isidore of Miletus ( c.  530 AD ), while commentaries on the works of Archimedes written by Eutocius in the same century helped bring his work to a wider audience. Archimedes' work was translated into Arabic by Thābit ibn Qurra (836–901 AD), and into Latin via Arabic by Gerard of Cremona (c. 1114–1187). Direct Greek to Latin translations were later done by William of Moerbeke (c. 1215–1286) and Iacobus Cremonensis (c. 1400–1453). During

4680-525: The Preface to the Lyrical Ballads (a work on which Coleridge collaborated), and a statement of his philosophical views. The first volume is mainly concerned with the evolution of Coleridge's philosophical views. At first an adherent of the associationist psychology of the philosopher David Hartley, he came to discard this mechanical system for the belief that the mind is not a passive but an active agent in

4797-573: The Renaissance and again in the 17th century , while the discovery in 1906 of previously lost works by Archimedes in the Archimedes Palimpsest has provided new insights into how he obtained mathematical results. Archimedes was born c. 287 BC in the seaport city of Syracuse , Sicily , at that time a self-governing colony in Magna Graecia . The date of birth is based on a statement by

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4914-574: The Renaissance , the Editio princeps (First Edition) was published in Basel in 1544 by Johann Herwagen with the works of Archimedes in Greek and Latin. The following are ordered chronologically based on new terminological and historical criteria set by Knorr (1978) and Sato (1986). This is a short work consisting of three propositions. It is written in the form of a correspondence with Dositheus of Pelusium, who

5031-475: The heliocentric theory of the solar system proposed by Aristarchus of Samos , as well as contemporary ideas about the size of the Earth and the distance between various celestial bodies . By using a system of numbers based on powers of the myriad , Archimedes concludes that the number of grains of sand required to fill the universe is 8 × 10 in modern notation. The introductory letter states that Archimedes' father

5148-622: The lever , he gave a mathematical proof of the principle involved in his work On the Equilibrium of Planes . Earlier descriptions of the principle of the lever are found in a work by Euclid and in the Mechanical Problems , belonging to the Peripatetic school of the followers of Aristotle , the authorship of which has been attributed by some to Archytas . There are several, often conflicting, reports regarding Archimedes' feats using

5265-439: The siege of Syracuse Archimedes had burned enemy ships. Nearly four hundred years later, Anthemius , despite skepticism, tried to reconstruct Archimedes' hypothetical reflector geometry. The purported device, sometimes called " Archimedes' heat ray ", has been the subject of an ongoing debate about its credibility since the Renaissance . René Descartes rejected it as false, while modern researchers have attempted to recreate

5382-445: The siege of Syracuse , when he was killed by a Roman soldier despite orders that he should not be harmed. Cicero describes visiting Archimedes' tomb, which was surmounted by a sphere and a cylinder that Archimedes requested be placed there to represent his most valued mathematical discovery. Unlike his inventions, Archimedes' mathematical writings were little known in antiquity. Alexandrian mathematicians read and quoted him, but

5499-535: The Byzantine Greek scholar John Tzetzes that Archimedes lived for 75 years before his death in 212 BC. Plutarch wrote in his Parallel Lives that Archimedes was related to King Hiero II , the ruler of Syracuse, although Cicero suggests he was of humble origin. In the Sand-Reckoner , Archimedes gives his father's name as Phidias, an astronomer about whom nothing else is known. A biography of Archimedes

5616-473: The Earth" ( Greek : δῶς μοι πᾶ στῶ καὶ τὰν γᾶν κινάσω ). Olympiodorus later attributed the same boast to Archimedes' invention of the baroulkos , a kind of windlass , rather than the lever. A large part of Archimedes' work in engineering probably arose from fulfilling the needs of his home city of Syracuse . Athenaeus of Naucratis quotes a certain Moschion in a description on how King Hiero II commissioned

5733-509: The Earth, Sun, and Moon, as well as Aristarchus ' heliocentric model of the universe, in the Sand-Reckoner . Without the use of either trigonometry or a table of chords, Archimedes determines the Sun's apparent diameter by first describing the procedure and instrument used to make observations (a straight rod with pegs or grooves), applying correction factors to these measurements, and finally giving

5850-566: The Romans ultimately captured the city, they suffered considerable losses due to Archimedes' inventiveness. Cicero (106–43 BC) mentions Archimedes in some of his works. While serving as a quaestor in Sicily, Cicero found what was presumed to be Archimedes' tomb near the Agrigentine gate in Syracuse, in a neglected condition and overgrown with bushes. Cicero had the tomb cleaned up and was able to see

5967-518: The Sphere and Cylinder , Archimedes postulates that any magnitude when added to itself enough times will exceed any given magnitude. Today this is known as the Archimedean property of real numbers. Archimedes gives the value of the square root of 3 as lying between ⁠ 265 / 153 ⁠ (approximately 1.7320261) and ⁠ 1351 / 780 ⁠ (approximately 1.7320512) in Measurement of

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6084-580: The air by a character seeking to express the freedom enjoyed "whilst a man is free". Balzac never explained his purpose behind the use of the symbol, and its significance to La Peau de chagrin is the subject of debate. A historic site in Geneva, Ohio , called Shandy Hall , is part of the Western Reserve Historical Society . The home was named after the house described in Tristram Shandy . In Anthony Trollope 's novel Barchester Towers ,

6201-527: The alleged obscenity of his prose, used Ferriar's findings to defame Sterne, and claimed that he was artistically dishonest, and almost unanimously accused him of mindless plagiarism. Scholar Graham Petrie closely analysed the alleged passages in 1970; he observed that while more recent commentators now agree that Sterne "rearranged what he took to make it more humorous, or more sentimental, or more rhythmical", none of them "seems to have wondered whether Sterne had any further, more purely artistic, purpose". Studying

6318-537: The apprehension of reality. The author believed in the "self-sufficing power of absolute Genius" and distinguished between genius and talent as between "an egg and an egg-shell". The first volume culminates in his gnomic definition of the imagination or "esemplastic power", the faculty by which the soul perceives the spiritual unity of the universe, as distinguished from the fancy or merely associative function. Coleridge writes: The IMAGINATION ... I consider either as primary, or secondary. The primary IMAGINATION I hold to be

6435-412: The areas of figures and the value of π . In Measurement of a Circle , he did this by drawing a larger regular hexagon outside a circle then a smaller regular hexagon inside the circle, and progressively doubling the number of sides of each regular polygon , calculating the length of a side of each polygon at each step. As the number of sides increases, it becomes a more accurate approximation of

6552-582: The brain of Sterne; and if I could, I would gladly lead you to the same affection for my father as you have for Tristram's. (The text of Tristram Shandy uses the phrase "my father" at the head of a paragraph fifty-one times.) Christopher Morley, editor of The Saturday Review of Literature , wrote a preface to the Limited Editions Club issue of Sterne's classic. That preface appears in Morley's book Streamlines published by Doubleday, Doran, in 1932, and

6669-416: The capture of Syracuse and Archimedes' role in it. Plutarch (45–119 AD) provides at least two accounts on how Archimedes died after Syracuse was taken. According to the most popular account, Archimedes was contemplating a mathematical diagram when the city was captured. A Roman soldier commanded him to come and meet Marcellus, but he declined, saying that he had to finish working on the problem. This enraged

6786-419: The capture of Syracuse in the Second Punic War , Marcellus is said to have taken back to Rome two mechanisms which were constructed by Archimedes and which showed the motion of the Sun, Moon and five planets. Cicero also mentions similar mechanisms designed by Thales of Miletus and Eudoxus of Cnidus . The dialogue says that Marcellus kept one of the devices as his only personal loot from Syracuse, and donated

6903-431: The carving and read some of the verses that had been added as an inscription. The tomb carried a sculpture illustrating Archimedes' favorite mathematical proof , that the volume and surface area of the sphere are two-thirds that of an enclosing cylinder including its bases. He also mentions that Marcellus brought to Rome two planetariums Archimedes built. The Roman historian Livy (59 BC–17 AD) retells Polybius's story of

7020-443: The case with a gentleman who spends one year to write the story of one day of his life, if he were able to write for an infinite length of time. The paradox depends upon the fact that "the number of days in all time is no greater than the number of years". Karl Popper , in contrast, came to the conclusion that Tristram Shandy—by writing his history of life—would never be able to finish this story, because his last act of writing: that he

7137-497: The construction of these mechanisms entitled On Sphere-Making . Modern research in this area has been focused on the Antikythera mechanism , another device built c.  100 BC probably designed with a similar purpose. Constructing mechanisms of this kind would have required a sophisticated knowledge of differential gearing . This was once thought to have been beyond the range of the technology available in ancient times, but

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7254-575: The contribution of D. W. Jefferson. Some of Sterne's contemporaries did not hold the novel in high esteem, but its bawdy humour was popular with London society. Through time, it has come to be seen as one of the greatest comic novels in English. Arthur Schopenhauer called Tristram Shandy one of "the four immortal romances" and Ludwig Wittgenstein considered it "one of my favourite books". Samuel Johnson in 1776 commented, "Nothing odd will do long. Tristram Shandy did not last." Schopenhauer privately rebutted Samuel Johnson, saying: "The man Sterne

7371-464: The density would be lower than that of gold. Archimedes found that this is what had happened, proving that silver had been mixed in. The story of the golden crown does not appear anywhere in Archimedes' known works. The practicality of the method described has been called into question due to the extreme accuracy that would be required to measure water displacement . Archimedes may have instead sought

7488-451: The design of a huge ship, the Syracusia , which could be used for luxury travel, carrying supplies, and as a display of naval power . The Syracusia is said to have been the largest ship built in classical antiquity and, according to Moschion's account, it was launched by Archimedes. The ship presumably was capable of carrying 600 people and included garden decorations, a gymnasium , and

7605-403: The dexterity and the good taste with which he has incorporated in his work so many passages, written with very different views by their respective authors. Ferriar believed that Sterne was ridiculing Burton's The Anatomy of Melancholy , mocking its solemn tone and endeavours to prove indisputable facts by weighty quotations. Victorian critics of the 19th century, who were hostile to Sterne for

7722-610: The dialect of ancient Syracuse. Many written works by Archimedes have not survived or are only extant in heavily edited fragments; at least seven of his treatises are known to have existed due to references made by other authors. Pappus of Alexandria mentions On Sphere-Making and another work on polyhedra , while Theon of Alexandria quotes a remark about refraction from the now-lost Catoptrica . Archimedes made his work known through correspondence with mathematicians in Alexandria . The writings of Archimedes were first collected by

7839-518: The discovery of the Antikythera mechanism in 1902 has confirmed that devices of this kind were known to the ancient Greeks. While he is often regarded as a designer of mechanical devices, Archimedes also made contributions to the field of mathematics . Plutarch wrote that Archimedes "placed his whole affection and ambition in those purer speculations where there can be no reference to the vulgar needs of life", though some scholars believe this may be

7956-619: The doctrines of religion to military discipline, from inland navigation to the morality of dancing schools. Much of the singularity of Tristram Shandy ' s characters is drawn from Burton. Burton indulges himself in a Utopian sketch of a perfect government in his introductory address to the reader, and this forms the basis of the notions of Tristram Shandy on the subject. And Sterne parodies Burton's use of weighty quotations. The first four chapters of Tristram Shandy are founded on some passages in Burton. In Chapter 3, Volume 5, Sterne parodies

8073-426: The dust with his hands, said 'I beg of you, do not disturb this ' "). The most widely known anecdote about Archimedes tells of how he invented a method for determining the volume of an object with an irregular shape. According to Vitruvius , a crown for a temple had been made for King Hiero II of Syracuse , who supplied the pure gold to be used. The crown was likely made in the shape of a votive wreath . Archimedes

8190-609: The effect using only the means that would have been available to Archimedes, mostly with negative results. It has been suggested that a large array of highly polished bronze or copper shields acting as mirrors could have been employed to focus sunlight onto a ship, but the overall effect would have been blinding, dazzling , or distracting the crew of the ship rather than fire. Using modern materials and larger scale, sunlight-concentrating solar furnaces can reach very high temperatures, and are sometimes used for generating electricity . Archimedes discusses astronomical measurements of

8307-436: The extent that Tristram's own birth is not even reached until Volume III. Consequently, apart from Tristram as narrator, the most familiar and important characters in the book are his father Walter, his mother, his Uncle Toby, Toby's servant Trim, and a supporting cast of popular minor characters, including the chambermaid Susannah, Doctor Slop and the parson Yorick, who later became Sterne's favourite nom de plume and

8424-527: The feasibility of the claw, and in 2005 a television documentary entitled Superweapons of the Ancient World built a version of the claw and concluded that it was a workable device. Archimedes has also been credited with improving the power and accuracy of the catapult , and with inventing the odometer during the First Punic War . The odometer was described as a cart with a gear mechanism that dropped

8541-535: The first comprehensive compilation was not made until c.  530   AD by Isidore of Miletus in Byzantine Constantinople , while Eutocius ' commentaries on Archimedes' works in the same century opened them to wider readership for the first time. The relatively few copies of Archimedes' written work that survived through the Middle Ages were an influential source of ideas for scientists during

8658-519: The first term in this series is the area of the triangle, then the second is the sum of the areas of two triangles whose bases are the two smaller secant lines , and whose third vertex is where the line that is parallel to the parabola's axis and that passes through the midpoint of the base intersects the parabola, and so on. This proof uses a variation of the series 1/4 + 1/16 + 1/64 + 1/256 + · · · which sums to  ⁠ 1 / 3 ⁠ . In The Sand Reckoner , Archimedes set out to calculate

8775-489: The genre of consolatio , mixing and reworking passages from three "widely separated sections" of Burton's Anatomy , including a parody of Burton's "grave and sober account" of Cicero 's grief for the death of his daughter Tullia . His text is filled with allusions and references to the leading thinkers and writers of the 17th and 18th centuries. Alexander Pope and Jonathan Swift were major influences on Sterne and Tristram Shandy . Satires of Pope and Swift formed much of

8892-473: The globe, it happened that the Moon followed the Sun by as many turns on that bronze contrivance as in the sky itself, from which also in the sky the Sun's globe became to have that same eclipse, and the Moon came then to that position which was its shadow on the Earth when the Sun was in line. This is a description of a small planetarium . Pappus of Alexandria reports on a now lost treatise by Archimedes dealing with

9009-532: The ground of the finite or human realm, but the true origin of all things lies in the Trinity. For Coleridge, the Trinity is the form in which the divine will instantiates itself, in a way which avoids the infinite deferral of a final synthesis in Schelling argument, and which does not derive from Schelling's two forces. The Life and Opinions of Tristram Shandy, Gentleman The Life and Opinions of Tristram Shandy, Gentleman , also known as Tristram Shandy ,

9126-570: The humour of Tristram Shandy , but Swift's sermons and Locke's Essay Concerning Human Understanding also contributed ideas and frameworks Sterne explored throughout the novel. Other major influences are Cervantes and Montaigne 's Essays , as well as the significant inter-textual debt to The Anatomy of Melancholy , Swift's Battle of the Books , and the Scriblerian collaborative work The Memoirs of Martinus Scriblerus . The shade of Cervantes

9243-430: The imprecision and arbitrariness of words and usage), and consequently spends much time discussing the very words he uses in his own narrative—with "digressions, gestures, piling up of apparent trivia in the effort to get at the truth". There is a significant body of critical opinion that argues that Tristram Shandy is better understood as an example of an obsolescent literary tradition of "Learned Wit", partly following

9360-442: The influence of one's name and noses, as well as explorations of obstetrics , siege warfare and philosophy, as he struggles to marshal his material and finish the story of his life. Though Tristram is always present as narrator and commentator, the book contains little of his life, only the story of a trip through France and accounts of the four comical mishaps which shaped the course of his life from an early age. Firstly, while he

9477-442: The language of prose and of metrical composition. A critique on the qualities of Wordsworth's poetry concludes the volume. The book contains Coleridge's celebrated and vexed distinction between "imagination" and "fancy". Chapter XIV is the origin of the famous critical concept of the "willing suspension of disbelief " when reading poetic works. At the beginning of chapter 13, Coleridge attempts to bring his philosophical argument to

9594-428: The leading scientists in classical antiquity . Regarded as the greatest mathematician of ancient history , and one of the greatest of all time, Archimedes anticipated modern calculus and analysis by applying the concept of the infinitely small and the method of exhaustion to derive and rigorously prove a range of geometrical theorems . These include the area of a circle , the surface area and volume of

9711-416: The lever to lift very heavy objects. Plutarch describes how Archimedes designed block-and-tackle pulley systems, allowing sailors to use the principle of leverage to lift objects that would otherwise have been too heavy to move. According to Pappus of Alexandria , Archimedes' work on levers and his understanding of mechanical advantage caused him to remark: "Give me a place to stand on, and I will move

9828-531: The living Power and prime Agent of all human Perception, and as a repetition in the finite mind of the eternal act of creation in the infinite I AM. The famous definition of the imagination emerges from a discussion of Immanuel Kant , Johann Gottlieb Fichte , and Friedrich Wilhelm Joseph von Schelling , amongst others. (Being fluent in German, Coleridge was one of the first major English literary figures to discuss Schelling's ideas, in particular.) The primary imagination

9945-442: The name in conveying it to the curate, and the child was christened Tristram. According to his father's theory, his name, being a conflation of "Trismegistus" (after the esoteric mystic Hermes Trismegistus ) and " Tristan " (whose connotation bore the influence through folk etymology of Latin tristis , "sorrowful"), doomed him to a life of woe and cursed him with the inability to comprehend the causes of his misfortune. Finally, as

10062-472: The narrator speculates that the scheming clergyman, Mr Slope, is descended from Dr Slop in Tristram Shandy (the extra letter having been added for the sake of appearances). Slope is also called "Obadiah", a reference to another character in Sterne's novel. Russian writer Alexander Zhitinsky made multiple references to Tristram Shandy in his novel The Flying House, or Conversations with Milord (the "milord" of

10179-430: The new meaning intended in Tristram Shandy . Tristram Shandy was highly praised for its originality, and nobody noticed these borrowings until years after Sterne's death. The first to note them was physician, poet and Portico Library Chair John Ferriar , who did not see them negatively and commented: If [the reader's] opinion of Sterne's learning and originality be lessened by the perusal, he must, at least, admire

10296-486: The nose". Sterne had written an earlier piece called A Rabelaisian Fragment that indicates his familiarity with the work of the French monk and doctor. Sterne was no friend of gravitas, a quality which excited his disgust. Tristram Shandy gives a ludicrous turn to solemn passages from respected authors that it incorporates, as well as to the consolatio literary genre. Among the subjects of such ridicule were some of

10413-653: The novel as a precursor to the " hysterical realism " of authors such as Rushdie and Thomas Pynchon . Novelist Javier Marías cites Tristram Shandy as the book that changed his life when he translated it into Spanish at 25, claiming that from it he "learned almost everything about novel writing, and that a novel may contain anything and still be a novel." The success of Sterne's novel got him an appointment by Lord Fauconberg as curate of St Michael's Church in Coxwold , Yorkshire, which included living at Sterne's model for Shandy Hall . The medieval structure still stands today, and

10530-402: The novel, stating that it "honks like John Coltrane , and is not nearly so funny." Tristram Shandy has also been seen by formalists and other literary critics as a forerunner of many narrative devices and styles used by modernist and postmodernist authors such as James Joyce , Virginia Woolf , Carlos Fuentes , Milan Kundera and Salman Rushdie . The critic James Wood identified

10647-527: The opinions contained in Robert Burton 's The Anatomy of Melancholy , a book that mentions sermons as the most respectable type of writing, and one that was favoured by the learned. Burton's attitude was to try to prove indisputable facts by weighty quotations. His book consists mostly of a collection of the opinions of a multitude of writers (he modestly refrains from adding his own) divided into quaint and old-fashioned categories. It discusses everything, from

10764-532: The oppression of a black servant in a sausage shop in Lisbon, which he had visited. This "tender tale" was published in Chapter 65 (Vol. IV) of Tristram Shandy . Sterne's widely publicised 27 July 1766 response to Sancho's letter became an integral part of 18th-century abolitionist literature. There is a strange coincidence, Sancho, in the little events (as well as in the great ones) of this world: for I had been writing

10881-576: The other to the Temple of Virtue in Rome. Marcellus's mechanism was demonstrated, according to Cicero, by Gaius Sulpicius Gallus to Lucius Furius Philus , who described it thus: Hanc sphaeram Gallus cum moveret, fiebat ut soli luna totidem conversionibus in aere illo quot diebus in ipso caelo succederet, ex quo et in caelo sphaera solis fieret eadem illa defectio, et incideret luna tum in eam metam quae esset umbra terrae, cum sol e regione. When Gallus moved

10998-420: The principles derived to calculate the areas and centers of gravity of various geometric figures including triangles , parallelograms and parabolas . In this work of 24 propositions addressed to Dositheus, Archimedes proves by two methods that the area enclosed by a parabola and a straight line is 4/3 the area of a triangle with equal base and height. He achieves this in one of his proofs by calculating

11115-490: The problem, Archimedes devised a system of counting based on the myriad . The word itself derives from the Greek μυριάς , murias , for the number 10,000. He proposed a number system using powers of a myriad of myriads (100 million, i.e., 10,000 x 10,000) and concluded that the number of grains of sand required to fill the universe would be 8 vigintillion , or 8 × 10 . The works of Archimedes were written in Doric Greek ,

11232-623: The reader should understand and follow each event. He relies heavily on his reader's close involvement to the text and their interpretations of the non-traditional plot. Tristram's presence inside of the narrative as the narrator engages the imagination, and his use of visual strategies, such as the marbled and blank pages, reflects the importance of the reader's participation in the novel. Sterne incorporated into Tristram Shandy many passages taken almost word for word from Robert Burton 's The Anatomy of Melancholy , Francis Bacon 's Of Death , Rabelais and many more, and rearranged them to serve

11349-452: The result in the form of upper and lower bounds to account for observational error. Ptolemy , quoting Hipparchus, also references Archimedes' solstice observations in the Almagest . This would make Archimedes the first known Greek to have recorded multiple solstice dates and times in successive years. Cicero's De re publica portrays a fictional conversation taking place in 129 BC. After

11466-453: The same weight, then immersing the apparatus in water. The difference in density between the two samples would cause the scale to tip accordingly. Galileo Galilei , who invented a hydrostatic balance in 1586 inspired by Archimedes' work, considered it "probable that this method is the same that Archimedes followed, since, besides being very accurate, it is based on demonstrations found by Archimedes himself." While Archimedes did not invent

11583-416: The screw. Archimedes is said to have designed a claw as a weapon to defend the city of Syracuse. Also known as " the ship shaker ", the claw consisted of a crane-like arm from which a large metal grappling hook was suspended. When the claw was dropped onto an attacking ship the arm would swing upwards, lifting the ship out of the water and possibly sinking it. There have been modern experiments to test

11700-404: The slave trade. "That subject, handled in your striking manner, would ease the yoke (perhaps) of many—but if only one—Gracious God!—what a feast to a benevolent heart!" he wrote. In July 1766 Sancho's letter was received by Sterne shortly after he had just finished writing a conversation between his fictional characters Corporal Trim and his brother Tom in Tristram Shandy , in which Tom described

11817-559: The soldier, who killed Archimedes with his sword. Another story has Archimedes carrying mathematical instruments before being killed because a soldier thought they were valuable items. Marcellus was reportedly angered by Archimedes' death, as he considered him a valuable scientific asset (he called Archimedes "a geometrical Briareus ") and had ordered that he should not be harmed. The last words attributed to Archimedes are " Do not disturb my circles " ( Latin , " Noli turbare circulos meos "; Katharevousa Greek , "μὴ μου τοὺς κύκλους τάραττε"),

11934-467: The title being Sterne). In Surprised by Joy , C. S. Lewis refers to Tristram Shandy in the context of trying to describe his interactions with his own father: My father—but these words, at the head of a paragraph, will carry the reader's mind inevitably to Tristram Shandy. On second thoughts I am content that they should. It is only in a Shandean spirit that my matter can be approached. I have to describe something as odd and whimsical as ever entered

12051-426: The use of the narrative technique of stream of consciousness is usually associated with modernist novelists, Tristram Shandy has been suggested as a precursor. As its title suggests, the book is ostensibly Tristram's narration of his life story. But it is one of the central jokes of the novel that he cannot explain anything simply, that he must make explanatory diversions to add context and colour to his tale, to

12168-418: The value of a geometric series that sums to infinity with the ratio 1/4. In this two-volume treatise addressed to Dositheus, Archimedes obtains the result of which he was most proud, namely the relationship between a sphere and a circumscribed cylinder of the same height and diameter . The volume is ⁠ 4 / 3 ⁠ π r for the sphere, and 2 π r for the cylinder. The surface area

12285-422: The way we assemble what we know of ourselves and our world from the "association of ideas" that come to us from our five senses. Sterne is by turns respectful and satirical of Locke's theories, using the association of ideas to construct characters' " hobby-horses ", or whimsical obsessions, that both order and disorder their lives in different ways. Sterne borrows from and argues against Locke's language theories (on

12402-423: The work far more structure and planning than is apparent on first glance. The work was originally intended as a preface to a collected volume of Coleridge's poems, explaining and justifying his own style and practice in poetry. The work grew to a literary autobiography , covering his education and studies, and his early literary adventures, an extended criticism of William Wordsworth 's theory of poetry as given in

12519-566: The world of intelligences with the whole system of their representations to rise up before you. The two forces were derived from Schelling's System of Transcendental Idealism of 1800. In that work, Schelling offers the first systematic use of dialectic (thesis, antithesis and synthesis), though it is not a term he uses. Dialectic only works if the original term (the thesis) already contains its opposite within itself. Schelling derived this original duality by arguing that: We thus have an origin for all things known in this world, an origin which

12636-411: Was a student of Conon of Samos . In Proposition II, Archimedes gives an approximation of the value of pi ( π ), showing that it is greater than ⁠ 223 / 71 ⁠ (3.1408...) and less than ⁠ 22 / 7 ⁠ (3.1428...). In this treatise, also known as Psammites , Archimedes finds a number that is greater than the grains of sand needed to fill the universe. This book mentions

12753-462: Was adapted by Martin Pearlman in 2018 as a comic chamber opera, The Life and Opinions of Tristram Shandy . Well known in philosophy and mathematics, the so-called paradox of Tristram Shandy was introduced by Bertrand Russell in his book The Principles of Mathematics to evidentiate the inner contradictions that arise from the assumption that infinite sets can have the same cardinality—as would be

12870-539: Was also one of the first to apply mathematics to physical phenomena , working on statics and hydrostatics . Archimedes' achievements in this area include a proof of the law of the lever , the widespread use of the concept of center of gravity , and the enunciation of the law of buoyancy known as Archimedes' principle . He is also credited with designing innovative machines , such as his screw pump , compound pulleys , and defensive war machines to protect his native Syracuse from invasion. Archimedes died during

12987-494: Was an astronomer named Phidias. The Sand Reckoner is the only surviving work in which Archimedes discusses his views on astronomy. There are two books to On the Equilibrium of Planes : the first contains seven postulates and fifteen propositions , while the second book contains ten propositions. In the first book, Archimedes proves the law of the lever , which states that: Magnitudes are in equilibrium at distances reciprocally proportional to their weights. Archimedes uses

13104-417: Was asked to determine whether some silver had been substituted by the goldsmith without damaging the crown, so he could not melt it down into a regularly shaped body in order to calculate its density . In this account, Archimedes noticed while taking a bath that the level of the water in the tub rose as he got in, and realized that this effect could be used to determine the golden crown's volume . Archimedes

13221-452: Was important to a man making his way in life. In a difficult birth, Tristram's nose was crushed by Dr. Slop's forceps. Thirdly, another of his father's theories was that a person's name exerted enormous influence over that person's nature and fortunes, with the worst possible name being Tristram. In view of the previous accidents, Tristram's father decreed that the boy would receive an especially auspicious name, Trismegistus . Susannah mangled

13338-914: Was presented at the Tabard Theatre in Chiswick . Tristram Shandy has been translated into many languages, including German (repeatedly, beginning in 1769), Dutch (repeatedly, by Munnikhuisen, 1779; Lindo, 1852 and Jan & Gertrude Starink, 1990), French (repeatedly, beginning in 1785; by Guy Jouvet, 2004), Russian (repeatedly, beginning 1804–1807; by Adrian Antonovich Frankovsky, 1949), Hungarian (by Győző Határ , 1956), Italian (by Antonio Meo, 1958), Czech (by Aloys Skoumal, 1963), Slovene (by Janez Gradišnik , 1968), Spanish (by José Antonio López de Letona, 1975; Ana María Aznar, 1976 and Javier Marías , 1978), Portuguese (by José Paulo Paes , 1984), Catalan (by Joaquim Mallafré, 1993), Norwegian (by Bjørn Herrman, 1995–96), Finnish (by Kersti Juva , 1998). Tristram Shandy

13455-471: Was so excited by this discovery that he took to the streets naked, having forgotten to dress, crying " Eureka !" ( Greek : "εὕρηκα , heúrēka !, lit.   ' I have found [it]! ' ). For practical purposes water is incompressible, so the submerged crown would displace an amount of water equal to its own volume. By dividing the mass of the crown by the volume of water displaced, its density could be obtained; if cheaper and less dense metals had been added,

13572-412: Was still only an homunculus , Tristram's implantation within his mother's uterus was disturbed. At the very moment of procreation, his mother asked his father if he had remembered to wind the clock. The distraction and annoyance led to the disruption of the proper balance of humours necessary to conceive a well-favoured child. Secondly, one of his father's pet theories was that a large and attractive nose

13689-783: Was written by his friend Heracleides, but this work has been lost, leaving the details of his life obscure. It is unknown, for instance, whether he ever married or had children, or if he ever visited Alexandria , Egypt, during his youth. From his surviving written works, it is clear that he maintained collegial relations with scholars based there, including his friend Conon of Samos and the head librarian Eratosthenes of Cyrene . The standard versions of Archimedes' life were written long after his death by Greek and Roman historians. The earliest reference to Archimedes occurs in The Histories by Polybius ( c. 200–118 BC), written about 70 years after his death. It sheds little light on Archimedes as

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