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69-517: La Géométrie was published in 1637 as an appendix to Discours de la méthode ( Discourse on the Method ), written by René Descartes . In the Discourse , Descartes presents his method for obtaining clarity on any subject. La Géométrie and two other appendices, also by Descartes, La Dioptrique ( Optics ) and Les Météores ( Meteorology ), were published with the Discourse to give examples of

138-481: A 0 > 0 {\displaystyle f(0)=a_{0}>0} and ends at f ( + ∞ ) = + ∞ > 0 {\displaystyle f(+\infty )=+\infty >0} , so it must cross the positive x-axis an even number of times (each of which contributes an odd number of roots), and glance (without crossing) the positive x-axis an arbitrary number of times (each of which contributes an even number of roots). The other case

207-463: A n a 0 > 0 {\displaystyle a_{n}a_{0}>0} , then Z ( f ) {\displaystyle Z(f)} is even. If a 0 a n < 0 {\displaystyle a_{0}a_{n}<0} , then Z ( f ) {\displaystyle Z(f)} is odd. f ( x ) {\displaystyle f(x)} starts at f ( 0 ) =

276-429: A with an area, a with a volume and so on, and treats them all as possible lengths of line segments. These notational devices permit him to describe an association of numbers to lengths of line segments that could be constructed with straightedge and compass . The bulk of the remainder of this book is occupied by Descartes's solution to "the locus problems of Pappus ." According to Pappus, given three or four lines in

345-473: A , b , c , etc. The germinal idea of a Cartesian coordinate system can be traced back to this work. In the second book, called On the Nature of Curved Lines , Descartes described two kinds of curves, called by him geometrical and mechanical . Geometrical curves are those which are now described by algebraic equations in two variables, however, Descartes described them kinematically and an essential feature

414-481: A convenient method for determining double roots of a polynomial, known as Hudde's rule , that had been a difficult procedure in Descartes's method of tangents. These editions established analytic geometry in the seventeenth century. Publishing Publishing is the activity of making information, literature, music, software, and other content available to the public for sale or free of charge. Traditionally,

483-462: A form of arithmetic and algebra and translating geometric shapes into algebraic equations . For its time this was ground-breaking. It also contributed to the mathematical ideas of Leibniz and Newton and was thus important in the development of calculus. This appendix is divided into three "books". Book I is titled Problems Which Can Be Constructed by Means of Circles and Straight Lines Only. In this book he introduces algebraic notation that

552-540: A modern, large-scale industry disseminating all types of information. " Publisher " can refer to a publishing company, organization, or an individual who leads a publishing company, imprint , periodical , or newspaper. The publishing process covering most magazine , journal , and book publishers includes: (Different stages are applicable to different types of publishers) Newspapers or news websites are publications of current reports, articles , and features written by journalists . They are free, sometimes with

621-419: A nonnegative even number. If b 0 > 0 {\displaystyle b_{0}>0} , then we can divide the polynomial by x b 0 {\displaystyle x^{b_{0}}} , which would not change its number of strictly positive roots. Thus WLOG, let b 0 = 0 {\displaystyle b_{0}=0} . Lemma  —  If

690-677: A particular field and often push the boundaries established in these fields. They usually have peer review processes before publishing to test the validity and quality of the content. A magazine is a periodical published at regular intervals. It features creative layouts, photography, and illustrations that cover a particular subject or interest. Magazines are available in print or digital formats and can be purchased on apps or websites like Readly or accessed free of charge on apps or websites like Issuu . The global book publishing industry consists of books categorized as fiction or non-fiction and print , e-book , or audiobook . The book market

759-508: A plane, the problem is to find the locus of a point that moves so that the product of the distances from two of the fixed lines (along specified directions) is proportional to the square of the distance to the third line (in the three line case) or proportional to the product of the distances to the other two lines (in the four line case). In solving these problems and their generalizations, Descartes takes two line segments as unknown and designates them x and y . Known line segments are designated

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828-400: A premium edition, or paid for, either individually or through a subscription . They are filled with photographs or other media and usually are subsidized with advertising . Typically, they cover local , national, and international news or feature a particular industry. Some organizations charge premium fees if they have the expertise and exclusive knowledge. The news industry is meant to serve

897-403: A registered ISBN to identify it. Directories contain searchable indexed data about businesses, products, and services. They were printed in the past but are now mostly online. Directories are available as searchable lists, on a map, as a sector-specific portal , as a review site (expert or consumer), or as a comparison site . Although some businesses may not consider themselves publishers,

966-435: A shop with a small margin (or none at all) compared to a website is very cost-effective because it acts as a huge billboard that offers a browsing experience that enables consumers to make purchasing decisions. It gives them a feel for the brand, has a presence in the community, and creates jobs. Also, using social media publishing to advertise has a good ROI if trending, high-quality content is created that reflects positively on

1035-758: A single franchise, e.g., Ballantine Del Rey LucasBooks has the exclusive rights to Star Wars in the United States; Random House UK (Bertelsmann)/Century LucasBooks holds the same rights in the United Kingdom. The video game industry self-publishes through BL Publishing/ Black Library ( Warhammer ) and Wizards of the Coast ( Dragonlance , Forgotten Realms , etc.). The BBC has its own publishing division that does very well with long-running series such as Doctor Who . These multimedia works are cross-marketed aggressively, and sales frequently outperform

1104-623: A subsidized income for publishers. If the advertising has a return on investment (ROI), the publisher can boost income exponentially by increasing the spending. An ROI of up to £10 per £1 invested is possible, as seen in the John Lewis & Partners Christmas campaigns . Likewise, any cost savings that harm the customer/consumer experience can impact a brand in the long term. Multichannel marketing can be more cost-effective in creating an immersive experience that cannot be replicated with one channel. For example, when considering marketing spend,

1173-459: A website, from which anyone can download and read it. An increasing number of authors are using niche marketing online to sell more books by engaging with their readers online. Refer to the ISO divisions of ICS 01.140.40 and 35.240.30 for further information. Publication is the distribution of copies or content to the public . The Berne Convention requires that this can only be done with

1242-426: Is Since nonreal roots of a polynomial with real coefficients must occur in conjugate pairs, it means that x − 1 has exactly two nonreal roots and one real root, which is positive. The subtraction of only multiples of 2 from the maximal number of positive roots occurs because the polynomial may have nonreal roots, which always come in pairs since the rule applies to polynomials whose coefficients are real. Thus if

1311-1332: Is a k − 1 {\displaystyle k-1} -multiple root of f ′ {\displaystyle f'} . Thus Z ( f ′ ) ≥ Z ( f ) − 1 {\displaystyle Z(f')\geq Z(f)-1} . If a 0 a 1 > 0 {\displaystyle a_{0}a_{1}>0} , then V ( f ′ ) = V ( f ) {\displaystyle V(f')=V(f)} , else V ( f ′ ) = V ( f ) − 1 {\displaystyle V(f')=V(f)-1} . In both cases, V ( f ′ ) ≤ V ( f ) {\displaystyle V(f')\leq V(f)} Together, we have Z ( f ) ≤ Z ( f ′ ) + 1 = V ( f ′ ) − 2 s + 1 ≤ V ( f ) − 2 s + 1 ≤ V ( f ) + 1 {\displaystyle Z(f)\leq Z(f')+1=V(f')-2s+1\leq V(f)-2s+1\leq V(f)+1} Further, since Z ( f ) {\displaystyle Z(f)} and V ( f ) {\displaystyle V(f)} have

1380-404: Is a modern term for publishing a book but printing so few copies or with such lack of marketing, advertising, or sales support that it effectively does not reach the public. The book, while nominally published, is almost impossible to obtain through normal channels such as bookshops, often cannot be ordered specially, and has a notable lack of support from its publisher, including refusal to reprint

1449-421: Is also undertaken by governments, civil society, and private companies for administrative or compliance requirements, business, research, advocacy, or public interest objectives. This can include annual reports , research reports , market research , policy briefings, and technical reports . Self-publishing has become very common. Publishing has evolved from a small, ancient form limited by law or religion to

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1518-448: Is an academic publisher run by a university. Oxford University Press is the largest in the world and specializes in research, education, and English language teaching internationally. A catalog is a visual directory or list of a large range of products that allow you to browse and buy from a particular company. In print, this is usually in the format of a softback book or directory. Smaller visual catalogs can be known as brochures. With

1587-434: Is equal to where p denotes the maximum number of positive roots, q denotes the maximum number of negative roots (both of which can be found using Descartes' rule of signs), and n denotes the degree of the polynomial. The polynomial has one sign change; so the maximum number of positive real roots is one. As has no sign change, the original polynomial has no negative real roots. So the minimum number of nonreal roots

1656-421: Is huge, with around 1.5 billion people speaking English. Translation services are also available to make these texts accessible in other languages. Self-publishing makes publishing widely accessible through small print-run digital printing or online self-publishing platforms. E-reader screen technology continues to improve with increased contrast and resolution making them more comfortable to read. Each book has

1725-704: Is obvious. Now assume n ≥ 2 {\displaystyle n\geq 2} . By induction hypothesis, Z ( f ′ ) = V ( f ′ ) − 2 s {\displaystyle Z(f')=V(f')-2s} for some integer s ≥ 0 {\displaystyle s\geq 0} . By Rolle's theorem , there exists at least one positive root of f ′ {\displaystyle f'} between any two different positive roots of f {\displaystyle f} . Also, any k {\displaystyle k} -multiple positive root of f {\displaystyle f}

1794-476: Is similar. From the lemma, it follows that Z ( f ) {\displaystyle Z(f)} and V ( f ) {\displaystyle V(f)} always have the same parity. It remains to show Z ( f ) ≤ V ( f ) {\displaystyle Z(f)\leq V(f)} . We induct on n {\displaystyle n} . If n = 0 , 1 {\displaystyle n=0,1} , then it

1863-494: Is still in use today. The letters at the end of the alphabet, viz., x , y , z , etc. are to denote unknown variables, while those at the start of the alphabet, a , b , c , etc. denote constants. He introduces modern exponential notation for powers (except for squares, where he kept the older tradition of writing repeated letters, such as, aa ). He also breaks with the Greek tradition of associating powers with geometric referents,

1932-488: Is the number of sign changes after multiplying the coefficients of odd-power terms by −1, or fewer than it by an even number. This procedure is equivalent to substituting the negation of the variable for the variable itself. For example, the negative roots of a x 3 + b x 2 + c x + d {\displaystyle ax^{3}+bx^{2}+cx+d} are the positive roots of Thus, applying Descartes' rule of signs to this polynomial gives

2001-491: The Harry Potter and James Bond franchises. The publishing landscape is continually evolving. Currently there are four major types of publishers in book publishing: These companies traditionally produce hardcopy books in large print runs. They have established networks which distribute those books to bricks-and-mortar stores and libraries. When a mainstream publisher accepts a book for publication, they require

2070-466: The Taylor series of the function e P ( x ). For sufficiently large a , there are exactly k such changes of sign. In the 1970s Askold Khovanskii developed the theory of fewnomials that generalises Descartes' rule. The rule of signs can be thought of as stating that the number of real roots of a polynomial is dependent on the polynomial's complexity, and that this complexity is proportional to

2139-589: The development of books . The Chinese inventor Bi Sheng made a movable type of earthenware c.  1045 , but there are no known surviving examples of his work. The Korean civil servant Ch'oe Yun-ŭi , who lived during the Goryeo Dynasty, invented the first metal moveable type in 1234–1250 AD. In what is commonly regarded as an independent invention, Johannes Gutenberg developed movable type in Europe around 1450, along with innovations in casting

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2208-469: The factor theorem for polynomials and gives an intuitive proof that a polynomial of degree n has n roots. He systematically discussed negative and imaginary roots of equations and explicitly used what is now known as Descartes' rule of signs . Descartes wrote La Géométrie in French rather than the language used for most scholarly publication at the time, Latin. His exposition style was far from clear,

2277-495: The Department of Justice, filing a permanent injunction on the merger. Although newspaper and magazine companies still often own printing presses and binderies, book publishers rarely do. Similarly, the trade usually sells the finished products through a distributor who stores and distributes the publisher's wares for a percentage fee or sells on a sale or return basis. Some major publishers have entire divisions devoted to

2346-468: The Internet, they have evolved into searchable databases of products known under the term e-commerce . Interactive catalogs and brochures like IKEA and Avon allow customers to browse a full range if they have not decided on their purchase. Responsive web and app design will allow further integration between interactive catalog visuals and searchable product databases. Until recently, physical books were

2415-612: The World Wide Web in 1989 soon propelled the website into a dominant publishing medium. Wikis and blogs soon developed, followed by online books , online newspapers , and online magazines . This also facilitated the technological convergence of commercial and self-published content and the convergence of publishing and production into online production through the development of multimedia content. A U.S.-based study in 2016 that surveyed 34 publishers found that straight, able-bodied, white females overwhelmingly represent

2484-496: The Writers' Guild of Great Britain (WGGB) have called for reform of the paid-for publishing sector. These unions, representing 14,800 authors, jointly published a report to expose widespread bad practices among companies that charge writers to publish their work while taking away their rights. When an author self-publishes a book, they retain all rights and assume responsibility for all stages of preparing, publishing and distributing

2553-632: The author must cover all the costs of publication, surrender some rights to the publisher, and pay royalties on sales. Vanity presses often engage in deceptive practices or offer costly, poor-quality services with limited recourse available to the writer. In the US, these practices have been cited by the Better Business Bureau as unfavorable reports by consumers. Given the bad reputation of vanity publishing, many vanity presses brand themselves as hybrid publishers. The Society of Authors (SoA) and

2622-633: The author to sign a contract surrendering some rights to the publisher. In exchange, the publisher will take care of all aspects of publishing the book at the publisher's cost. They rely entirely on sales of the book to recoup those costs and make a profit. The author receives a royalty on each sale (and sometimes an advance on royalties when the book is accepted ). Because of the financial risk , mainstream publishers are extremely selective in what they will publish, and reject most manuscripts submitted to them. In 2013, Penguin (owned by Pearson ) and Random House (owned by Bertelsmann ) merged, narrowing

2691-510: The average stand-alone published work, making them a focus of corporate interest. The advent of the Internet has provided an alternative mode of book distribution and most mainstream publishers also offer their books in ebook format. Preparing a book for e-book publication is the same as print publication, with only minor variations in the process to account for the different publishing mediums; E-book publication also eliminates some costs like

2760-614: The book. The author may hire professionals on a fee-for-service basis as needed, (e.g. an editor, cover designer, proofreader) or engage a company to provide an integrated package. Accessible publishing uses the digitization of books to mark them up into XML and produce multiple formats to sell to customers, often targeting those who experience difficulty reading. Formats include a variety of larger print sizes, specialized print formats for dyslexia , eye tracking problems, and macular degeneration , as well as Braille , DAISY , audiobooks , and e-books . Green publishing means adapting

2829-566: The brand. Film, television, radio, and advertisements publish information to their audiences. Computer games, streaming apps, and social media publish content in various ways that can keep audiences more engaged. Marketing additional products closely related to a major film, such as Star Wars , is an example of tie-in publishing. These products include but are not limited to spin-off books, graphic novels, soundtrack albums, computer games, models and toys, social media posts, and promotional publications. Examples of tie-in publishing based on books are

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2898-547: The consent of the copyright holder, which initially is always the author. In the Universal Copyright Convention , "publication" is defined in Article VI as "the reproduction in tangible form and the general distribution to the public of copies of a work from which it can be read or otherwise visually perceived." Privishing ( priv ate publ ishing , but not to be confused with self-publishing )

2967-422: The discount given to retailers (usually around 45 percent). Small publishers, also called independent or indie publishers, operate on a traditional model (i.e. the author surrenders some rights in exchange for the publisher bearing all costs of publishing), but their precise terms can vary greatly. Often, they do not pay an advance on royalties. A hybrid publisher shares the costs of publication (and therefore

3036-409: The kinds of successes he had achieved following his method (as well as, perhaps, considering the contemporary European social climate of intellectual competitiveness, to show off a bit to a wider audience). The work was the first to propose the idea of uniting algebra and geometry into a single subject and invented an algebraic geometry called analytic geometry , which involves reducing geometry to

3105-576: The mainstream publishing industry to a handful of big publishers as it adapted to digital media. The merger created the largest consumer book publisher globally, with a global market share of more than 25 percent. As of 2022 , approximately 80% percent of the United States trade market for books was controlled by the " Big Five " publishing houses: Penguin Random House , Hachette , HarperCollins , Simon & Schuster , and Macmillan . In November 2020, ViacomCBS agreed to sell Simon & Schuster,

3174-402: The material was not arranged in a systematic manner and he generally only gave indications of proofs, leaving many of the details to the reader. His attitude toward writing is indicated by statements such as "I did not undertake to say everything," or "It already wearies me to write so much about it," that occur frequently. Descartes justifies his omissions and obscurities with the remark that much

3243-619: The maximum number of negative roots of the original polynomial. The polynomial has one sign change between the second and third terms, as the sequence of signs is (+, +, −, −) . Therefore, it has exactly one positive root. To find the number of negative roots, change the signs of the coefficients of the terms with odd exponents, i.e., apply Descartes' rule of signs to the polynomial f ( − x ) = − x 3 + x 2 + x − 1. {\displaystyle f(-x)=-x^{3}+x^{2}+x-1.} This polynomial has two sign changes, as

3312-578: The normal at any point of a curve whose equation is known. The construction of the tangents to the curve then easily follows and Descartes applied this algebraic procedure for finding tangents to several curves. The third book, On the Construction of Solid and Supersolid Problems , is more properly algebraic than geometric and concerns the nature of equations and how they may be solved. He recommends that all terms of an equation be placed on one side and set equal to 0 to facilitate solution. He points out

3381-418: The number of positive roots of the polynomial is either equal to the number of sign changes between consecutive (nonzero) coefficients, or is less than it by an even number. A root of multiplicity k is counted as k roots. In particular, if the number of sign changes is zero or one, the number of positive roots equals the number of sign changes. As a corollary of the rule, the number of negative roots

3450-434: The original polynomial. The following is a rough outline of a proof. First, some preliminary definitions: With these, we can formally state Descartes' rule as follows: Theorem  —  The number of strictly positive roots (counting multiplicity) of f {\displaystyle f} is equal to the number of sign changes in the coefficients of f {\displaystyle f} , minus

3519-429: The polynomial is known to have all real roots, this rule allows one to find the exact number of positive and negative roots. Since it is easy to determine the multiplicity of zero as a root, the sign of all roots can be determined in this case. If the real polynomial P has k real positive roots counted with multiplicity, then for every a > 0 there are at least k changes of sign in the sequence of coefficients of

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3588-573: The primary source of recording knowledge. For accessibility and global reach, this content can be repurposed for the web. The British Library , for example, holds more than 170 million items with 3 million new additions each year. With consent, content can be published online through e-books, audio books, CMS -based websites, online learning platforms, videos, or mobile apps. On the Internet, writers and copy editors are known as content writers and content editors, although their roles vary from their print-based counterparts. Advertising can provide income or

3657-489: The public interest, hold people and businesses to account, and promote freedom of information and expression. Editors manage the tone of voice of their publication; for example, negative versus positive articles can affect the reader's perspective. A journal is an academic or technical publication also available in digital and(or) print format, containing articles written by researchers, professors, and individuals with professional expertise. These publications are specific to

3726-457: The publishing industry in the US. Salon described the situation as a "lack of diversity behind the scenes in book world." A survey in 2020 by the same group found there has been no significant statistical change in the lack of diversity since the 2016 survey. Lack of diversity in the American publishing industry has been an issue for years. Within the industry, the least amount of diversity

3795-410: The publishing process to minimize environmental impact. One example is the concept of on-demand printing, using digital or print-on-demand technology. This cuts down the need to ship books since they are manufactured close to the customer on a just-in-time basis. A further development is the growth of online publishing, where no physical books are produced. The author creates an e-book and uploads it to

3864-442: The risks) with the author. Because of this financial risk, they are selective in what they publish. The contract varies according to what is negotiated between author and company, but will always include the surrender of some rights to the publisher. Hybrid publishing is the source of debate in the publishing industry, due to the tendency of vanity presses to masquerade as hybrids. A vanity press will publish any book. In return,

3933-435: The roots. This approach is used in the fastest algorithms today for computer computation of real roots of polynomials (see real-root isolation ). Descartes himself used the transformation x → − x for using his rule for getting information of the number of negative roots. The rule states that if the nonzero terms of a single-variable polynomial with real coefficients are ordered by descending variable exponent, then

4002-429: The same parity, we have Z ( f ) ≤ V ( f ) {\displaystyle Z(f)\leq V(f)} . Any n th degree polynomial has exactly n roots in the complex plane , if counted according to multiplicity. So if f ( x ) is a polynomial with real coefficients which does not have a root at 0 (that is a polynomial with a nonzero constant term) then the minimum number of nonreal roots

4071-483: The scribes of Europe had produced since Constantine founded his city in A.D. 330." The history of modern newspaper publishing started in Germany in 1609, with the publication of magazines following in 1663. Missionaries brought printing presses to sub-Saharan Africa in the mid-18th century. Historically, publishing has been handled by publishers , although some authors self-published. The establishment of

4140-400: The sequence of signs is (−, +, +, −) , meaning that this second polynomial has two or zero positive roots; thus the original polynomial has two or zero negative roots. In fact, the factorization of the first polynomial is so the roots are −1 (twice) and +1 (once). The factorization of the second polynomial is So here, the roots are +1 (twice) and −1 (once), the negation of the roots of

4209-735: The term refers to the creation and distribution of printed works , such as books , comic books , newspapers , and magazines . With the advent of digital information systems, the scope has expanded to include digital publishing such as e-books , digital magazines , websites , social media , music , and video game publishing . The commercial publishing industry ranges from large multinational conglomerates such as News Corp , Pearson , Penguin Random House , and Thomson Reuters to major retail brands and thousands of small independent publishers. It has various divisions such as trade/retail publishing of fiction and non-fiction, educational publishing, and academic and scientific publishing . Publishing

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4278-497: The third largest book publisher in the United States, to Penguin Random House in a deal that, if it had gone through, would have formed the largest publishing company in the world. On November 2, 2021, the United States Department of Justice filed a lawsuit (U.S. v. Bertelsmann SE & CO. KGaA, et al.) to block the merger on antitrust grounds, and on October 31, 2022, the D.C. District Court ruled in favor of

4347-540: The title. A book that is privished may be referred to as "killed." Depending on the motivation, privishing may constitute a breach of contract , censorship , or good business practice (e.g., not printing more books than the publisher believes will sell in a reasonable length of time). Publishing became possible with the invention of writing and became more practical upon the introduction of printing . Before printing, distributed works were copied manually by scribes . Due to printing, publishing progressed hand-in-hand with

4416-469: The type based on a matrix and hand mould . The invention of the printing press gradually made books less expensive to produce and more widely available. Early printed books, single sheets, and images created before 1501 in Europe are known as incunables or incunabula . "A man born in 1453, the year of the fall of Constantinople , could look back from his fiftieth year on a lifetime in which about eight million books had been printed, more perhaps than all

4485-453: The way the data is displayed is published. A textbook is an educational book, or e-book, that contains information on a particular subject and is used by people studying that subject. The need for textbook publishing continues due to the global need for education. Textbooks from major publishers are being integrated with online learning platforms for expert knowledge and access to a library of books with digital content. A university press

4554-527: Was deliberately omitted "in order to give others the pleasure of discovering [it] for themselves." Descartes is often credited with inventing the coordinate plane because he had the relevant concepts in his book, however, nowhere in La Géométrie does the modern rectangular coordinate system appear. This and other improvements were added by mathematicians who took it upon themselves to clarify and explain Descartes' work. This enhancement of Descartes' work

4623-527: Was in higher-level editorial positions. Publishing on specific contexts Publishing tools Descartes%27 rule of signs A linear fractional transformation of the variable makes it possible to use the rule of signs to count roots in any interval. This is the basic idea of Budan's theorem and the Budan–Fourier theorem . Repeated division of an interval in two results in a set of disjoint intervals, each containing one root, and together listing all

4692-462: Was primarily carried out by Frans van Schooten , a professor of mathematics at Leiden and his students. Van Schooten published a Latin version of La Géométrie in 1649 and this was followed by three other editions in 1659−1661, 1683 and 1693. The 1659−1661 edition was a two volume work more than twice the length of the original filled with explanations and examples provided by van Schooten and his students. One of these students, Johannes Hudde provided

4761-426: Was that all of their points could be obtained by construction from lower order curves. This represented an expansion beyond what was permitted by straightedge and compass constructions. Other curves like the quadratrix and spiral , where only some of whose points could be constructed, were termed mechanical and were not considered suitable for mathematical study. Descartes also devised an algebraic method for finding

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