Since 2008, *Convergence* has carried the feature “Mathematical Treasures.” This is a large collection, an archive, of images connected to the history of mathematics: its development, documentation, use, learning, and teaching. It has been assembled with several goals in mind, principally:

- to provide visual materials that can be used in mathematics instruction,
- to call attention to the rich variety of resources about and from the history of mathematics and where they might be obtained and explored further, and
- lastly, to attract researchers whose work could extend the impact and meanings of these objects.

Occasionally, members of the mathematical community have challenged the intent and richness of this collection with such objections as, "Whose treasures are they? I see no value in looking at a mathematical diagram in an old book." Such utterances are unfortunate, and I would advise the speaker to look, and see, more carefully. I believe anyone who loves mathematics can find a personally meaningful piece of mathematical history or heritage among *Convergence*'s collection of hundreds of mathematical treasures. And if not, there are many other sources! Seeking out and recognizing mathematical treasures is an adventure in which anyone can participate, especially in this age of freely accessible digital archives and of greater leeway in personal camera use in libraries, archives, and museums.

**Figure 1.** Cover of 1740 issue of *The Ladies Diary, or Woman's Almanack*, featuring a portrait of Caroline, Queen Consort of King George II from 1727 until her death in 1737. From the start, to further attract women readers, its editors displayed on its cover pictures of prominent English women, most often reigning queens, as well as slogans offering genteel and patriotic praise for women. By 1740, editors praised both the "charms" and "wit" of women. (*Source:* Princeton University Library via Google Books)

A recent treasure that I have discovered will, upon examination, raise little objection to its mathematical value. This is *The Ladies Diary, or the Womans Almanack*, a periodical published in England from 1704 to 1841. Despite its strange name and, by modern standards, grammatically incorrect spelling and punctuation, this modest 40-page annual was a milestone in the history of modern mathematics education. The *Diary*’s historical uniqueness and importance is supported by several facts:

- It was one of the first English language publications devoted to women.
- Women readers instigated and focused its content direction toward mathematics and problem solving.
- Through this almanac, women demonstrated both their interest and ability in mathematics at a time and within a culture in which mathematics was a “male activity.”
- Its popularity, surviving in a very competitive market for over 100 years, 1704–1840, is a testimony to its value and sustained interest.
- The
*Diary*was a precursor to the formal scientific journal. - The
*Diary*became a model to be actively emulated by an extended series of other periodicals promoting mathematical problem solving. - The evolution of mathematical interests demonstrated over the lifetime of the publication paralleled the mathematical movements taking place in England.
- Mathematically significant personages, both editors and correspondents, were involved in its development.

**Figure 2.** Black and white copy of the cover of the 1787 edition of the *Ladies' Diary or Woman’s Almanack*, which bears a portrait of Charlotte, who reigned as Queen Consort of King George III from 1761 until her death in 1818. (*Source:* Internet Archive, from a book held by Oxford University Library and digitized by Google.)

By the beginning of the 18^{th} century, England had asserted herself as a major international power. Her navy ruled the seas and her colonies, particularly those in North America, provided a lucrative trade network. The Industrial Revolution was just starting to take hold and the nation was experiencing a period of relative peace. Spawned by such advantageous conditions, a rising middle class of “Ladies and Gentlemen” was affecting English daily life. Usually offspring of financially and/or professionally successful parents, they disdained physical work and embraced fashion, pleasant manners and, most of all, leisure. A Gentleman would most likely attend a Public School where he would be exposed to Latin and Greek and be prepared for entering a university, preferably Oxford or Cambridge, or a profession of approved status. In contrast, Ladies, preordained as wives, would most likely be trained at home, learning domestic skills and appropriate behavior. A few might attend a private Ladies' Academy where they would be exposed to a limited set of higher arts contributing to polite behavior, such as music, singing and poetry.

Both sexes of the rising middle class, along with many who aspired to it, enjoyed reading both as a pastime and as a means for acquiring new knowledge of their rapidly changing world. To meet this need, publishers supplied a large and varied source of materials: newspapers, broadsheets, periodicals, and books. Principal among this collection of print material were almanacs (Capp, 1979). Such modest books, usually just a few pages in length, were very popular for their chronological referencing, supplying an augmented calendar noting official holidays, church feast days, and days of advised action, such as when to harvest or plant a crop or undertake a journey. Unfortunately, this predictive capacity most often involved astrology, a practice adhered to by many English common folk. Some almanac editors attempted to extend their scope of information, and the attractiveness of their publications, by including political diatribes and tantalizing anecdotes and gossip.

One such enterprising editor was John Tipper (1663-1713), a Coventry schoolmaster and sometime textbook author. Mindful of the growing leisure class of young women and their intellectual restlessness, he conceived of an almanac just for women, the *Ladies Diary or Woman's Almanack. *At this time there were no specific periodicals or magazines for women. In the latter part of the seventeenth century, a publisher, John Dutton, had attempted two journals designed for women, but his content demeaned and preached to its female readers. These journals failed quickly. Tipper believed he could cater successfully to the “Fair Sex” by supplying “genteel” subject matter, such as household tips, recipes, health advice, poems, and “delightful” romantic stories, along with the standard calendar and chronological reckonings of an almanac. His program was devised without any female input, not even that of his own wife.

**Figure 3.** A typical almanac calendar page, this one for the month of April, 1831, from the 1831 *Ladies Diary.* Pages like this one, featuring meaning and ordering of numerals, comprised about one third of the *Ladies Diary. *Such pages became familiar to readers and helped advance numeracy. (*Source:* HathiTrust Digital Archive, from a book held by Harvard University Library and digitized by Google)

One prominent feature of Tipper's *Ladies Diary* was the inclusion of "enigmas," or word puzzles, a pastime that was all the rage among English women at the time. This practice had been adopted from France, where fashionable ladies asserted themselves by demonstrating their wit and knowledge through posing and solving such riddles. Tipper encouraged interaction and correspondence, both with himself and between his readers, and much of it was about these puzzles.

**Figure 4.** A typical "enigma" puzzle from* the Ladies Diary* of 1835 (p. 27). The answer is "a candle."

At this time, the publishing of all almanacs in England was controlled by the London-based Worshipful Company of Stationers, a monopoly instituted by royal decree (Feist, 2005). Thus, John Tipper had to secure this organization's compliance in publishing and marketing his proposed periodical. The Company reluctantly agreed, but limited the first release to just three thousand issues and demanded a higher-than-market sales price for the almanac. Despite such misgivings and limitations, the* Ladies Diary* was a great success from its first issue in 1704, and remained so for the next century and a half, becoming one of the longest continuously running periodicals in the history of Great Britain.

After the initial 1704 issue of the *Ladies Diary,* editor John Tipper maintained his original format of the materials he thought would please women readers, but soon these readers made their wishes known. They particularly liked the "enigma" puzzles whose correct solutions earned prizes. The answers and their prizewinners would be revealed in the following issue. While the *Diary* was a women’s periodical, men were also drawn to its contents and joined the ladies as puzzle-solvers and correspondents. In the 1707 issue of the *Diary*, the editor acknowledged a “Mr. John White from Rutterly in Devon” who had sent in correct answers for the previous year’s enigmas and also enclosed two of his own “arithmetical enigmas,” shown in Figure 5 below.

**Figure 5.** Two problems originally posed in the *Ladies Diary* of 1707 were reprinted on the first page of Volume I of Thomas Leybourn's 1817 *Mathematical Questions Proposed in the Ladies’ Diary and Their Original Answers, together with Some New Solutions, from its Commencement in the Year 1704 to 1816* (4 vols.). (*Source:* HathiTrust Digital Archive, from a book held by the University of Michigan Library and digitized by Google)

By 1709, the almanac’s readership was requesting more of these word puzzles, both in enigmatic form and arithmetical in nature. Tipper complied, noting a change in policy and set new standards that would radically alter the mathematical and educational impact of his publication. First, he revised his content to comply with his female readers' preference for intellectually challenging problem-solving situations over cooking advice:

Having observed by a multitude of Letters I have receive from all parts of the Kingdom, That the *Enigmas, *an *Arithmetical Questions, *above all other Particulars, give the greatest Satisfaction and Delight to the obliging Fair, I shall in the Diary insist the Longer upon them, and for that Reason defer the *Receipts of Cookery, &*c. to a more favourable Opportunity: And First of the Nature. (*Ladies Diary,* 1709, p. 3)

Secondly, he cautioned that the arithmetical problems be within the capacity of his women readers:

I have received several *Arithmetical Questions *which are Very unfit for this place; my design being not to *puzzle, *but to *Please; *not to *perplex the Understanding, *but to *exercise the *wit, and a moderate knowledge in *Numbers;* and therefore those who are pleased to send me any *Arithmetical Questions, *I desire they may be very *Pleasant,* and not *too hard; *and likewise that they may be proposed in *verse; *which will still be the more taking among the Ladies. (*Ladies Diary,* 1709, p. 3)

The reserved and socially constrained "Ladies" of England wanted to do mathematics! John Tipper’s accommodation and solicitation for mathematics problems acknowledged the lack of mathematical training provided young women. If they had acquired skills in mathematics, it was usually through self-study and or tutoring by liberal-minded parents or a governess. The prevailing conception held was that females could not engage in anything scientific, let alone mathematics; exposure to it would “fever their brains.” However, the first prize problem was sent in by a man and answered correctly by Mrs. Mary Wright. Over several years, Mrs. Wright would distinguish herself by solving many of the mathematical problems set in the *Diary.* While the problem was originally given as a lengthy, verbose, one-page verse, it was simply summarized when reprinted with its solution:

**Figure 6.** A problem originally posed in the *Ladies Diary* of 1709, together with its solution by prolific problem-solver Mary Wright, was reprinted on page 12 of Volume I of Thomas Leybourn's *Mathematical Questions Proposed in the Ladies’ Diary and Their Original Answers ... *(1817).

The requirement that problem and answer submissions had to be in verse had been yet another aspect of the *Diary* promoting gentility and catering to an existing fashionable trend; it was believed that word play, as rendered in verse, marked an agile mind. However, Tipper’s acquiescence in increasing the number of enigmas and adding mathematics problems was a fateful move. It changed the essence and intent of the *Ladies Diary* to make it a problem-solving journal, a function for which it would be recognized and in which it would excel for over a century.

While the* Ladies Diary*, over the course of its life, would be directed by a variety of editors, each imposing his particular objectives and experiences, the basic features established by Tipper dominated the* Diary*:

- The cover exhibited a portrait of the reigning queen.
- An almanac calendar was provided accompanied by astronomical details.
- Answers to previous puzzles, enigmas, paradoxes and mathematical problems would be given and then new sets of puzzles and problems would be posed for the year. Prize questions and enigmas would be designated.
- Occasionally, an expository article on a scientific or mathematical concept would be included. (See Figure 7).
- The scientific integrity of the content was upheld.

**Figure 7.** Editor John Tipper was especially interested in astronomy and published several articles on the subject, including this one in the 1709 *Ladies Diary* (p. 3). The prediction Tipper reported here had been made by Edmund Halley ("The Ingenious Captain Hally") in 1705.

John Tipper died in 1713 and the editorship of the *Diary *passed through the hands of several individuals:

- Henry Beighton, 1714-1743;
- Henry’s wife, Elizabeth Beighton, assisted by Anthony Thacker, 1744;
- Robert Heath, 1745-1760;
- Thomas Simpson, 1754-1760;
- Edward Rollinson, 1761-1773;
- Charles Hutton, 1774-1818 and
- Olinthus Gregory, 1819-1840.

Tipper was a dedicated schoolmaster, particularly knowledgeable in astronomy, who exerted great efforts, as editor, in pleasing the women readers. Henry Beighton was an engineer and inventor, more interested in the applications of mathematics. Anthony Thacker was a skilled mathematician and Robert Heath, a military engineer. Rollinson was an avid mathematics problem solver, quite familiar with that aspect of the* Ladies Diary. *Simpson, Hutton, and Gregory were well-respected mathematicians and instructors of mathematics at the Royal Military Academies. Several of these men were elected Fellows of the Royal Society (FRS) and Charles Hutton was even considered by some to be the greatest English mathematician of his time (Wardhaugh, 2017).

**Figure 8.** Charles Hutton (1737-1823)

All of these editors were professionals whose work seriously involved them in the study and uses of mathematics. Accordingly, they brought their experiences into their editorship tasks and, with each new editor, the mathematical tenor of the *Diary* changed: the mathematics became more difficult and the problem situations became more complex and directed towards applications. The ability to grapple with the new forms of mathematical problems was beyond the limited educational preparation and contextual interest of many females. Ostensibly, the periodical was still meant for women, but the mathematical direction it had taken eliminated most female participation in this former area of involvement. Women, as problem solvers, still excelled and dominated at finding the solutions to enigmas and other word puzzles.

In the first few years of the *Diary*’s existence, mathematical problems reflected the traditional recreational themes: “Guess my age,” “Find the number such that...." However, that soon began to change to more timely, relevant subjects. A chronological survey, sampling mathematical problems from some ensuing years, may be informative for readers.

Year |
Mathematical Question |
||

1714 | From a given cone to cut the greatest cylinder possible. | ||

1739 | Suppose a cask in the form of a middle frustum of a hyperbolic spindle, whose length is 24 inches, bung diameter 30, head diameter 20, and traverse axis of the generating hyperbola 100 inches. Required its content in ale gallons? | ||

1743 |
Three staves being erected, or set up on end, in some certain place on earth, perpendicular to the plane of the horizon, in the points A, B, and C; whereof that which is at A, is 6 feet long; that in B,18; that in C, 8; the line AB being 33 feet long: It happens on a certain day in the year, that the end of the shadow of the staff A passes through the points B and C; and the staff B through A and C; and of the staff C, through the point A. To find the sun’s declination, and the elevation of the pole or day, and the place where this shall happen. [Both René Descartes and Isaac Newton unsuccessfully grappled with this problem!] (Albree and Brown, 2009, p. 18) |
||

1759 | To determine the curve in which a body must move, so as to continue always at the invariable distance from another body moving uniformly in a right line; the velocity of the former body being also uniform, and exceeding that of the latter, in any given ratio. | ||

1802 | Given the base and height of a cone, it is required to find the height of the greatest parabolic conoid which can be inscribed in the cone? | ||

1825 | Describe equilateral triangles (the vertices being all outward or inward) upon the three sides of any triangle ABC: then the lines which join the centres of gravity of those three equilateral triangles will constitute an equilateral triangle. Required a demonstration. [This is a variation of “Napoleon’s Theorem.”] | ||

1840 | If the lines bisecting the angles of a scalene triangle meet the opposite sides in three points, and each side of the triangles formed by joining these points be produced to meet a line drawn to its adjacent angle parallel to its opposite side, the three points of intersection will be in the one and the same straight line. Required a demonstration. |

**Table 1. **Sample problems from the *Ladies Diary*

Problem situations became more dynamical, theoretical, and philosophical in nature, with many coming from physics and other applied sciences. This was perhaps a reflection of the prevailing Industrial Revolution impacting Great Britain. Compilations of the* Ladies Diary*’s mathematical problems and their solution schemes were in great demand. Several were published, the most popular collection being that of Thomas Leybourn. Leybourn (1770-1840) was a British mathematician and teacher at the Royal Military Academy, Sandhurst. He edited and published several mathematical periodicals, but his most popular work was his compilation of the mathematical problems from the *Ladies Diary.* This valuable resource, which has the answers for the above problems, among many others, can be consulted today via the HathiTrust Digital Archive.

**Figure 9.** Title page for Volume I (of 4 volumes) of Thomas Leybourn's *Mathematical Questions Proposed in the Ladies' Diary, and Their Original Answers, Together with Some New Solutions* (1817). (*Source:* HathiTrust Digital Archive, from a book held by the University of Michigan Library and digitized by Google.)

While the problems themselves offered a challenge for the *Diary*’s readers, personal satisfaction was brought by the publication of correct solutions for the problems and, especially, by the supplying of demonstrations and explanations of the solution process. This feedback both strengthened the mathematical confidence of the problem solvers and further increased their knowledge of mathematical techniques. As an example, shown below is a problem from the 1720 issue of the *Diary* as duplicated in Leybourn’s collection (Leybourn, 1817, p. 100). The “Scholium” was added by Charles Hutton, who signed his notes "H".

**Figure 10.** Problem, or question, and solution from the *Ladies Diary* of 1720, as it appears on page 100 of Volume I of Leybourn's 1817 *Mathematical Questions Proposed in the Ladies’ Diary ...*. (*Source:* HathiTrust Digital Archive, from a book held by the University of Michigan Library and digitized by Google.)

Although perhaps not recognized at the time, the appearance of the* Ladies Diary* at the beginning of the eighteenth century was more than an opportunist business venture; it was a fortunate event in the popular mathematical movements taking place at the time. When Queen Elizabeth I (who reigned from 1558 to 1603) was prompted by her advisors to support mathematical studies within her realm as an aid to navigation and increased trade, she shifted the responsibility to her business community, saying "Since this practice would most benefit them, let the merchants and traders support investment in mathematics training for the common people." And they did! Henry Billingsley (d. 1606), a London milliner, published the first English language translation of *Euclid’s Elements* in 1570. Robert Recorde (ca. 1570-1658) wrote a series of accessible mathematics books in English.

**Figure 11.** Title page of *The Elements of Geometrie of ... Euclide,* Henry Billingsley’s English translation of Euclid's *Elements. *For additional images and information, see "Mathematical Treasures - Billingsley's Euclid" here in *Convergence*.

The large trading companies, such as the Muscovy and East India corporations, hired mathematical consultants to train their navigators. Both John Dee (1527-1609) and Robert Recorde (ca. 1570-1658) worked for the Muscovy Company (O'Connor and Robertson, 2002), while Thomas Harriot (1560-1621) trained navigators for Walter Raleigh's expeditions (Ross, 1975, p. 50). Meanwhile, Leonard Digges and his son Thomas Digges (1546-1595) wrote books on surveying and cartography, and Thomas wrote a military manual, all in English (O'Connor and Robertson, 2002). Books like these, written in the common English language and promising beneficial and rewarding knowledge, were readily consumed. This new trend of basic mathematics books stressing the uses of the subject in daily life caught on and many applied books on topics such as surveying, navigation, gauging, and commercial computations were published to satisfy the ready market. Two examples are shown in Figure 12. Mathematical study groups such as the Spitalfields Society sprung up around the country (Cassels, 1979, 1980). Free mathematical lectures and instruction were provided in London coffeehouses. The services of reckoning teachers became available for private tuition and patrons emerged to fund mathematics schools and academies. The most notable of these new institutions was the Royal Mathematical School founded at Christ’s Hospital, London, in 1673 (Jones, 2015).

**Figure 12.** In the 17th century, a variety of self-learning resources appeared. The *Pocket Book* (1677), shown at left, by John Seller, was such a resource. (Four additional pages from this book can be seen here in *Convergence*.) The book on the right, John Taylor’s *Treasury of Mathematicks,* was very popular. (Seven additional pages from this book can be seen here in *Convergence*.) England, especially the region around London, became the realm of “mathematical practitioners,” skilled users of mathematics.

From the 17th through the early 18th centuries, the momentum of popular mathematics appreciation and learning grew. New sources, opportunities, and challenges were needed to feed the movement. Problem-solving exercises helped to satisfy the need for new experiences, creativity, and the further enrichment of this expanding area of acquired knowledge. The* Ladies Diary,* with its changing selection of mathematical problems and published solution schemes, supporting discussions, and advice, satisfied a waiting and ready audience. So successful was this feature that it encouraged the emergence of a large number of similarly styled publications: periodicals, newspaper columns, and compilations devoted to mathematical problem solving. While the* Ladies Diary* can be classified as a journal devoted to recreational mathematics, a few of the emerging periodicals were more academic and rigorous in their mathematical considerations and would eventually evolve into proper “research journals.” Thus, the *Diary*’s legacy of promoting the exploration and investigation of mathematical problems in actuality advanced the growth and enrichment of mathematics.

While the format of the* Ladies Diary* was admired and copied in Great Britain, it was also exported to the Continent and North America. George Baron (1769-1812), an immigrant from England, became a mathematics instructor at the new American Military Academy at West Point. In 1804, Baron began to publish a mathematical periodical directly fashioned after the* Ladies Diary*. He called it the *Mathematical Correspondent.* As a young man in England, he had solved several problems in the *Diary* and felt that a journal of its kind would benefit the people of his new country. Soon after initiating this project, Baron died. Editorship of the fledgling journal passed into the hands of Robert Adrain (1775-1843), also an expatriate from England and a self-taught mathematician (Swetz, 2008, p. 334). Baron had managed the *Correspondent* poorly and its new editor could not save it. It faltered, but in 1808 Adrain began a new journal, *The Analyst or Mathematical Museum,* which also reflected the *Diary *in its purpose and composition. But readers found its mathematics too difficult and this journal lasted only until 1814. A schoolmaster in New York City, Melatiah Nash (ca. 1768-1830), published another periodical influenced by the *Ladies Diary*. Started in 1820, he called his publication the *Ladies and Gentleman’s Diary. *It lasted only two years. Despite these stops and starts, the beginnings of popular mathematics literature in the United States can be traced to the *Ladies Diary,* the English almanac designed for women and begun in 1704 by a Coventry schoolmaster.

By the middle of the nineteenth century, mathematics institutions for learning and teaching, had become more formally established in Great Britain. New philosophies in teaching and textbook writing greatly improved the opportunities for the learning of mathematics. Industrial and technological advances heightened the recognition and importance of applied mathematics. With the availability of these resources, sales of the *Ladies Diary* decreased and it was amalgamated with a companion journal in 1841 to become *The Lady’s and Gentleman’s Diary*, a publication that would serve problem-solvers for the next thirty years.

**Figure 13.** Cover of the last issue of the *Ladies' Diary,* featuring Queen Victoria, who reigned from 1837 until her death in 1901.

Let the final comments be from a qualified observer of the period, John Playfair (1748-1819), an eminent mathematician, highly respected teacher, and active mathematical reformer. In a detailed 1808 review of the published volumes of Laplace’s *Traité de Mécanique Céleste, *Playfair lamented England’s scientific isolation from the Continent. Further commenting on the state of British mathematics, he noted:

At the same time that we state these facts as incontrovertible proofs of the inferiority of the English mathematicians to those of the Continent, in the higher departments; it is but fair to acknowledge, that a certain degree of mathematical science, and indeed no inconsiderable degree, is perhaps more widely diffused in England, than in any other country of the world. The Ladies' Diary, with several other periodical and popular publications of the same kind, are the best proofs of this assertion. In these, many curious problems, not of the highest order indeed, but still having a considerable degree of difficulty, and far beyond the mere elements of science, are often to be met with; and the great number of ingenious men who take a share in proposing and answering these questions, whom one has never heard of any where else, is not a little surprising. Nothing of the same kind, we be believe, is to be found in any other country. The Ladies Diary has now been continued for more than a century.... (Playfair, 1808, p. 282)

Playfair went on to berate the "enigma" puzzles of the *Diary* as foolish and a waste of time, an opinion that many, myself included, would consider incorrect. Rather, the enigma was another form of problem-solving. Playfair had high praise for the "geometrical part" of the *Diary:*

The geometrical part, however, has always been conducted in a superior style; the problems proposed have tended to awaken curiosity, and the solutions to convey instruction in a much better manner than is always to be found in more splendid publications. If there is a decline, therefore, or a deficiency in mathematical knowledge in this country, it is not to the genius of the people, but to some other cause that it must be attributed. (Playfair, *ibid.*)

The “other cause” Playfair referred to was the tradition bound, conservative rationale for the learning and teaching of mathematics held by the English: that is, mathematics viewed mainly as a commercial activity or merely as a mental exercise of limited worth to a gentleman and of no value or relevance to a lady. Both the social and intellectual changes of the nineteenth century were rapidly altering this situation and the *Ladies Diary* served as a major forerunner and provocateur of these changes.

Albree, Joe and Scott H. Brown. 2009. “A valuable monument of mathematical genius:* The Ladies Diary* (1704-1840).” *Historia Mathematica.* 36:10-47.

Blagden, Cyprian. 1977. *The Stationers**’** Company: A History, 1403-1959.* Palo Alto, CA: Stanford University Press. (Originally published 1960. London: Allen and Unwin.)

Capp, Bernard. 1979. *Astrology and the Popular Press*: *English Almanacs, 1500-1800.* London: Faber & Faber*.*

Cassels, S. W. 1979, 1980. “The Spitalfields Mathematics Society.” *Bulletin of the London Mathematical Society. *(1979) 11:241-258. (1980) 12:343.

Costa, Shelly. 2002. “*The Ladies Diary: *Gender*, *Mathematics and Civil Society in Early Eighteenth Century England.”* Osiris*. 17:49-73.

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Wardhaugh, Benjamin. 2017. “Charles Hutton: One of the Greatest Mathematicians in Europe.”* British Society for the History of Mathematics Bulletin, *32:1-91, 99.