Distant Reader - subject-mathematic-freebo

Introduction

This is a Distant Reader "study carrel", a set of structured data intended to help the student, researcher, or scholar use & understand a corpus.

This study carrel was created on 2021-05-24 by Eric Morgan <emorgan@nd.edu>. The carrel was created using the Distant Reader zip2carrel process, and the input was a Zip file locally cached with the name input-file.zip. Documents in the Zip file have been saved in a cache, and each of them have been transformed & saved as a set of plain text files. All of the analysis -- "reading" -- has been done against these plain text files. For example, a short narrative report has been created. This Web page is a more verbose version of that report.

All study carrels are self-contained -- no Internet connection is necessary to use them. Download this carrel for offline reading. The carrel is made up of many subdirectories and data files. The manifest describes each one in greater detail.

Size

There are 21 item(s) in this carrel, and this carrel is 744,595 words long. Each item in your study carrel is, on average, 35,456 words long. If you dig deeper, then you might want to save yourself some time by reading a shorter item. On the other hand, if your desire is for more detail, then you might consider reading a longer item. The following charts illustrate the overall size of the carrel.

Readability

On a scale from 0 to 100, where 0 is very difficult and 100 is very easy, the documents have an average readability score of 94. Consequently, if you want to read something more simplistic, then consider a document with a higher score. If you want something more specialized, then consider something with a lower score. The following charts illustrate the overall readability of the carrel.

Word Frequencies

By merely counting & tabulating the frequency of individual words or phrases, you can begin to get an understanding of the carrel's "aboutness". Excluding "stop words", some of the more frequent words include:

line, one, sine, angle, may, will, first, two, side, given, right, radius, shall, tangent, find, altitude, proportion, number, declination, second, distance, point, foot, equal, hour, must, place, lines, square, make, difference, latitude, parts, take, found, sines, angles, co, inches, meridian, therefore, complement, set, non, say, also, sides, time, now, required

Using the three most frequent words, the three files containing all of those words the most are The sector on a quadrant, or A treatise containing the description and use of four several quadrants two small ones and two great ones, each rendred many wayes, both general and particular. Each of them accomodated for dyalling; for the resolving of all proportions instrumentally; and for the ready finding the hour and azimuth universally in the equal limbe. Of great use to seamen and practitioners in the mathematicks. Written by John Collins accountant philomath. Also An appendix touching reflected dyalling from a glass placed at any reclination., Mathematicall recreations. Or, A collection of many problemes, extracted out of the ancient and modern philosophers as secrets and experiments in arithmetick, geometry, cosmographie, horologiographie, astronomie, navigation, musick, opticks, architecture, statick, mechanicks, chemistry, water-works, fire-works, &c. Not vulgarly manifest till now. Written first in Greeke and Latin, lately compi''ld in French, by Henry Van Etten, and now in English, with the examinations and augmentations of divers modern mathematicians whereunto is added the description and use of the generall horologicall ring: and the double horizontall diall. Invented and written by William Oughtred., and The country-survey-book: or Land-meters vade-mecum Wherein the principles and practical rules for surveying of land, are so plainly (though briefly) delivered, that any one of ordinary parts (understanding how to add, substract, multiply and divide,) may by the help of this small treatise alone and a few cheap instruments easy to be procured, measure a parcel of land, and with judgment and expedition plot it, and give up the content thereof. With an appendix, containing twelve problems touching compound interest and annuities; and a method to contract the work of fellowship and alligation alternate, very considerably in many cases. Illustrated with copper plates. By Adam Martindale, a friend to mathematical learning..

The most frequent two-word phrases (bigrams) include:

roman non, versed sine, right angled, one foot, equal parts, sine co, versed sines, suns declination, nearest distance, suns altitude, right line, right angles, sine complement, angle sought, two sides, meridian line, given angle, given side, meridian altitude, english books, early english, side sought, right angle, right ascension, angle opposite, sine tangent, right hand, tangent co, opposite side, half sum, books online, hour lines, like manner, sine sine, foot long, shall reach, one side, one point, two angles, three sides, triangle abc, third side, tangent complement, one another, suns azimuth, right edge, superficial content, two places, left hand, angle required

And the three file that use all of the three most frequent phrases are Due correction for Mr Hobbes· Or Schoole discipline, for not saying his lessons right. In answer to his Six lessons, directed to the professors of mathematicks. / By the professor of geometry. The trissotetras: or, a most exquisite table for resolving all manner of triangles, whether plaine or sphericall, rectangular or obliquangular, with greater facility, then ever hitherto hath been practised: most necessary for all such as would attaine to the exact knowledge of fortification, dyaling, navigation, surveying, architecture, the art of shadowing, taking of heights, and distances, the use of both the globes, perspective, the skill of making the maps, the theory of the planets, the calculating of their motions, and of all other astronomicall computations whatsoever. Now lately invented, and perfected, explained, commented on, and with all possible brevity, and perspicuity, in the hiddest, and most re-searched mysteries, from the very first grounds of the science it selfe, proved, and convincingly demonstrated. / By Sir Thomas Urquhart of Cromartie Knight. Published for the benefit of those that are mathematically affected., and An introduction of the first grounds or rudiments of arithmetick plainly explaining the five common parts of that most useful and necessary art, in whole numbers & fractions, with their use in reduction, and the rule of three direct. Reverse. Double. By way of question and answer; for the ease of the teacher, and benefit of the learner. Composed not only for general good, but also for fitting youth for trade. / By W. Jackson student in arithmetick..

While often deemed superficial or sophomoric, rudimentary frequencies and their associated "word clouds" can be quite insightful:

Keywords

Sets of keywords -- statistically significant words -- can be enumerated by comparing the relative frequency of words with the number of times the words appear in an entire corpus. Some of the most statistically significant keywords in the carrel include:

tcp, meridian, line, suns, angle, south, proportion, triangle, table, rule, radius, circle, azimuth, tangent, sine, reader, prop, prob, north, latitude, horizon, geometry, figure, english, difference, diameter, content, compasses, center, altitude, west, vowel, time, timber, thread, syllable, sunne, sun, sum, subtendent, square, son, secant, scale, roman, rockets, resolver, rank, quadrant, prov

And now word clouds really begin to shine:

Topic Modeling

Topic modeling is another popular approach to connoting the aboutness of a corpus. If the study carrel could be summed up in a single word, then that word might be 10, and The description and use of a joynt-rule fitted with lines for the finding the hour of the day and azimuth of the sun, to any particular latitude, or, to apply the same generally to any latitude : together with all the uses of Gunters quadrant applyed thereunto ... / contriv''d & written by J. Brown, philomath. is most about that word.

If the study carrel could be summed up in three words ("topics") then those words and their significantly associated titles include:

If the study carrel could be summed up in five topics, and each topic were each denoted with three words, then those topics and their most significantly associated files would be:

Moreover, the totality of the study carrel's aboutness, can be visualized with the following pie chart:

Noun & Verbs

Through an analysis of your study carrel's parts-of-speech, you are able to answer question beyonds aboutness. For example, a list of the most frequent nouns helps you answer what questions; "What is discussed in this collection?":

line, side, angle, sine, number, distance, parts, point, foot, proportion, difference, lines, inches, place, length, hour, time, sides, altitude, degrees, declination, part, thread, tangent, -, angles, d, end, way, example, day, complement, numbers, feet, figure, measure, b, deg, table, co, extent, use, hours, sum, sines, viz, work, square, latitude, points

An enumeration of the verbs helps you learn what actions take place in a text or what the things in the text do. Very frequently, the most common lemmatized verbs are "be", "have", and "do"; the more interesting verbs usually occur further down the list of frequencies:

is, be, are, have, being, given, find, make, take, found, was, say, said, set, required, were, made, let, draw, do, had, according, sought, having, been, finde, divided, see, taken, done, called, makes, put, lay, added, drawn, give, placed, did, know, fall, angled, note, come, suppose, laid, shew, measure, multiply, divide

Proper Nouns

An extraction of proper nouns helps you determine the names of people and places in your study carrel.

〉, sine, ◊, 〈, radius, line, angle, c., suns, meridian, latitude, tangent, sines, sun, azimuth, quadrant, north, south, ab, c, triangle, circle, altitude, declination, center, ●, s., a, east, prop, west, complement, square, b, ark, arch, m, diameter, s, scale, co, base, rule, glasse, hour, -, cosine, angles, ac, horizon

An analysis of personal pronouns enables you to answer at least two questions: 1) "What, if any, is the overall gender of my study carrel?", and 2) "To what degree are the texts in my study carrel self-centered versus inclusive?"

it, you, i, your, his, their, them, they, he, we, my, its, him, us, me, our, thy, her, themselves, one, she, thee, himself, yours, ''s, s, mine, ours, em, ∷, whereof, p, yourself, ye, ts, u, ty, thou, nour, l, e, ♓, ●, †, yt, wil, whosoever, whee, vp, throng

Below are words cloud of your study carrel's proper & personal pronouns.

Adjectives & Verbs

Learning about a corpus's adjectives and adverbs helps you answer how questions: "How are things described and how are things done?" An analysis of adjectives and adverbs also points to a corpus's overall sentiment. "In general, is my study carrel positive or negative?"

other, first, same, -, second, equal, right, non, roman, third, many, such, greater, more, fourth, true, former, great, whole, last, much, square, little, opposite, good, lesser, less, small, plain, like, double, perpendicular, next, several, equall, nearest, long, common, general, greatest, versed, own, sine, natural, parallel, middle, new, solid, left, large

then, so, not, thus, therefore, also, now, as, first, here, out, more, on, thereof, very, only, together, before, is, that, down, again, well, off, most, much, up, right, yet, never, just, there, long, onely, else, all, lastly, twice, in, easily, sometimes, secondly, likewise, too, always, otherwise, over, once, ever, already

Next steps

There is much more to a study carrel than the things outlined above. Use this page's menubar to navigate and explore in more detail. There you will find additional features & functions including: ngrams, parts-of-speech, grammars, named entities, topic modeling, a simple search interface, etc.

Again, study carrels are self-contained. Download this carrel for offline viewing and use.

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