A project on which I spent a bit of time, today, was cataloguing old, family books that are in my possession. As with other physical possessions, I will be attempting to dispose of the books - either to family, local (to the area in which the original owners lived) museums, or to a different spot in our basement.
Each time I have gone through the books in the past 20-30 years, I have come across so many items of interest that it is difficult to remain on task. (The file linked at the bottom is the listing that I made of the books.)4
Stu and I have had, on occasion, an email exchange concerning what each of us meant by certain wording that each of us used. As Stu is fluent in several languages, and as I am semi-fluent only in English, I generally learn more from these exchanges than does he; but, he is game and sticks with me in the effort. One of the books that intrigued me, today, is Ray's Arithmetic, Third Book: Practical Arithmetic1 (published before 1900, at which time Grandmother was 16 years old) which just happens to use some of the mathematical terms that Stu and I have discussed. It is a fascinating book that leads the presumed student, step-by-step through mathematics that one was to learn in USA third grade. Starting with a major section of the book, these are the things one is to learn.
XI. COMMON FRACTIONS
Articles 121 through 124 are untitled, but Article 124 includes, "Fractions are divided into two classes, Common and Decimal."
Article 125. ANOTHER METHOD
Article 126 through128 are untitled.
Article 129. DEFINITIONS which provides definitions of the following: Fraction, Improper Fraction, Simple Fraction, Compound Fraction, Mixed Number, and Complex Fraction.
Article 130. PARTS OF FRACTIONS
Article 131. GENERAL PRINCIPLES
Articles 132 through 136 are untitled, but include some of the general principles.
Article 137. REDUCTION OF FRACTIONS
Articles 138 through 164 continue to present mathematical operations on fractions.
Article 165. PROMISCUOUS EXAMPLES - Gee, folks, I probably should leave you in the dark about what the term means (it is certainly not defined in the book); but, from context, I gather that it presents 21 problems that advanced (read: smarter) kids might be encouraged to attempt to solve.
XII. DECIMAL FRACTION which contains Articles 166 through 190
XIII. RATIO which contains Articles 191 through 196
XIV. PROPORTION which contains Articles 197 through 205
XV. ALIQUOTS, OR PRACTICE which contains Articles 206 and 207 - Perhaps I should let you look up "aliquots"; but, having read in the book that "One number is an aliquot part of another, when it will exactly divide it (Art. 110). Thus, 5 cents, 10 cts, 20 cts., &c., are aliquot parts of $1." I'll let you in on it.
There are a total of 28 sections, concluding with
I should have reviewed this little (4" wide x 6.5" tall x 1" thick - 336 pages) book before starting discussions with Stu on fractions, ratios, and permutations.
In an 11-page pamphlet re-printed when I was two years old (that would be 1940), CLOTHING: I.--Sewing Practices for the Beginner2, are the instructions for sewing an apron for oneself.
... you may make an apron according to the directions which follow.
Checked or plaid gingham is used for the apron and is made with a hem at the top which serves as a casing for a tape or belt. Cut the material in a size suitable for the girl who will wear it. An apron 16 inches long and 24 inches wide is a good size for a completed apron for a girl of ten years. In estimating the amount of material necessary to make this apron, allow enough for hems to finish at the top, bottom and sides of the apron.
Straighten the edges by drawing a thread. Turn a hem one inch wide at the top. The hem at the bottom may be 1 1/2 inches wide, and at the sides may be turned the width of the checks or according to the plaid in the ginham. Turn and cut out the corners as shown on page 27 of Extension Circular 373, "If You Would Learn to Sew." Baste all hems carefully and stitch close to the edge of the fold with thread which harmonizes with the color of the material. Tie threads securely and overhand at the corners. Press the finished apron carefully and insert a tape or fabric belt in the top hem for a tie. If desired the top of the apron may be gathered into a belt which is long enough to tie at the back. See page 15 of Extension Circular 373, "If You Would Learn to Sew."
If you wish to know how well you have made your apron, check it with the following:
1. Are the hems folded evenly?
2. Is the machine stitching straight and near the edge?
3. Did you use a thimble in basting and overhanding ends?
4. Have the basting threads been removed?
5. Is the apron clean and well pressed?
What intrigues me is comparing the above directions which take exactly one page of the pamphlet (the only illustrations are in the referenced circular, which the sewer probably won't have on hand!) to the video and color illustrations that would be in a sewing guide published, today. Below, I embed a video - just in case you don't wish to take my word for it.
Obviously, the video wants one to make a much fancier apron than the 1940 pamphlet addresses.
Grandmother had a book on citizenship - The American Citizen: West Virginia Edition3 published in 1897. I found the following section compelling. It is contained in a chapter on "The People Acting in Congress"
The Federal Union. -- For a little while after the War of Independence, the States tried the experiment of acting almost independently of each other. It proved a bad and dangerous experiment. New York might make laws to hurt or to tax the commerce of the people of New Jersey or Connecticut. There was no sure way to provide for the common good or the defence of the States. There was no treasury with money in it, or the means to secure money, to provide for the large debt which the Confederation had borrowed to carry on the war. [Omitted two sentences concerning the 1787 convention in Philadelphia.] It [the Convention] worked out the plan for our present Union, and recommended it to the people. According to the new plan the States agreed, by the vote of their people, to give up some of their independence, and to commit to Congress the charge of matters which concern all the people of the nation. No State now could do anything to injure the people of another State. No State could erect custom-houses on its boundaries to collect taxes from the commerce of the other States. The Union could have a treasury and courts with the necessary authority to command obedience. No State could justly resist the authority of the general government; neither could any State withdraw from the others and set up and independent government. Since permanent union proved to be for the general good, it was not only unfair for any State selfishly to threaaten the good of all by withdrawal from the Union, but the State which cut itself off from the rest would be likely to suffer in the long run.
What now, if Congress, which represents all the nation is unwise and passes laws that seem to hurt any part of the people? The remedy is to send wiser and better delegates, or to persuade the mistaken majority; because it is a harm only to the few to acquiesce for the time in what the majority have unwisely decreed, whereas it would injure every one if any portion of the nation were to resist or break up the government. This was abundantly demonstrated in the Civil War.
1 Eclectic Educational Series: Ray's Arithmetic, Third Book: Practical Arithmetic by Induction and Analysis, Ray, Joseph MD, Late Professor of Mathematics in Woodward College. One Thousandth [sic] Edition - Improved. Wilson, Hinkle & Co; Cincinnati, New York
2 Clothing: I.--Sewing Practices for the Beginner, 4-H Club Circular 21. Cooperative Extension Work in Agriculture and Home Economics. University of Missouri College of Agriculture and the United States Department of Agriculture Cooperating, January 1938 (Second Reprint April 1940).
3 The American Citizen: West Virginia Edition, Dole, Charles F.; D.C. Heath & Co., Publishers 1897.
4 The link to the file has been removed as I could not make it work!