Marveling At The Historical

Math Oldies But Goodies

  • About This Blog

    This blog is mostly about math procedures in textbooks dated from about 1825-1900. I’m writing about them because some of the procedures are exquisite and much more powerful, and simpler, than some of the procedures in current text books. Really!

    I update this blog as frequently as possible ... every 2-3 days. And, if you are a lover of old texts and unique procedures, you might want to talk to me about them, at I’m not an antiquarian; the books I have are dusty, musty, brown-paged scribbled-in texts written by authors with insights into how math works. Unfortunately, most of their procedures have vanished. They’ve been overcome by more traditional perspectives, but you have to realize that at that time, they were teaching the traditional methods.

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One 1873 View of Percent

Posted by mark schwartz on February 18, 2017


I’m writing this short piece to give you the flavor of what students had to do when they studied percent using Rev. York’s 1873 The Man of Business and Railroad Calculator. Today’s texts typically present one formula for percent and then discuss variations on it, like percent increase, decrease, percent proportion or finding values given a percent. Also, typically, the problems are very similar to the examples given and rarely, if ever, include fractional values. Rev. York presents a much more demanding idea.

The Story

In his book he discusses percent across 11 pages, making 13 different conditions (like ‘given x, find y’) and ends the discussion with a presentation of 8 formulae. In essence, these 8 formulae are simple variations on ‘percent = part/whole’ but his presentation gives the appearance that these 8 formulae are to be used depending on the nature of the problem. In addition to the typical presentation of percent in today’s text, you can see my concept of percent proportion in this blog (see Percent Proportion). At no point does he state the basic, simple relationship algebraically.

The best way to show what students had to do is to list the kinds of problems he presented. I’ve included the answers as well. I’m not going to list his 8 statements. Let me remind you that students in the 1870s had no calculators and that the work Rev. York presented suggests the importance of mastering fractions. At that time, units of measurement weren’t as standardized and a lot of conversion between systems involved fractional relationship.

The problems as he presented them are below; the answers are at the bottom, in the event you want to play with the problems.

  1. What percent is 1/4 of 2/5?
  2. If a merchant sell calico at 12 1/2 cents per yard and makes 12 1/2 percent. ; what did it cost per yard?
  3. If I sell an article for $250, and make 125 percent; what did it cost me?
  4. One of the stockholders of a rail road company owns 19 shares of $50 each; the dividend is declared to be 7 1/2 per cent premium; what ought he to receive?
  5. If I sell 4/7 of an article for as much as I paid for 2/3 of it; what percent did I make?




  1. 62 1/2 percent
  2. 11 1/2 cents
  3. $111 1/9
  4. $67.50
  5. 14 2/7 percent

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