While major mathematical problems were discussed already in the seventeenth century in such serial publications as the Philosophical Transactions (1665) and Acta Eruditorum (1682), it was not till the early part of the eighteenth century that serials containing elementary problems of wide appeal commenced to appear. The first of these seems to have been the Lady’s Diary, started in London in 1704, and “designed for the sole use of the female sex”. It had an immediate success, and continued to appear in various forms for 168 consecutive years. Of the second, Delights for the Ingenious, there were only eight numbers, in 1711. The third publication of the kind was possibly Kunstfrüchte 1. Sammlung (1723), a publication (I have not seen it) of the Hamburg mathematical society, founded thirty-three years before. The Jahrbriefe of this same society were published irregularly during the 140 years 1732-1871. For the fifth and sixth publications we come back to England, Miscellanece Curiosce (York, 1734-35) and Gentleman’s Diary, started in 1741 and continued for a century before its union with the Ladies’ Diary. Then followed five other English serials before Holland’s Mathematische Liefhebberye (Purmerende, 1754), issued annually for seventeen years. During the next 175 years the number of these minor publications became very large. It is my purpose to bring together brief notes on minor English serials and their editors of the past two and a quarter centuries, and to indicate where more information regarding them may be found. It will not be possible, within the limits of this article, to indicate more than very occasionally anything of the contents (often rich and varied) of such serials, many results appearing in their pages for the first time. Problems and their solutions usually occupied the greater part of the space, and most of the prominent English mathematicians of the time were contributors. While some may incline to frown upon such mathematical occupations, it may be recalled that “Sätze und Aufgaben” were to be found in such an exalted source as Crelle’s Journal, so recently as 1858.

A Well-Known treatise on Physics written in 1892 begins with the words:

Such was the accepted doctrine in the latter part of the nineteenth century. I want to show how it originated and to what extent we have now departed from it.

In an equation with real coefficients, if the terms are vectors, they must be codirectional if the equation is possible with all the quantities real. Thus to obtain a geometrical solution of the equation a cos θ + b sin θ =c, a and b must be drawn at right angles to each other since a cos θ makes an angle θ with a, and b sin θ makes an angle 90° − θ with b. The solution is obtained by the intersections of the circles r=a cos θ + b sin θ, r=c.

When it is said that Descartes was the inventor of analytical geometry, the impression is often given that by Cartesian Geometry is simply meant a system in which the position of a point is determined by means of its coordinates referred to two fixed straight lines, either at right angles or oblique. A little consideration shows us that it is not correct to say that this system was invented by Descartes, as we find that Apollonius, Bk. V, Prop. 52, gives the values of the coordinates of the centre of curvature of a point on a conic referred to two rectangular axes. It will no doubt interest the readers of the Mathematical Gazette to know what is was that Descartes invented, and what led him to it.

The belief entertained by some writers that Newton’s edition of Bernhard Varen’s Geographia generalis was simply a verbatim reprint of the original Amsterdam edition of 1650, or of 1664 or 1671, which did not demand Newton’s thoughtful attention, is erroneous. When the first edition went through the press, Varen is said to have been in a bad state of health, which would account for certain gross errors in the text which needed correction, and for the absence of geometric figures which the reader finds it irksome to supply from the statements in the text. The editions of 1650 and 1671 contain only three figures. In Newton’s edition (1672) these are redrawn in improved form and thirty other geometric figures are added. This fact alone indicates that Newton read the text critically. That these drawings are really Newton’s own work is evident from his remark in a letter of May 25, 1672, to Collins : “The book here in the press is Varenius his Geography, for which I have prepared schemes.”