Since all manner of quantities require to be compared together, in mathematical computations, and their various relations searched out and determined and as most of our knowledge in mathematical subjects depends on the proportions of several things to one another: so it is requisite that the nature of proportion, and the methods of reasoning…

This work is chiefly a compilation from other books; and but very little new is added except a more full explanation, than has yet been published, of rectangular surveying, or the method of calculating the area of fields arithmetically, without drawing a plot of them and measuring with a scale and dividers, as has been the common practice; and…

Results of using platonic solids for probability experiments are presented. (JG)

Reprinted is "Shanks, Ferguson and pi" by T. A. A. Broadbent. It describes the historical development of the mechanical calculation of the number pi. (CT)

Discusses how intriguing arithmetic images from geometric situations, which serves to remind students that mathematics is interrelated. Discusses also how the teacher can anticipate the possible dialogue in a class and thereby stress points of emphasis "ahead of time". (BR)

Examples are given of proofs to standard geometric theorems using physics and mechanics. (PK)

Shows how integer-sided triangles can be nested, each nest having a single enclosing isosceles triangle. Brings to light what can be seen as a relatively simple generalization of Pythagoras' theorem, a result that should be readily accessible to many secondary school pupils. (Author/KHR)

Discusses number patterns and Fibonacci numbers found in nature. (YDS)