Excerpt from Plane Trigonometry
Some of the features of this book are:
(1) Abandonment of the "Academic Triangle."
The "academic triangle" is one, certain of whose parts are known exactly and whose remaining parts are calculable free from all errors except such as are due to the "place" of the tables used. In the academic triangle one side may show one figure and another seven figures, and the angles may show any readings the caprice of the maker may suggest.
(2) Replacement of the "Academic Triangle" by triangles having variety of form, but always such form as they should have if they had been actually measured in the field:
(i) Showing in all measured lines of a diagram the same number of significant figures, thus indicating about the same care in each measurement.
(ii) Giving in all calculated lines of a diagram not more significant figures than in its measured lines, since such extra figures are misleading and of no value.
(iii) Letting the angles of a diagram show such readings as exhibit care in angle-reading in keeping with that indicated in line-measurement.
While the student is learning to calculate, he might as well learn at the same time what form intelligent measurement should take and what reliability calculated results have as related to the data.
(3) What place tables to use to suit the data and how to cut a large table to suit short data.
(4) How checks should check to suit the data.
(5) The fundamental principles of calculation with approximate data (Chapter II.).
(6) The suggestion of simple laboratory exercises in connection with fundamental things.
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