Briggs' original book has no table of contents. The first 14 chapters are concerned with the construction of Logarithms. I have used some of Hutton's wording from p.61 - p.75 of the preamble to his Tables to introduce the chapters. Each chapter is in pdf format.
Introductory Chapter:A mainly mathematical biography of Briggs, relying mainly on J. Ward's : Lives of the Professors of Gresham College. Biographical material is also inserted in the various chapter notes and comments as appropriate. You can link to the document Biography of Briggs, by clicking here.
Rational Logarithms as indices of powers of ten and by the taking of roots of 10.
Base ten Logarithms can be found by two methods: one due to Napier, which is expanded on at length to find log 2 and log 7, essentially by counting the number of figures in very large equal powers of 2 and 10; while the other method is the main subject of this book.
The Logarithms are formed from continued means: in which the repeated square root of 10 is taken to establish eventually a proportionality between the fractional part of the root and the index. Some non-fatal but time wasting errors are uncovered by the translator.
The Logarithm of 2 is found by this method, and subsequently the logs of 5 and 3.
The continued extraction of square roots of numbers just larger than one is facilitated by a method invented by Briggs relying on finite differences.
An ingenious method is found by Briggs to find the logs of prime numbers.
The Logarithms of fractions is considered.
Use is made of proportional parts to increase the accuracy of Logarithms found in the Chiliades.
The first method of subtabulation, used extensively by Briggs.
The second method of subtabulation, proposed by Briggs for the completion of the tables, relying on central finite differences of orders up to 20. The most ambitious mathematics in the book, but not explained by Briggs, only illustrated as a numerical way of correcting differences. A modern explanation of the method is given.
To find the number agreeing with a given Logarithm.
The rest of the book is concerned with applications of Logarithms.
To find the missing number of four numbers in proportion.
To find a root of a given number.
To find any number in a series of numbers in continued proportion; i.e. the intermediate terms in a G.P. ; Financial problems involving repayment of interest, annuities, etc.
Uses of logs in solving for the various parameters of mainly right-angled triangles, given the sides.
Eight problems concerning right-angled triangles are solved
About a given base, to describe a triangle isoperimetric and of equal area to a given triangle.
A theorem of Apollonius is demonstrated geometrically and numerically by Briggs.
For a given base, the difference of the legs, and the area of the triangle, to find the legs of the triangle.
To find a triangle for which the area is equal to the perimeter.
Constructing cyclic quadrilaterals.
Area and perimeter of circle; surface area and volume of sphere.
Concerning ellipses, spheroids, and cask gauging.
To divide a line according to the mean and extreme ratio. [i.e. the Fibonacci Numbers].
To find the sides and areas of regular figures inscribed in a given circle. Including 3-, 4-, 5-, 6-, 8-, 10-, 12-, and 16-gon.
Concerning the regular 7- and 9-, 15-, 24-, and 30-gons.
Concerning isoperimetric regular figures.
Concerning regular figures of the same area.
Concerning the five Platonic solids.
Ian Bruce. August 2006 latest revision. Copyright : I reserve the right to publish this translated work in book form. However, if you are a student, teacher, or just someone with an interest, you can copy part or all of the work for personal or educational use.