Mathematical Art Commonly called Algebra

In 1673 John Kersey published the Elements of that Mathematical Art Commonly called Algebra. We give below a version of John Kersey's Preface. We have modernised the spelling but left much of the 17th century style of English.

Preface to the Mathematical Art Commonly called Algebra.

It is an undoubted truth, that among all human Arts and Sciences, arithmetic and geometry have obtained the greatest evidence of certainty. This prerogative results from the verity and perspicuity of their principles, which consists of Definitions, Postulates (or Petitions), and Axioms; for these being intelligible, reasonable and certain, are sure foundations of the right reasoning, by all judicious and impartial students in sciences. Hence it is, that all propositions which are proved by those certain principles are likewise certain, and called Demonstrative Truths, by which are meant strictly and properly, infallible consequences, or conclusions, deduced from clear and undeniable premises. For which cause, divers philosophers have endeavoured, as far as the quality of their discourses would admit, to make the force of their arguments amount to mathematical demonstration, which, by universal consent of the learned, is the clearest and most convincing proof of the truth of a proposition, that can possibly be given by human reasoning. Nor was it without reason, that the Ancients (as many of the learned affirm), taught their scholars Arithmetic and Geometry, next after the rudiments of Letters, as expedients to take off their minds from levity, and to render them capable of sound judgement, before they entered upon the study of philosophy: which method of schooling was in great esteem with Plato (as his book of Common-weal testifies); who was of the opinion that ingenious and pregnant proficients in Arithmetic were apt to learn any Arts whatsoever, and he permitted no student that was ignorant of geometry to enter into his school.

This also may be added concerning the excellency of those twin-like Arts of Sciences, that they depend not upon any other sciences, either for help or demonstration; nor do they owe their dignity to the suffrage or vote of our senses, which oft-times deceive us; but since Quantity, about which Arithmetic and Geometry are conversant, may be considered abstractively, and separate from all kinds of matter, the verity of their propositions is examined and proved in the mind only; where, among all the exercises that conduce to search of truth, none are found so pure, clear and comprehensible (right reason being judge), as Arithmetic and Geometry; thence they are called Pure Mathematics, and are properly to be learnt before any of the rest of the Mathematical Arts.

Nor are Arithmetic and Geometry excellent in themselves only, but highly esteemed also for their manifold utility, as well in the employments of men about Accounts, Trade, Building, Measuring of Land, and divers other common affairs, as in facilitating and enlivening divers other Noble Arts.; for how can Harmonical Composition in Music, or exact Measure and Proportion in Painting be performed, without the assistance of Arithmetic and Geometry. Besides, these Sciences (as the mathematician very well knows) like the two pillars, Jachim and Booz, in the porch of Solomon's Temple, are the stability and support of all the rest of the Mathematical Arts; for if Astronomy, Navigation, Dialling, Optics, Fortification, and the rest of the Arts called Mixed Mathematics, be stripped of the demonstrations and operations imparted by Geometry and Arithmetic, that which remains will be as barren as the Earth without the influence of the Sun, and as inactive as a human body without a reasonable soul.

The premises may suffice to give a hint of the excellency and utility of Arithmetic and Geometry, whence we may reasonably infer; First, that so great and so profitable a subject is worthy of the study of all ingenious minds, in a degree proportional to their respective stations or employments, as well as promoting their own, as the public good. Secondly, that that Art by a more easy, and not less sure method than that called Synthetic, finds out the solutions and demonstrations of the more knotty propositions, as well Geometrical as Arithmetical (and oftentimes by the way too, discovers unexpected and admirable speculations), may very well deserve the enquiry of such lovers of Art as have hours to spare, and are desirous to be acquainted with the choicest pieces in the Common-wealth of learning: but such an Art is that commonly called Algebra which first assumes the quantity sought, whether it be a number of a line in a question, as if it were known, and then, with the help of one or more quantities given, proceeds by undeniable consequences, until the quantity which at first was but assumed or supposed to be known, is found equal to some quantity certainly known, and is also known also.

Which analytical way of reasoning produces in conclusion, either a Theorem declaring some Property, Proportion or Equality, justly inferred from things given or granted in a proposition, or else a canon directing infallibly how that may be found out or done which is desired; and discovers demonstrations of the certainty of the resulting Theorem or Canon, in the Synthetical Method, or by way of composition, by the steps of the Analysis, or Resolution. These are but glances of the many rare effects produced by the Analytic or Algebraic Art, which is an inexhaustible fountain of theorems, a key truly golden for the unlocking of Problems as well Geometrical as Arithmetical; and not only a sure, but delightful guide to such students, who not being satisfied with a bare knowledge of the truth or practical use of those sublime inventions that have rendered the ancient mathematicians so venerable, are desirous to know how they were found out, and how to prosecute their search of truth, so, as to advance knowledge upon solid foundations.

But the excellency of the Algebraical Art is best known to those that are acquainted with the most eminent writers upon that subject; among which, these are deservedly famous, namely, Diophantus of Alexandria (the first inventor of this rare Art, as some by his Preface to Dionysius do conjecture; but others give the honour of that noble invention to Geber an Arabian astronomer, whence, as is conceived, the work Algebra took rise), Cardanus, Tartaglia, Clavius, Stevinus, Vieta (the first inventor, or at least the happy restorer of Specious, or Literal Algebra, so called, because it operates chiefly by Alphabetical letters), Mr William Oughtred (our learned country-man), whose Clavis Mathematica, for solid matter neat contractions, and succinct demonstrations, is hardly to be paralleled), Mr Thomas Harriot (another learned mathematician of our Nation), Ghetaldus, Andersonus, Bachetus, Herigonius, Cartesius, Fran van Schooten, Florimond de Beaune, Hugenius, Huddenius, Slusius, Fermatius, Billius, Rhenaldinus, and many others too numerous to be here recited; but to bring up the rear of these renowned analysists, I shall mention four more of our own nation, and now living (whose pardon I humbly beg for this my boldness), namely, the Right Reverend Father in God, Seth, Lord Bishop of Sarum [Seth Ward], Dr John Wallis, Professor of Geometry in the University of Oxford, Dr Isaac Barrow Master of Trinity College in Cambridge, and one of his Majesties Chaplains, and Dr John Pell.; the learned works of which four worthies proclaim their rare talents in universal mathematics.

Now because this excellent Art is but very sparingly treated of in our native language and since according to the old maxim, Bonum quò communius eò melius, Good the more common the better it is; I have, in imitation of the industrious bee that gathers honey from various flowers, yet without any diminution either of their beauties or virtues, extracted out of the before-mentioned authors, the treatise consisting of Four Books (the two first of which are printed, a good progress made in the third, and the fourth ready for the Press), and have designed it chiefly to give such of my mathematical country-men as are altogether strangers to, and desirous to be acquainted with the so much celebrated Art called Algebra, a plain and intelligible introduction to its doctrine, as also a considerable taste of its use, in finding out theorems and solving problems, as well Arithmetical as Geometrical.

And here, to avoid the stain of ingratitude, I cannot but declare to the World, that my old and much respected friend, Mr John Collins, a person well known to be both singularly skilful in, and an industrious promotor of the mathematics in general, has been a principal instrument of bringing this work to light, as well by animating me to compile it, as by endeavouring to procure it to be well printed.

To conclude, I have earnestly endeavoured to render the fundamentals, and most important rules of the Algebraical Art in both kinds, to wit, Numeral and Literal, very clear and easy to capacities competently exercised in the elements of Arithmetic and Geometry. And the favourable acceptance, which my additions to Mr Wingate's Treatise of Common Arithmetic have found, with divers eminent mathematicians and other lovers of Art, does encourage me to hope, that the younger students of Symbolical Arithmetic and Analytical doctrine, will be well pleased with the following discourse, and that my labours therein will be as candidly accepted, as they have been cordially intended to serve my native Country.

From my house at the Sign of
the Globe in Shandois-Street,
in Covent-garden, the 15th
day of April, 1673.

John Kersey

Last Updated September 2023