Historical Math and Science Blog

Precision machine design is as old as metalworking, dating back to the bronze age, forward to the watch and clock makers, and then to the scientific instrument makers. Today, watch makers still use many of the classical techniques, although powered tools have made a huge impact on repeatability and precision. The question naturally arises: how did people make things out of brass and copper before we had powered machine tools? The purpose here is to consider the fabrication and/or machining of various ornamental, engineering, or scientific devices throughout the 18th and 19th centuries. The devices under consideration will be on the smaller scale, so e.g. architectural manufacturing processes are not considered. This is particularly concerned with scientific apparatus of these centuries. Some resources: Durham's The Artificial Clock-maker (ca. 1696) Saunier’s The Watchmakers’ Hand-book (1888) This page: https://watchmaking.weebly.com/the-turns.html Gee’s The Silversmith’s Handbook ...

 Recently, my brother and I were driving near Harrisburg, PA, when we stumbled across a used book store on the side of the street. In this wonderful little store, I found something I hadn't seen before: math textbooks from the pre-civil war era. A few were arithmetic, and just one was on algebra. Being a sucker for old textbooks, especially on math and physics, I paid $40 for the book, and today we can take a look at what's inside.  The cover is in surprisingly good condition, as are the pages, considering the age. At this age, you might expect 'red rot' to set in, and the pages to be covered in 'foxing', or faint red spots and marks. But as we'll see, many of the pages are in good shape.  The book is Stoddard and Henkle's  The University Algebra . It's available online thanks to Google, see here , so you can follow along without the price of admission. Published in 1859, the book targeted Normal schools, highschools, and colleges, and it covers a ra...

 In 1798, Pierre-Simon de Laplace (of the newly formed École Polytechnique in Paris) published the first two volumes of his landmark treatise, Mécanique Céleste . Three years later, Jean-Baptiste Biot (of the famous Biot-Savart law) published one of the earliest analytical papers applying mathematics from Laplace's treatise to the recent results demonstrated by Coulomb, that electric force changes with the inverse squared law in the same manner as gravity.  The paper, titled  Sur un probléme de physique, relatif à l'électricité , was published in the Bulletin de la Société Philomathique, Tome 3 (1801), pp. 21 - 23. It was a tough paper to track down, and little mention is made of it anywhere online, but for one source, an article by R. W. Home in the BJHS, 1983, vol 16, titled Poisson's memoirs on electricity: academic politics and a new style physics . Biot's paper is significant not only for being an early example of analytical electromagnetism, but also because it se...

Many math and science papers make use of the subjunctive mood (expressing doubt, uncertainty, etc) just by the nature of science and mathematics in general. This goes for any language. Conjunctions and short phrases make up much of the vocabulary needed for translation, as well as cognates; words more common in language (compare integral  with root , the latter being much more common in everyday usage in a variety of meanings) will require translation. It is sometimes the case that the meaning of a word or phrase is a false cognate, and other times the translation of a word from one language to another is imperfect. The best source of information on word meanings in a given context is a native language dictionary. The definitions can often be translated easily into English for a more reliable translation and meaning.  References for translating French: Dictionnaire Larousse - French language dictionary, very useful web interface, a great reference for all words Google Transla...

 Today, by chance, I decided to check out Joseph-Louis Lagrange's works, Oeuvres Lagrange , in particular tome 3. It's a remarkable coincidence, because I have only downloaded one book (tome) of Oeuvres Lagrange, book 3, and for no reason in particular I decided to browse it, finding that the first article relates to the solution of general algebraic and transcendental equations! This is a coincidence because the papers from Euler and Lambert that I've been working on (see Welcome article for now) relate to this very topic, and Lagrange is essentially picking up where Lambert left off, using series to represent the roots of polynomials.       Lagrange's paper, Nouvelle méthode pour résoudre les équations littérales par le moyen des séries  (Mémoires de l'Académie royale des Sciences et Belles-Lettres de Berlin, t. XXIV, 1770) does a far superior job to Lambert's series solution of the same problem, because Lambert's series could only determine any power of ...

It should come as little surprise that math notation has changed in the last few centuries. Since the time of Newton and Leibniz, the operations including addition, subtraction,multiplication, division, integration, differentiation, limits, logs, sums, powers, trig functions, and so on have all changed. This adds a layer of translation to works from e.g. Euler and Lambert (1750s-1780s) which I'm working on now. Below I'll share some notation and typesetting norms from this period.  Elementary Arithmetic The typesetting of these symbols included variations depending on the publisher and the writer. Examples: Arithmetic Symbols Zero o (lowercase O) One ı (small dotless i) ɪ (Latin small capital i) I (uppercase i) Equals a ＝ b (full width equals sign) Addition a ☩ b (cross of Jerusalem) a ✠ b (Maltese cross) a 🞣 b (Greek cross) Subtraction a – b (en-dash) a — b (em-dash) Multiplication 1 . 2 (period) ab (adjacent symbols) a ⨉ b (times operator) Division \(\fr...

 Welcome to the historical math and science blog! My name is Sam Gallagher, I'm a 24 year old electrical engineer from Pennsylvania with a particular interest in the history of math and science. This hobby of mine has taken me through many projects, and because much of the work I'm doing is unique, is hard to find elsewhere, or is simply interesting and fun, I decided it was time to make a website where people could share in the adventures. I'll also be managing resources for various topics of interest, especially when there is little information about a topic available from Googling or using Wikipedia.  Some examples of projects, both from the past and looking into the future: A recreation of Nobili's astatic galvanometer This instrument was used by Faraday in making his electrical measurements, detecting currents into the microampere (uA) range. It allowed Faraday to discover electromagnetic induction. Named for Leopoldo Nobili, who corresponded with Faraday. I have m...