vector

The story surprised me to hear that the world's most common mental model is something like "a vector is an arrow" or "a vector is a quantity with direction and magnitude".

A New and Complete Dictionary of Arts and Sciences of 1764

vector explains it as "an astronomical term, a line connecting a planet and its center (or elliptical focus).

It also says that the origin of the name is because the planets look like they are being CARRIED by the lines.

By the way, vector means "carry" in Latin.

http://gyazo.com/7d3e1f537d091d5add09d900ab04bab2

Encyclopaedia Perthensis of 1816

The idiom Radius Vector appears, but there is no occurrence of vector by itself.

A book written in 1855 explaining Newtonian mechanics

The word vector appears, but only in the idiomatic form "radius vector.

As far as the equation goes, it's not what we would call a vector today.

r is, in today's terms, "the length of the line segment connecting the focal point of the ellipse to a point on the ellipse."

http://gyazo.com/dd77e478a5d85e864a5650d91af73bd7

1687 Newton's Principia Mathematica

1835 Hamilton, Definition of complex numbers without square roots of negative numbers

1843 Hamilton generalizes complex numbers and defines quaternions, calling the imaginary part by the term vector

1878 Clifford invents the concept of inner and outer products, showing that the equivalent of the product of quaternions can be defined for three pairs of numbers

1881 Gibbs, in writing a textbook on electromagnetism, uses only the three pairs of numbers in the imaginary part (vector part) of the quaternions in isolation.

It was much later that the non-3D "arrows" that we now read as vectors came to be called vectors.

1636 Affine transformations studied as a branch of geometry

1857 Linear transformations including Cayley and affine transformations are represented by matrices

In the same year, Glassman, in the course of his research, creates the concepts of linear independence, scalar times dimension, and

1888 Peano gives a modern definition of vector space

In this area, the vector is finally formulated, as we now call it.

Elements of Vector Analysis by Gibbs (1881)

https://gyazo.com/20ef5347adc43921d21c7440fa325544

The beginning is similar to the current definition of a vector space

But when you start saying there are three unit vectors, you're implicitly assuming a three-dimensional space.

https://gyazo.com/d84d0852eaf8956b27790e51e5742802

Define two types of multiplication for vectors on p. 5

https://gyazo.com/da7744c6707dfc4542f2d44877fa7df3

And this result

https://gyazo.com/79af5c3758a1c5c236b81ad83df58769

and attributed to [quaternion

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