Why is a matrix pencil called a pencil?

Question

I'm trying to understand the historical context behind the word pencil in matrix pencils, or pencil of curves so on.

I am aware that even Gantmacher 1959 has this terminology however I don't know where it originates from. I am also curious what he uses in the original Russian version in place for that word (though I don't know any Russian, I can handle a literal translation ala Körper etc.).

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EDIT Since there are answers given towards the meaning of the word "pencil" which is really good to know, I would appreciate if the context is also taken into account. It is from the definition of the pencil forms that some sort of bundling or parameterization is involved. However the definition itself of the word pencil does not introduce the context.

Compare it with the word affine which comes from the similar meaning (Latin affinis) "adjacent,connected" but this is not preferred for some reason although the structure of matrix pencils resembles $a\lambda - b$ more an affine transformation in my opinion. Obviously, it might be a nonlinear function of $\lambda$ but that context looks like long forgotten (until recently the computational tools for quadratic and nonlinear eigenvalue problems started to emerge).

Thus, I would speculate that some circles deliberately avoided either pencil or the affine word at some point. That's what I would like to understand.

Answer 1

The Oxford English Dictionary has an example from 1665 of "pencil" in the sense of "A group of rays or a beam of radiation converging to or diverging from a point." And one from 1840 in the geometric sense of "A set of lines meeting in a point"

Answer 2

After Speaking about French, English, Italian and Russian I checked the Greek, my language. Then, I found the greek verb δέσμη which means "to bind".

My interpretation of the etymology is that pencil represents a group bound by a property. In the projective geometry (older in Greek) the term a pencil of lines, δέσμη ευθειών, means lines passing through a common point. It is like the common handle of the brush and the filaments - wire or bristles or other. It works with parallel lines also and then it can mean the light beam etc. Hesiod uses the verb as in "to tie together, as corn in the sheaf".http://www.perseus.tufts.edu/hopper/morph?l=de%2Fsmh&la=greek#lexicon . It is that old. Linearity follows the geometry notion e.g. of lines through a point.

The pencil, used for writing, in Greek as in Russian, is a different word and not a metaphore. I do not know why they coincide in English. Probably, because it means a paintbrush, but it is now obsolete.