Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Synthetic foundations of cevian geometry II: The center of the cevian
  conic   This paper continues the investigation of Part I, by studying the conic
$\mathcal{C}_P$ on the five points $ABCPQ$, where $ABC$ is a given ordinary
triangle and $Q$ is the isotomcomplement of $P$, defined as the complement of
the isotomic conjugate $P'$ of $P$ with respect to triangle $ABC$. We show that
$\mathcal{C}_P$ also lies on the points $P'$ and $Q'$, where $Q'$ is the
isotomcomplement of $P'$. The conic $\mathcal{C}_P$ lies on six other points
which are the images of the vertices of $ABC$ under the affine mapping
$\lambda=T_{P'} \circ T_P^{-1}$ and its inverse, where $T_P$ and $T_{P'}$ are
the unique affine maps taking $ABC$ to the cevian triangles of $P$ and $P'$,
respectively. In the paper we characterize the center $Z$ of $\mathcal{C}_P$ as
the unique fixed point of $\lambda$ in the extended plane, when $\mathcal{C}_P$
is a parabola or an ellipse, and the unique ordinary fixed point of $\lambda$,
when $\mathcal{C}_P$ is a hyperbola. We also show that $Z=GV \cdot T_P(GV)$,
where $G$ is the centroid of $ABC$ and $V=PQ \cdot P'Q'$. When $P$ is the
Gergonne point of $ABC$, this gives a new characterization of the Feuerbach
point $Z$. All of our arguments are purely synthetic.

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The categories of this paper are: chem-ph
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
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The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph