This paper presents new principles of transpose in the fixed point theory as for example: Let $X$ be a nonempty set and let $\mathfrak{C}$ be an arbitrary formula which contains terms $x,y \in X$, $\leq$, $+$, $\preccurlyeq$, $\oplus$, $T: X \to X$, and $\rho$. Then, as assertion of the form: For every $T$ and for every $\rho(x,y)\in \mathbb{R}_{+}^{0} := [0,+\infty)$ the following fact (A) $\qquad \mathfrak{C}(x,y\in X,\leq, +, T, \rho)$ implies $T$ has a fixed point is a theorem if and only if the assertion of the form: For every $T$ and for every $\rho(x,y)\in C$, where $C$ is a cone of the set $G$ of all cones, the following fact in the form (TA) $\qquad \mathfrak{C}(x,y\in X, \preccurlyeq, T, \rho)$ implies $T$ has a fixed point is a theorem. Applications of the principles of transpose in nonlinear functional analysis and fixed point theory are numerous.