Literary notes about Orthogonal (AI summary)
In these examples, the term "orthogonal" is used primarily in a geometric sense to denote perpendicularity between curves or surfaces. Specifically, it describes trajectories and directrices that intersect at right angles, as seen in the discussions of orthogonal trajectories within elliptical or circular cylinders [1], the intersections of conoids and cylinders [2], and the converging sections of a cylinder [3]. Additionally, the term is employed more abstractly in solving geometric problems, as with the reference to an "orthogonal appareil" [4], and in characterizing a directrix relationship in a right conoid [5]. This collection of usages reflects a consistent emphasis on the inherent perpendicular relationships underlying various geometric constructions and analyses.
- True and principal properties of the orthogonal trajectories of the parallel sections of an elliptical or circular cylinder.
— from The Declaration of Independence of the United States of America by Thomas Jefferson - The intersection of this conoid by a cylinder about the same axis is an orthogonal trajectory for a series of parallel sections.
— from The Declaration of Independence of the United States of America by Thomas Jefferson - Orthogonal trajectories of the converging sections of a cylinder.
— from The Declaration of Independence of the United States of America by Thomas Jefferson - Second solution: Orthogonal appareil .
— from The Declaration of Independence of the United States of America by Thomas Jefferson - Right conoid, having for directrices the axis of the circular cylinder and an orthogonal trajectory.
— from The Declaration of Independence of the United States of America by Thomas Jefferson
