Linear aggregates of vectors in space
Abstract
In the article "A Simple and Accurate Representation of Points of Four-Dimensional Space on a Plane by Means of Vectors," not only is the system of vectors on a plane examined in detail, but also the foundations for constructing a linear prima of vectors in space from two given ones are indicated, namely, that this linear prima consists of segments generating a hyperbolic paraboloid, enclosed between two directrices, one of which is the line of initial points and the other the line of terminal points, with the construction itself being achievable by decomposing the two given vectors into components along three coordinate axes and by constructing, from the components, linear primas of parallel vectors; three vectors with a common initial point, but parallel to the coordinate axes, whatever directions we may choose for the latter, are precisely the component vectors of the linear prima; the terminal point of the latter lies on the line of terminal points.
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