It is shown that the fundamental space-time-velocity relations of Einstein’s original restricted theory of relativity, when the observed point, line, or ray of light moves in the direction of the observers themselves, can be represented quantitatively and visualized by using two sets of oblique time-space coordinates, forming the Lorentzian plane. For the observer moving in the positive direction at the relative velocity q, the angle between the coordinate axes is 90° − α, for the observer moving in the negative direction the angle is 90° + α, where sin α = q/c; α has been named the velocity angle.The concept of intrinsic coordinates of an event is introduced, and certain simple phenomena are expressed in these coordinates. A spatium is defined as a vector which can be differently resolved into space and time components by different observers. The general method is illustrated by showing graphically the Fitzgerald contraction of a length, the slowing down of a clock, the fact that two velocities always add to one less than that of light, the Doppler effect, reflection from a moving mirror, etc.A simple mechanical model is described which conveys some of the foregoing relations directly to the eye and which can be used for demonstrations before a large audience. Terms and Notation used.a, a′acceleration of a moving pointcvelocity of lightEoenergy added to a system of moving particles, Eq. (66)hintrinsic spatium of a moving line*iused as a subscript means incidence; Fig. 10l, l′lengthsMNin Fig. 6, a spatium, that is, a vector which may be resolved into a length and a time interval*OB, OBnuniversal bisectors, positive and negative, Figs. 3 and 7*OHFig. 7, space-time line or curveqrelative velocity between S and S′rspatium vector of a point in the Lorentzian plane, Fig. 3*rused as a subscript means rebound or reflectionS, S′two systems or observers moving at a relative velocity q with respect to each other; Fig. 1T, T′time intervalst, t′ordinates along the time axesv, v′velocities of a pointXX′OTT′Lorentzian plane, Fig. 3*x, x′lengths plotted as abscissaeαvelocity angle, Eq. (3) and Fig. 3*γ, γ′coordinate angles, between the coordinate axes and the universal bisector OB, Eqs. (4) and (5); Fig. 3*θorientation angle of a space-time line, Fig. 7*λ, λ′wave lengths of lightμ, μ′values of the refraction coefficientν, ν′frequencies of lightϕorientation angle of a spatium vector, Fig. 3*