Clinical electrocardiography . 6 6 4 8 2 10 0 * After Einthoven determined it is possible to determine the manifest size of thevarious deflections by trigonometry: E = Ei E = E = cos (a —60°) E3 cos (120°— a) Mann recently has suggested the substitution of the rectangularsystem of co-ordinates for the polar system for the purpose ofmathematic simplification. He believes that it is simpler to think MATHEMATIC BASIS OF ELECTROCARDIOGRAPHY 49 of a point with the value X = 4, Y = 3, than it is to think of thesame point with the value E = 5, a = 37°. Figure 19 repres
Clinical electrocardiography . 6 6 4 8 2 10 0 * After Einthoven determined it is possible to determine the manifest size of thevarious deflections by trigonometry: E = Ei E = E = cos (a —60°) E3 cos (120°— a) Mann recently has suggested the substitution of the rectangularsystem of co-ordinates for the polar system for the purpose ofmathematic simplification. He believes that it is simpler to think MATHEMATIC BASIS OF ELECTROCARDIOGRAPHY 49 of a point with the value X = 4, Y = 3, than it is to think of thesame point with the value E = 5, a = 37°. Figure 19 represents an equilateral triangle in which the rec-tangular system of co-ordinates is applied. The values of therectangular co-ordinates (X, Y) of a point (A) are found alge-braically in terms of the three derivations (Ei, E2, and E3). Proposition: The longest projection on the sides of an equi-lateral triangle of any straight line drawn within an equilateraltriangle equals the sum of the projections on the other two Fig. 19.—Equilateral triangle using rectangular system of co-ordinates. (Aft* Mann.) Let A 0* be any straight line drawn within the equilateraltriangle R L F. Let eh s2, and e3 be the projections of A 0 on thethree sides of the triangle, obtained by dropping perpendiculars(AAx, AA2, AA3, OOi, 002, 003) from the ends of the line A Oupon the sides of the triangle. To prove that e2 = ss + d: * In the figure the point O has been made the center of the triangle for thesake of simplicity in construction, but the proof does not depend on this fact,and will hold whatever be the position of the line O A. As a matter of fact, thepoint O is taken at the center of the triangle in the subsequent part of this book. 4 A303 + A3Bj €3 + A3B3 €3 + JKB; 50 CLINICAL ELECTROCARDIOGRAPHY Construction : 1. Produce A2A until it meets 001 at B. 2. Draw BB3 perpendicular to L F. 3. Draw A H parallel to R L, cutting B O at Draw K B3 parallel to A. H. 5. Draw R 03* the pe
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