Graphical Calculus

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Di\dding through by PL = QM = RN, we have— LS MT _ NU PL ■*" QM ~ RN 55 Fig. 26.
that is, when S is close to P, and therefore T and U close to Q and R respectively — /P^ + /Q' = ^'R' (see note on p. 48).
56 Graphical Calculus.
Roughly speaking, the meaning of this is, that if we have two slopes (which we may imagine as wedges cut out of a pack of cards) of the same length piled on top of one another in the way shown in Fig. 27, the resulting slope (tangent of angle) is the same as that of the o
...ther two added together. This can be easily seen.
Now, the equation to curve (T) in Fig. 26 is evidently — Ord. of(3).
y Ord. of (i).
Ord. of (2).
Our result tells us that its derived equation is — Slope of (3).
Slope of (i).
2X + Slope of (2).
(I) as already shown in §§ 17 and 24.
Exactly similar rleasoning applies to the differential co-efficient of differences of func- tions. In this case the ordinates of curve (3) are to be made = the differences of the ordinates of (7) and (T). The figure can be easily made from Fig.


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