Basic Addition Nomogram

10

10

20

18

16

14

12

10

8

6

4

2

0

0

0

9

8

7

6

5

4

3

2

1

9

8

7

6

5

4

3

2

1

19

17

15

13

11

9

7

5

3

1

Operation

A = Intersect(a, n)
B = Intersect(c, n)
C = Intersect(b, n)
D = Intersect(b, m)
E = Intersect(b, l)
F = Intersect(b, k)
G = Intersect(b, j)
H = Intersect(b, i)
I = Intersect(b, h)
J = Intersect(b, g)
K = Intersect(b, f)
L = Intersect(b, e)
M = Intersect(b, d)
N = Intersect(a, d)
O = Intersect(c, d)
poly1, a_1, n_1, o, b_1 = Polygon(A, N, O, B)
P = Intersect(a, m)
Q = Intersect(a, l)
R = Intersect(a, a_1)
S = Intersect(a, k)
T = Intersect(a, j)
U = Intersect(a, i)
V = Intersect(a, h)
W = Intersect(a, g)
Z = Intersect(a, f)
A_1 = Intersect(a, e)
B_1 = Intersect(c, o)
C_1 = Intersect(c, m)
D_1 = Intersect(c, l)
E_1 = Intersect(c, k)
F_1 = Intersect(c, j)
G_1 = Intersect(c, i)
H_1 = Intersect(c, h)
I_1 = Intersect(c, g)
J_1 = Intersect(c, f)
K_1 = Intersect(c, e)
L_1 = Intersect(n, a)
M_1 = Midpoint(C, D)
N_1 = Midpoint(D, E)
O_1 = Midpoint(E, F)
P_1 = Midpoint(F, G)
Q_1 = Midpoint(G, H)
R_1 = Midpoint(H, I)
S_1 = Midpoint(I, J)
T_1 = Midpoint(J, K)
U_1 = Midpoint(K, L)
V_1 = Midpoint(L, M)
p = Segment(C, M)
W_1 = Point(o)
Z_1 = Point(a_1)
q = Segment(Z_1, W_1)
y0: y(N)
y1: y(A_1)
y2: y(Z)
y3: y(W)
y4: y(V)
y5: y(U)
y6: y(T)
y7: y(S)
y8: y(Q)
y9: y(P)
y10: y(A)
yL: y(Z_1)
yR: y(W_1)
text1: "" + yL + ""
text2: "" + yR + ""
A_2 = Intersect(p, q)
sumP: yL + yR
text3: "" + sumP + ""
text4: "" + yL + " + " + yR + " = " + sumP + ""
r = false

Tool: Complex Multiplication (command ComplexMultiplication)
Select Points at O(0, 0), P(0, -1), A and B for A*B
Input: O, P, A, B
Output: j, AB

c = Circle(O, A)
d = Circle(O, B)
D = Intersect(c, xAxis, 2)
b = Segment(O, A)
f = Segment(O, B)
G = Intersect(d, xAxis, 1)
g = Circle(D, P, G)
E = Intersect(g, yAxis, 2)
e = Circle(O, E)
a, h = AngularBisector(f, b)
D' = Mirror(D, a)
i = Ray(O, D')
AB = Intersect(e, i, 1)
j = Segment(O, AB)

Tool: Complex Division (command ComplexDivision)
Select Points O(0, 0), P(0, -1), A and B for A/B
Input: O, P, A, B
Output: l, C

A/B

c = Circle(O, A)
d = Circle(O, B)
D = Intersect(c, xAxis, 2)
e = AngularBisector(A, O, D)
B' = Mirror(B, e)
f = Ray(O, B')
E = Intersect(c, yAxis, 1)
F = Intersect(d, xAxis, 1)
g = Segment(F, E)
G = Midpoint(g)
h = OrthogonalLine(G, g)
i = Segment(P, F)
H = Midpoint(i)
j = OrthogonalLine(H, i)
I = Intersect(h, j)
k = Circle(I, F)
J = Intersect(k, xAxis, 2)
p = Circle(O, J)
C = Intersect(p, f)
l = Segment(O, C)

Tool: Complex Addition (command ComplexAddition)
Select Points O(0, 0), A and B for A + B
Input: O, A, B
Output: C', c

A + B

u = Vector(O, B)
C' = Translate(A, u)
c = Segment(O, C')

Tool: Complex Subtraction (command ComplexSubtraction)
Select Points O(0, 0), A and B for A - B
Input: O, A, B
Output: c, A'

A - B

u = Vector(B, O)
A'_1 = Translate(A, u)
A' = Translate(A, u)
c = Segment(O, A')