Let A = a(cos a+j sin a) be divided by J5 = 6(cos ,5+y sin /5),Equation Atlas
This atlas exposes the mathematical breadth already present in the processed corpus. It is a review map, not a final equation canon: OCR formula lines can contain wrong symbols, missing fractions, page headers, figure references, or broken typography.
Use rule: read these as formula candidates. A formula becomes canonical only after scan verification, notation cleanup, variable definition, derivation review, and physical-meaning review.
3845
equation and formula candidates in the corpus.
2528
reviewable relation candidates after OCR scoring.
1330
strong formula candidates to prioritize.
15
processed sources with mathematical records.
Formula Families
Section titled “Formula Families”Symbolic AC And Complex Quantities364 candidates. Routes equations where Steinmetz turns alternating quantities into symbolic algebra.Impedance, Reactance, And Admittance211 candidates. Routes the formulas that became the everyday language of AC circuit calculation.Inductance, Capacity, And Stored Energy329 candidates. Routes equations involving field storage, charge, discharge, and frequency-dependent opposition.Transients, Oscillation, And Damping907 candidates. Routes time-domain formulas that separate permanent terms from natural or temporary terms.Waves, Lines, Radiation, And Frequency354 candidates. Routes equations connecting electric waves, propagation, light, transmission lines, and frequency.Magnetism, Hysteresis, And Core Loss38 candidates. Routes formulas for magnetic materials, flux, loss, effective resistance, and hysteresis behavior.Power, Energy, Work, And Efficiency73 candidates. Routes equations where electrical quantities become work, heat, output, loss, or system performance.Engineering Mathematics Foundations336 candidates. Routes the mathematical language Steinmetz used to train engineers in calculation itself.Apparatus, Machines, And Power Systems410 candidates. Routes formulas tied to machines, apparatus, synchronism, and operating power systems.General Equation Candidates823 candidates awaiting classification.
Highest-Priority Formula Candidates
Section titled “Highest-Priority Formula Candidates”If, A=ai +ja2 = a (cos a+j sin a), thenAt the moment 0 = 0, let the e.m.f. e = E cos (0 - 00) bei = io cos (0 - 7) = io cos 7 cos <j> + i0 sin 7 sine = 2;oCe-”’ sin (0 =F co - 7) ji = e~ ”’ J ai cos </) cos co + 6i sin cf) cos co + Ci cos 0 sin coand ai + ja2 = a (cos 6 + j sin d) ;or ai -\-ja2 = A(cos 0+j sin 6).and A ==5 (cos 37 deg. H-j sin 37 deg).C = AB = ah (cos a+j sin a) (cos /?+ / sin /5)A = ai +ja2 = a(cos a+j sin a),e = 2 7r/n$ sin r the instantaneous generated e.m.f.B = 6’ + jh” = 6(cos 13 + j sin /3)is r - j (x -f x0} = r = .6, x + x0 = 0, and tan S>0 = 0 ;is r - j {x + Xo) = r = 0.6, x -{- Xo = 0, and tan do = 0; that= - J = (tan a - j) (7)Since e = E cos (0 - 00) = impressed e.m.f.,i = -z | cos (I? - 00- 0J- i~x° cos (00 + OJ j (9)if = 140 cos 0.2 1 - 80 sin 0.2 1,20. If ai+y6i=6+2.5 J is represented by the point Pi;and the vertical distance 6i=2.5. If a2+jb2 = S+4:j is repre-If an alternating current i = I0 sin 6 passes through a resist-1.) Ohm’s law : i = e j r, where r, the resistance, is a1.) Ohm’s law : i = e j r, where r, the resistance, is aor, if E = e -\-je’ is the impressed E.M.F., and 7 = i ’ -\- ji’E.M.F. of the generator OE°, where Z0 = r0 - jx0 = inter-/, upon the e.m.f., or by IE cos d, where 9 = angle of time-but E = E^y I^E^j z. If x^ > - 2,t-, it raises, if ;r < - 2 jr,Then, if E0 = impressed E.M.F.,-a maximum for dP^j db = 0, that is, according to § 61, if -e.m.f., e = EQ sin 6.w=j*pdt, (10)f = j (13)K = j^; (21)(B = -j =/z JClinespercm2.7 = -j = yG am-Source-Level Math Coverage
Section titled “Source-Level Math Coverage”Promotion Standard
Section titled “Promotion Standard”- Open the source text and workbench.
- Check the scan or source PDF for exact typography.
- Preserve Steinmetz’s original notation before translating it.
- Define every variable.
- Add the modern equivalent only as a labeled translation.
- Add a worked example only after the formula is mathematically reviewed.