Chapter 1: The General Number
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Source Metadata
Section titled “Source Metadata”| Field | Value |
|---|---|
| Source | Engineering Mathematics: A Series of Lectures Delivered at Union College |
| Year | 1911 |
| Section ID | engineering-mathematics-chapter-01 |
| Location | lines 915-3491 |
| Status | candidate |
| Word Count | 10319 |
| Equation Candidates In Section | 300 |
| Figure Candidates In Section | 4 |
| Quote Candidates In Section | 0 |
Opening Source Excerpt
Section titled “Opening Source Excerpt”CHAPTER I. THE GENERAL NUMBER. A. THE SYSTEM OF NUMBERS. Addition and Subtraction. . I. From the operation of counting and measuring arose the art of figuring, arithmetic, algebra, and finally, more or less, the entire structure of mathematics. During the development of the human race throughout the ages, which is repeated by every child during the first years of life, the first conceptions of numerical values were vague and crude: many and few, big and Httle, large and small. Later the ability to count, that is, the knowledge of numbers, developed, and last of all the ability of measuring, and even up to-day, measuring is to a considerable extent done by count- ing: steps, knots, etc. From counting arose the simplest arithmetical operation — addition. Thus we may count a bunch of horses: 1,Source-Located Theme Snippets
Section titled “Source-Located Theme Snippets”Complex quantities
Section titled “Complex quantities”... then 3 steps back, from B to C, brings us to C, 2 steps away from A. 12 3 4 5 H S 1 1 ®- C B Fig. 2. Subtraction. Trying the case of subtraction which was impossible, in the example with the horses, 5 steps -7 steps = ? We go from the starting point. A, 5 steps, to J5, and then step back 7 steps; here we find that sometimes we can do it, sometimes we cannot do it; if back of the starting point A is a stone wall, we cannot step back 7 steps. If A is a chalk mark in the road, we may step back beyond it, and come to C in Fig. 3. In the latter ...Ether references
Section titled “Ether references”... ng is to a considerable extent done by count- ing: steps, knots, etc. From counting arose the simplest arithmetical operation — addition. Thus we may count a bunch of horses: 1, 2, 3, 4, 5, and then count a second bunch of horses, 1, 2, 3; now put the second bunch together with the first one, into one bunch, and count them. That is, after counting the horses 2 ENGINEERING MATHEMATICS. of the first bunch, we continue to count those of the second bunch, thus : 1, 2, 3, 4, 5-6, 7, 8; which gives addition, 5 + 3 = 8; or, in general, a- ...Impedance / reactance
Section titled “Impedance / reactance”... lled an operator, as it carries out the operation of rotating the direction and changing the length of the multiplicand. 26. In multiplication, division and , other algebraic opera- tions with the representations of physical quantities (as alter- nating currents, voltages, impedances, etc.) by mathematical symbols, whether ordinary numbers or general numbers, it is necessary to consider whether the result of the algebraic operation, for instance, the product of two factors, has a physical meaning, and if it has a physical meaning, whether this meaning ...Alternating current
Section titled “Alternating current”CHAPTER I. THE GENERAL NUMBER. A. THE SYSTEM OF NUMBERS. Addition and Subtraction. . I. From the operation of counting and measuring arose the art of figuring, arithmetic, algebra, and finally, more or less, the entire structure of mathematics. During the development of the human race throughout the ages, which is repeated by every child during the f ...Chapter-Local Concept Hits
Section titled “Chapter-Local Concept Hits”| Concept Candidate | Hits In Section | Status |
|---|---|---|
| Ether | 12 | seeded |
| Illumination | 5 | seeded |
| Frequency | 2 | seeded |
Chapter-Local Glossary Hits
Section titled “Chapter-Local Glossary Hits”| Term Candidate | Hits In Section | Status |
|---|---|---|
| ether | 12 | seeded |
Equation Candidates
Section titled “Equation Candidates”| Candidate ID | OCR / PDF-Text Candidate | Source Location |
|---|---|---|
engineering-mathematics-eq-candidate-0001 | 5 + 3 = 8; | line 957 |
engineering-mathematics-eq-candidate-0002 | 8-3 = 5; | line 970 |
engineering-mathematics-eq-candidate-0003 | a distance from a starting point A (Fig. 1), for instance in steps, | line 995 |
engineering-mathematics-eq-candidate-0004 | then 3 steps, from B to C, gives the distance from A to C, as | line 1002 |
engineering-mathematics-eq-candidate-0005 | 5 steps +3 steps =8 steps; | line 1005 |
engineering-mathematics-eq-candidate-0006 | subtract. another distance, for instance (Fig. 2), | line 1016 |
engineering-mathematics-eq-candidate-0007 | 5 steps— 3 steps = 2 steps; | line 1018 |
engineering-mathematics-eq-candidate-0008 | example with the horses, 5 steps -7 steps = ? We go from the | line 1033 |
Figure Candidates
Section titled “Figure Candidates”| Candidate ID | OCR / PDF-Text Candidate | Source Location |
|---|---|---|
engineering-mathematics-fig-005 | ■e- FiG. 5. tance in the direction rotated 90 deg. from +2, or in quadrature | line 1635 |
engineering-mathematics-fig-006 | +3 Fig. 6. For instance, in problems dealing with plain geometry, as in | line 1689 |
engineering-mathematics-fig-010 | There are therefore n different valuesof av^ + 1, which lie equidistant on a circle with radius 1, as shown for n = 9 in Fig. 10. 14. In the operation of addition, a + 6 = c, th… | line 1872 |
engineering-mathematics-fig-020 | d) — I — 1 0 (D — I — I — I — I — I — I — I — © — I — • — I O A B C Fig. 20. horses, multiplication has no physical meaning. If they repre- sent feet, the product of multiphcati… | line 2895 |
Hidden-Gem Quote Candidates
Section titled “Hidden-Gem Quote Candidates”| Candidate ID | Candidate Passage | Source Location |
|---|---|---|
| No chapter-local candidates yet | - | - |
Modern Engineering Reading Prompts
Section titled “Modern Engineering Reading Prompts”- Complex quantities: Track how Steinmetz preserves geometric rotation and quadrature while translating the same operation into symbolic form.
- Ether references: Verify exact wording before drawing conclusions. Ether language must be separated from later interpretive systems.
- Impedance / reactance: Translate historical opposition terms into modern impedance, admittance, conductance, susceptance, and complex-plane notation.
- Alternating current: Compare Steinmetz’s AC language with modern sinusoidal steady-state analysis, RMS quantities, phase, and phasor notation.
- Radiation / light: Compare the chapter’s radiation vocabulary with modern electromagnetic radiation, spectral frequency, wavelength, absorption, and illumination engineering.
Ether-Field Interpretive Boundary
Section titled “Ether-Field Interpretive Boundary”- Ether references: If Steinmetz mentions ether, quote only the verified source words first; any broader ether-field synthesis belongs in a labeled interpretive layer.
- Radiation / light: Radiation and wave language can invite ether-field comparison, but source wording, modern radiation theory, and speculative synthesis must stay separated.
Promotion Checklist
Section titled “Promotion Checklist”- Open the full source text and the scan or raw PDF.
- Verify the chapter boundary and surrounding context.
- Promote exact quotations only after checking the source image.
- Move mathematical candidates into canonical equation pages only after formula typography is corrected.
- Move diagram candidates into the diagram archive only after image extraction, crop verification, and manifest creation.
- Keep Steinmetz wording, modern translation, and ether-field interpretation in separate labeled layers.