Trigonometry and Double Algebra
E428887
"Trigonometry and Double Algebra" is a 19th-century mathematical treatise by Augustus De Morgan that develops trigonometric theory alongside an early systematic treatment of complex numbers and symbolic algebra.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Trigonometry and Double Algebra canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T4290524 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Trigonometry and Double Algebra Context triple: [Augustus De Morgan, notableWork, Trigonometry and Double Algebra]
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A.
Trigon
Trigon is a powerful demonic supervillain in the Teen Titans universe, best known as Raven’s tyrannical father and a major cosmic threat.
-
B.
Sine
Sine was a precolonial Serer kingdom in what is now Senegal, known for its rich Serer culture, religious traditions, and resistance to Islamic and later French expansion.
-
C.
Weierstrass substitution
The Weierstrass substitution is a trigonometric substitution technique that transforms integrals involving sine and cosine into rational functions, simplifying their evaluation.
-
D.
Algebra II
"Algebra II" is the second volume of Bartel Leendert van der Waerden’s influential algebra textbook series, which helped shape modern abstract algebra through its rigorous and systematic treatment of the subject.
-
E.
Angles
The Angles were a Germanic people who migrated to Britain in the early Middle Ages and gave their name to England and the English.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Trigonometry and Double Algebra Target entity description: "Trigonometry and Double Algebra" is a 19th-century mathematical treatise by Augustus De Morgan that develops trigonometric theory alongside an early systematic treatment of complex numbers and symbolic algebra.
-
A.
Trigon
Trigon is a powerful demonic supervillain in the Teen Titans universe, best known as Raven’s tyrannical father and a major cosmic threat.
-
B.
Sine
Sine was a precolonial Serer kingdom in what is now Senegal, known for its rich Serer culture, religious traditions, and resistance to Islamic and later French expansion.
-
C.
Weierstrass substitution
The Weierstrass substitution is a trigonometric substitution technique that transforms integrals involving sine and cosine into rational functions, simplifying their evaluation.
-
D.
Algebra II
"Algebra II" is the second volume of Bartel Leendert van der Waerden’s influential algebra textbook series, which helped shape modern abstract algebra through its rigorous and systematic treatment of the subject.
-
E.
Angles
The Angles were a Germanic people who migrated to Britain in the early Middle Ages and gave their name to England and the English.
- F. None of above. chosen
Statements (40)
| Predicate | Object |
|---|---|
| instanceOf |
19th-century mathematical treatise
ⓘ
mathematics book ⓘ nonfiction book ⓘ |
| author | Augustus De Morgan ⓘ |
| contribution |
early systematic treatment of complex numbers
ⓘ
integration of trigonometry with algebraic methods ⓘ |
| countryOfOrigin | United Kingdom ⓘ |
| describes |
algebra of complex numbers
ⓘ
properties of trigonometric functions ⓘ symbolic rules for algebraic operations ⓘ |
| educationalUse | university-level mathematics instruction ⓘ |
| field |
algebra
ⓘ
mathematical analysis ⓘ |
| genre | mathematics ⓘ |
| hasAuthor | Augustus De Morgan ⓘ |
| hasPart |
development of double algebra
ⓘ
discussion of imaginary quantities ⓘ symbolic manipulation rules ⓘ treatment of trigonometric functions ⓘ |
| historicalPeriod | Victorian era ⓘ |
| historicalSignificance |
early work in the formalization of complex-number algebra
ⓘ
represents 19th-century British approaches to algebra ⓘ |
| influencedBy |
classical trigonometry
ⓘ
earlier 19th-century algebraic notation ⓘ |
| intendedAudience |
advanced students of mathematics
ⓘ
professional mathematicians ⓘ |
| language | English ⓘ |
| mainSubject |
complex numbers
ⓘ
symbolic algebra ⓘ trigonometry ⓘ |
| mathematicalDomain |
complex analysis (foundational aspects)
ⓘ
elementary functions ⓘ |
| publicationCentury | 19th century ⓘ |
| relatedPerson |
George Boole
ⓘ
William Rowan Hamilton ⓘ |
| relatedWork | Elements of Algebra ⓘ |
| timePeriodOfWork | mid-19th century ⓘ |
| topic |
algebraic symbolism
ⓘ
imaginary numbers ⓘ trigonometric identities ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Trigonometry and Double Algebra Description of subject: "Trigonometry and Double Algebra" is a 19th-century mathematical treatise by Augustus De Morgan that develops trigonometric theory alongside an early systematic treatment of complex numbers and symbolic algebra.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.