Arithmetica Infinitorum
E587240
Arithmetica Infinitorum is a 1656 mathematical treatise by John Wallis that systematically develops methods of infinitesimal calculus and infinite series, laying groundwork for later advances in analysis.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Arithmetica Infinitorum canonical | 3 |
| The Arithmetic of Infinites | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T6355600 — 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: Arithmetica Infinitorum Context triple: [John Wallis, notableWork, Arithmetica Infinitorum]
-
A.
De institutione geometrica
De institutione geometrica is a late antique Latin treatise on geometry that adapts and transmits classical Greek mathematical knowledge within the framework of the quadrivium.
-
B.
The Method of Mechanical Theorems
The Method of Mechanical Theorems is a treatise by Archimedes in which he uses heuristic mechanical arguments, involving balances and centers of mass, to discover and justify results in geometry and calculus-like area and volume calculations.
-
C.
Elementa curvarum linearum
Elementa curvarum linearum is a 17th-century mathematical treatise by Johan de Witt that systematically studies the geometry and properties of linear curves.
-
D.
De institutione arithmetica
De institutione arithmetica is a foundational late antique Latin treatise on arithmetic that transmitted and systematized ancient Greek number theory for the medieval West.
-
E.
Quadrature of the Parabola
Quadrature of the Parabola is a treatise by Archimedes in which he determines the area of a parabolic segment using an early form of infinite series and geometric summation.
- 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: Arithmetica Infinitorum Target entity description: Arithmetica Infinitorum is a 1656 mathematical treatise by John Wallis that systematically develops methods of infinitesimal calculus and infinite series, laying groundwork for later advances in analysis.
-
A.
De institutione geometrica
De institutione geometrica is a late antique Latin treatise on geometry that adapts and transmits classical Greek mathematical knowledge within the framework of the quadrivium.
-
B.
The Method of Mechanical Theorems
The Method of Mechanical Theorems is a treatise by Archimedes in which he uses heuristic mechanical arguments, involving balances and centers of mass, to discover and justify results in geometry and calculus-like area and volume calculations.
-
C.
Elementa curvarum linearum
Elementa curvarum linearum is a 17th-century mathematical treatise by Johan de Witt that systematically studies the geometry and properties of linear curves.
-
D.
De institutione arithmetica
De institutione arithmetica is a foundational late antique Latin treatise on arithmetic that transmitted and systematized ancient Greek number theory for the medieval West.
-
E.
Quadrature of the Parabola
Quadrature of the Parabola is a treatise by Archimedes in which he determines the area of a parabolic segment using an early form of infinite series and geometric summation.
- F. None of above. chosen
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
book
ⓘ
mathematical treatise ⓘ |
| author | John Wallis ⓘ |
| authorAffiliation | University of Oxford ⓘ |
| contributesTo |
early integral calculus
ⓘ
generalization of binomial theorem ⓘ |
| countryOfOrigin | England ⓘ |
| discusses |
areas under curves
ⓘ
binomial expansions ⓘ infinite products ⓘ interpolation of series ⓘ quadrature of curves ⓘ summation of series ⓘ |
| field | mathematics ⓘ |
| genre |
mathematical analysis text
ⓘ
scientific literature ⓘ |
| hasPart |
treatment of convergent series
ⓘ
treatment of divergent series ⓘ treatment of fractional exponents ⓘ treatment of polynomial curves ⓘ |
| historicalPeriod | 17th century ⓘ |
| influenced |
Isaac Newton
ⓘ
development of calculus ⓘ history of analysis ⓘ |
| introduces | systematic use of infinite series in algebraic problems ⓘ |
| language | Latin ⓘ |
| laysGroundworkFor |
integral calculus
ⓘ
real analysis ⓘ theory of infinite series ⓘ |
| notableFor |
early rigorous treatment of infinite series
ⓘ
influence on Newton’s work on fluxions ⓘ systematic development of infinitesimal methods ⓘ |
| publicationYear | 1656 ⓘ |
| relatedTo |
classical analysis
ⓘ
geometric quadrature ⓘ method of exhaustion ⓘ |
| subject |
algebra
ⓘ
analysis ⓘ combinatorics ⓘ infinite series ⓘ infinitesimal calculus ⓘ |
| timePeriodOfWork | Scientific Revolution ⓘ |
| title | Arithmetica Infinitorum ⓘ |
| translatedTitle |
The Arithmetic of Infinites
ⓘ
linked to:
Arithmetica Infinitorum
|
| usesMethod |
indivisibles
ⓘ
infinitesimal methods ⓘ |
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: Arithmetica Infinitorum Description of subject: Arithmetica Infinitorum is a 1656 mathematical treatise by John Wallis that systematically develops methods of infinitesimal calculus and infinite series, laying groundwork for later advances in analysis.
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Arithmetica Infinitorum