De triangulis omnimodis
E541455
De triangulis omnimodis is a foundational 15th-century mathematical treatise by Regiomontanus that systematically develops plane and spherical trigonometry.
All labels observed (1)
| Label | Occurrences |
|---|---|
| De triangulis omnimodis canonical | 2 |
How this entity was disambiguated
This entity first appeared as the object of triple T5685954 — 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: De triangulis omnimodis Context triple: [Regiomontanus, notableWork, De triangulis omnimodis]
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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.
Euclides adauctus et methodicus
Euclides adauctus et methodicus is a 17th-century mathematical treatise by Guarino Guarini that expands and systematizes Euclidean geometry for advanced study and architectural application.
-
C.
Libellus de quinque corporibus regularibus
Libellus de quinque corporibus regularibus is a 15th-century mathematical treatise by Piero della Francesca that systematically studies the five Platonic solids and their geometric properties.
-
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.
Book II of Geometry (Descartes)
Book II of Geometry (Descartes) is the section of René Descartes’ seminal work where he develops and applies his new algebraic methods to solve classical geometric problems, helping to lay the foundations of analytic geometry.
- 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: De triangulis omnimodis Target entity description: De triangulis omnimodis is a foundational 15th-century mathematical treatise by Regiomontanus that systematically develops plane and spherical trigonometry.
-
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.
Euclides adauctus et methodicus
Euclides adauctus et methodicus is a 17th-century mathematical treatise by Guarino Guarini that expands and systematizes Euclidean geometry for advanced study and architectural application.
-
C.
Libellus de quinque corporibus regularibus
Libellus de quinque corporibus regularibus is a 15th-century mathematical treatise by Piero della Francesca that systematically studies the five Platonic solids and their geometric properties.
-
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.
Book II of Geometry (Descartes)
Book II of Geometry (Descartes) is the section of René Descartes’ seminal work where he develops and applies his new algebraic methods to solve classical geometric problems, helping to lay the foundations of analytic geometry.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
book
ⓘ
mathematical treatise ⓘ trigonometry text ⓘ |
| aim |
to provide mathematical tools for astronomy
ⓘ
to systematize plane and spherical trigonometry ⓘ |
| audience | scholars of astronomy and mathematics ⓘ |
| author | Regiomontanus ⓘ |
| century | 15th century ⓘ |
| completionYear | 1464 ⓘ |
| compositionPeriod | 1460s ⓘ |
| culturalContext | Renaissance humanism ⓘ |
| dedication | Cardinal Bessarion ⓘ |
| field |
mathematics
ⓘ
plane trigonometry ⓘ spherical trigonometry ⓘ trigonometry ⓘ |
| genre | scholarly Latin mathematics ⓘ |
| hasPart |
Book I
ⓘ
Book II ⓘ Book III ⓘ Book IV ⓘ Book V ⓘ |
| historicalSignificance |
first systematic treatise devoted entirely to trigonometry in Europe
ⓘ
standard reference for trigonometry in the 15th and 16th centuries ⓘ |
| influenceOn |
Renaissance astronomy
ⓘ
development of early modern trigonometry ⓘ navigation and surveying ⓘ |
| legacy | considered a foundational work in the history of trigonometry ⓘ |
| method | Euclidean-style axiomatic presentation ⓘ |
| notation | pre-modern trigonometric notation based on chords and sines ⓘ |
| originalLanguage | Latin ⓘ |
| placeOfWriting | Vienna ⓘ |
| printingStatus | circulated in manuscript before print ⓘ |
| relatedPerson |
Georg von Peuerbach
ⓘ
Ptolemy ⓘ
linked to:
Ptolemaios
|
| relatedWork | Almagest ⓘ |
| structure | five books ⓘ |
| subject |
astronomical applications
ⓘ
chord function ⓘ cosine-related ratios ⓘ plane triangles ⓘ properties of triangles ⓘ sine function ⓘ spherical triangles ⓘ trigonometric functions ⓘ |
| titleTranslation | On Triangles of Every Kind ⓘ |
| uses |
geometric proofs
ⓘ
numerical trigonometric tables ⓘ |
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: De triangulis omnimodis Description of subject: De triangulis omnimodis is a foundational 15th-century mathematical treatise by Regiomontanus that systematically develops plane and spherical trigonometry.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.