De triangulis omnimodis

work by Regiomontanus

Also known as: “On Triangles of Every Kind”

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June 25, 2026

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De triangulis omnimodis (On Triangles of All Kinds), written by Regiomontanus around 1464, is considered the first Western book dedicated solely to trigonometry. This work was significant because it presented plane and spherical trigonometry independently of astronomy.123

The book contains all the necessary theorems for solving triangles, though it uses verbal descriptions rather than symbolic algebra, which had not yet been invented. It notably includes the law of sines in a form similar to its modern expression. De triangulis omnimodis was highly regarded by later scientists, including Nicolaus Copernicus, who studied an annotated copy of the work.1

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Regiomontanus
…plane and spherical trigonometry in De triangulis omnimodis (1464; “On Triangles of All Kinds”) to his discovery of a Greek manuscript (incomplete) of Arithmetica, the great work of Diophantus of Alexandria (fl. c. ad 250). His writings also show his interest in perfect numbers (numbers equal to the sum of…
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…plane and spherical trigonometry in De triangulis omnimodis (1464; “On Triangles of All Kinds”) to his discovery of a Greek manuscript (incomplete) of Arithmetica, the great work of Diophantus of Alexandria (fl. c. ad 250). His writings also show his interest in perfect numbers (numbers equal to the sum of…
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trigonometry
Passage to Europe
…in 1533 under the title On Triangles of Every Kind. Its author was the astronomer Regiomontanus (1436–76). On Triangles contains all the theorems needed to solve triangles, planar or spherical—although these theorems are expressed in verbal form, as symbolic algebra had yet to be invented. In particular, the law of…
Read More
…in 1533 under the title On Triangles of Every Kind. Its author was the astronomer Regiomontanus (1436–76). On Triangles contains all the theorems needed to solve triangles, planar or spherical—although these theorems are expressed in verbal form, as symbolic algebra had yet to be invented. In particular, the law of…
Read More