What did David Hume mean by relations of ideas?

For the Scottish philosopher David Hume, "relations of ideas" refers to one of two fundamental ways the mind apprehends truth, the other being "matters of fact".1

Propositions concerning relations of ideas are those that can be intuited—seen directly—or deduced from other propositions through rational inspection. These truths are characterized by the following:12

• Certainty: Because they are based on logical relations between meanings, their negations are inherently contradictory. Consequently, disciplines like arithmetic and algebra are considered more certain than those based on experience.12
• Independence from Experience: Unlike matters of fact, which require empirical observation, relations of ideas are held before the mind simply as meanings. For instance, the idea of a triangle entails the equality of its internal angles to two right angles, regardless of whether such a shape exists in the physical world.2
• Demonstrative Knowledge: Hume asserts that this level of "mere meanings" is the only domain where demonstrative knowledge is possible.2

In his work An Enquiry Concerning Human Understanding, Hume ultimately placed geometry on an equal footing with other mathematical sciences as a study of these relations.1