<Tr> <Td_colspan="2"> <Ul> <Li> </Li> <Li> </Li> <Li> </Li> </Ul> </Td> </Tr> <Ul> <Li> </Li> <Li> </Li> <Li> </Li> </Ul> <P> In logical argument and mathematical proof, the therefore sign (∴) is generally used before a logical consequence, such as the conclusion of a syllogism . The symbol consists of three dots placed in an upright triangle and is read therefore . It is encoded at U + 2234 ∴ therefore (HTML & #8756; &there4;). For common use in Microsoft Office hold the ALT key and type "8756". While it is not generally used in formal writing, it is used in mathematics and shorthand . It is complementary to U + 2235 ∵ because (HTML & #8757;). </P> <P> According to Cajori, A History of Mathematical Notations, Johann Rahn used both the therefore and because signs to mean "therefore"; in the German edition of Teutsche Algebra (1659) the therefore sign was prevalent with the modern meaning, but in the 1668 English edition Rahn used the because sign more often to mean "therefore". Other authors in the eighteenth century also used three dots in a triangle shape to signify "therefore," but as with Rahn, there wasn't much in the way of consistency as to how the triangle was oriented; because with its current meaning appears to have originated in the nineteenth century . In this century, the three - dot notation for therefore became very rare in continental Europe, but it remains popular in the British Isles . </P>

The meaning of three dots in a triangle