Therefore sign specialized keyboards and fonts, and to prevent compatibility issues, it's often substituted by a colon followed by a period (":.") even if it's considered more elegant to use the original therefore character in printing. Therefore sign 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 . For common use in Microsoft Office hold the ALT key and type "8756". While it is not generally used in
Three-body problem effective potential. In 1767, Leonhard Euler found three families of periodic solutions in which the three masses are collinear at each instant. In 1772, Lagrange found a family of solutions in which the three masses form an equilateral triangle at each instant. Together, these solutions form the "central configurations" for the three-body problem. These solutions are valid for any mass ratios, and the masses move on Keplerian ellipses. These four families are the only known solutions for which there are explicit analytic formulae. In the special case of the circular restricted three-body problem, these solutions, viewed in a frame rotating