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
Napoleon points three triangles "XBC", "YCA", "ZAB" erected over the sides of the triangle "ABC" need not be isosceles for the three lines "AX", "BY", "CZ" to be concurrent. The concurrence of the lines "AX", "BY", and "CZ" holds even in much relaxed conditions. The following result states one of the most general conditions for the lines "AX", "BY", "CZ" to be concurrent. The point of concurrency is known as the Jacobi point. Coxeter and Greitzer state the Napoleon Theorem thus: "If equilateral triangles are erected externally on the sides of any triangle, their centers form an equilateral triangle". They observe that