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X(10269) lies on these lines: {1,3}, {2,104}, {4,5253}, {5,6256}, {8,6940}, {11,6923}, {12,6958}, {21,2096}, {30,7956}, {100,7967}, {106,1480}, {140,958}, {182,2810}, {329,1006}, {355,474}, {388,6891}, {404,944}, {497,5840}, {499,6842}, {515,6692}, {572,2178}, {601,1201}, {631,2975}, {859,1790}, {912,997}, {952,1376}, {956,6735}, {957,4216}, {993,3452}, {1001,6914}, {1012,1519}, {1125,3560}, {1478,6882}, {1483,3913}, {1621,6950}, {2829,3816}, {3085,6961}, {3086,6850}, {3434,6955}, {3436,6967}, {3525,5260}, {3600,6926}, {3616,6906}, {4297,6985}, {4299,7491}, {4413,5790}, {4423,7489}, {5080,6963}, {5265,6908}, {5303,6875}, {5433,6863}, {5438,5534}, {5550,6920}, {5603,6909}, {5731,6905}, {6684,8666}, {6691,6959}, {6825,7288}, {6928,7354}, {7330,8583}

X(10269) = midpoint of X(i),X(j) for these {i,j}: {1,3359}, {3,999}, {497,6948}, {4293,6827}, {4297,7682} X(10269) = reflection of X(i) in X(j) for these (i,j):(3820,140), (6929,3816) X(10269) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,36,1470), (1,5193,999), (3,1385,10267), (3,10246,55), (36,3576,3), (993,10165,6883), (1125,5450,3560), (6256,10200,5)

X(10270) lies on these lines: {1,3}, {63,2057}, {84,1376}, {104,4853}, {223,1167}, {580,937}, {601,2999}, {603,1103}, {936,1158}, {2550,6705}, {2551,6256}, {4652,6735}, {5438,6001}, {5450,9623}, {5720,7992}, {5732,6796}, {7330,8580}

X(10270) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3,165,10268), (3,3359,1), (40,3576,3057), (1697,5193,1)

Let A'B'C' be the intouch triangle; Ma = midpoint of AA', and define Mb and Mc cyclically; M1 = midpoint of A'X(1), and define M2 and M3 cyclically. The circumcircles of MaM2M3, MbM3M1, McM1M2 concur in X(10271); the circumcircles of M1MbMc, M2McMa, M3MaMb concur in X(1387). See Antreas Hatzipolakis and Peter Moses, 24436 ).

X(10271) lies on these lines: {{1,1537}, {55,108}, {123,3816}, {676,2804}, {1359,1388}, {2817,9957}, {2823,4353}

X(10271) = midpoint of X(108) and X(3318)

In the plane of a triangle ABC, let NaNbNc be the pedal triangle of N = X(5) and OaObOc the pedal triangle of O = X(3). Let N1 = reflection of N in BC, and define N2 and N3 cyclically. Let O1 = reflection of O in BC, and define O2 and O3 cyclically. Let La be the line through Na parallel to O1N1, and define Lb and Lc cyclically. The lines La, Lb, Lc concur in X(10272). See Antreas Hatzipolakis and Peter Moses, 24449 ).

Let (Oa) be the circle centered at A and tangent to the Euler line. Define (Ob) and (Oc) cyclically. Let La be the polar of X(4) wrt (Oa), and define Lb and Lc cyclically. (Note: X(4) is the perspector of any circle centered at a vertex of ABC.) Let A' = Lb∩Lc, and define B' and C' cyclically. Triangle A'B'C' is the reflection of ABC in X(5972), which is the radical center of (Oa), (Ob), (Oc); and X(10272) = X(140)-of-A'B'C'. (Randy Hutson, December 10, 2016)

X(10272) lies on these lines: {2,399}, {3,146}, {4,7666}, {5,49}, {30,113}, {69,10201}, {74,549 }, {125,3628}, {140,5663}, {403,3043}, {468,1986}, {495,10091}, {496,10088}, {542,547}, {546,9820} ,{548,2777}, {550,7728}, {597, 9976}, {1125,2771}, {1154,10096}, {1656,3448}, {2931,5654}, {2948,5886}, {3564,6593}, {3582, 6126}, {3584,7343}, {3850,10113} ,{5055,9143}, {5066,7687}, { 5432,7727}, {5876,10125}, {5898, 7693}, {6140,6592}, {6153,10095} ,{6677,9826}, {7525,10117}, {7542,7723}, {7722,10018}

The descriptor MAY have the additional properties set out below and MAY contain any number of other properties (not defined in this specification).

The following is an illustration of this structure:

A field descriptor MUST be a JSON object that describes a single field. The descriptor provides additional human-readable documentation for a field, as well as additional information that may be used to validate the field or create a user interface for data entry.

Here is an illustration:

The field descriptor object MAY contain any number of other properties. Some specific properties are defined below. Of these, only the name property is REQUIRED .

The field descriptor MUST contain a name property. This property SHOULD correspond to the name of field/column in the data file (if it has a name). As such it SHOULD be unique (though it is possible, but very bad practice, for the data file to have multiple columns with the same name). name SHOULD NOT be considered case sensitive in determining uniqueness. However, since it should correspond to the name of the field in the data file it may be important to preserve case.

A human readable label or title for the field

A description for this field e.g. "The recipient of the funds"

type and format properties are used to give The type of the field (string, number etc) - see below for more detail. If type is not provided a consumer should assume a type of "string".

A field's type property is a string indicating the type of this field.

A field's format property is a string, indicating a format for the field type.

Both type and format are optional: in a field descriptor, the absence of a type property indicates that the field is of the type "string", and the absence of a format property indicates that the field's type format is "default".

Types are based on the type set of json-schema with some additions and minor modifications (cf other type lists include those in Elasticsearch types ).

The type list with associated formats and other related properties is as follows.

The field contains strings, that is, sequences of characters.

format :

default binary

The field contains numbers of any kind including decimals.

The lexical formatting follows that of decimal in XMLSchema : a non-empty finite-length sequence of decimal digits separated by a period as a decimal indicator. An optional leading sign is allowed. If the sign is omitted, "+" is assumed. Leading and trailing zeroes are optional. If the fractional part is zero, the period and following zero(es) can be omitted. For example: '-1.23', '12678967.543233', '+100000.00', '210'.

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