Microsoft Word - Proposal to encode ACMS.docx

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1 Proposal to encode Ancient Chinese Mathematical Symbols Kushim Jiang ( 姜兆勤 ) (kushim_jiang@outlook.com) July 12, Introduction 1.1 Counting Rods Since the Shang period, the Chinese had already fully developed a decimal system. Since early times, Chinese understood basic arithmetic, algebra, equations, and negative numbers with counting rods, which were used for calculating. Some of them were added to UCS, but there is also something left. Both L2/ and L2/ have several mistakes, and after discussing we failed to reach a consensus. The amendments are list below. 1.2 Mathematical Symbols During Ming and Qing Dynasty China continued to use vertical text for a long time, so when a lot of western mathematics books were translated verbally and introduced into China by western missionaries in Ming and Qing Dynasty, the horizontal text and formulas should be converted to vertical ones. These changes are mainly reflected in the following aspects: Mathematical Symbols. Some of them were reformed. Names of unknowns. The Latin letters and the Greek letters would be translated into Heavenly Stems, Earthly Branches, Twenty-Eight Mansions or Sixty-Four Hexagrams. Equations. The simple equations would be rotated, and the complex equations would be written horizontally, where the numerator is below the denominator. Sometimes the column was as long as the equation, but sometimes an equation could cross several columns. 1.3 New Block - Ancient Chinese Mathematical Symbols Ancient Chinese mathematical symbols are self-contained, and they should be collect in a special block. The new block, Ancient Chinese Mathematical Symbols, will be set from U+1EF00 to U+1EF3F. If other symbols found in ancient Chinese books, they will be put in this block.

2 2 Character Information 2.1 Counting Rods First, the values in the Character properties are obviously wrong. The writer of those two proposals think that the current name reflects the fact that the digits have different value it s just that they take different values depending on their position. This is a common misconception. In fact, the value has no relation with its position. For example, in Fig.7 mean 4, in Fig.7 means 945, in Fig.7 means 476, in Fig.1 means In these cases, the value of should be 4 instead of 40, 400, 4000 Therefore, the value 10 to 90 should be corrected as 1 to 9. Second, from the description above, the use of vertical or horizontal counting rods has no limit. People would use them interchangeably to make the structure compact, but the specific digits to put vertical or horizontal counting rods were not stipulated. Many mathematical books in the series listed below can prove it. Therefore, the character names of UNIT and TENS should be corrected as HORIZONTAL and VERTICAL. Third, Suzhou numerals appears much later than the counting rods. So, all the Suzhou numerals should be directed to Counting Rods instead of the opposite. Suzhou Numerals 〡〢〣〤〥〦〧〨〩 Counting Rods 2.2 Combining Diacritical Marks [,, ] Like point Aʹ, point Aʺ in western symbol system, ancient Chinese books used some left-falling strokes ( 撇 ). One to three left-falling strokes were found in Qiuyishu Tongjie ( 求一術通解 ). [ ] In the process of copying and printing, mistakes were made occasionally. Later when people corrected the content of books, the wrong words would be marked by rectangles with cut corners. Lots of examples were found in Siyuan Yujian ( 四元玉鑑 ). 2.3 Enclosed Ideographic To give numbers to the order of formulas, the ideographic enclosed by circles and squares were used. The former can be found in Pingsanjiao Bianjiao Huqiushu ( 平三角邊角互求術 ), Weiji Suyuan ( 微積溯源 ), Qiuyishu Tongjie ( 求一術通解 ), Duishu Xiangjie ( 對數詳解 ), Daishushu ( 代數術 ) and Zhusuan ( 珠算 ). The latter can be found in Yuanlü Kaozhen Tujie ( 圓率攷眞圖解 ), Daishu Beizhi ( 代數備旨 ), Subu Yancao ( 粟布演草 ),

3 Duishu Xiangjie ( 對數詳解 ) and Siyuan Yujian Xicao ( 四元玉鑑細草 ). 2.4 Ancient Chinese Mathematical Symbols [,, ] Found in Daiweiji Sheji ( 代微積拾級 ). means plus (+), means minus (-), and means plus or minus (±). [, ] Found in Xingxue Beizhi ( 形學備旨 ) and Daishu Beizhi ( 代數備旨 ). is the variant of, and is the variant of. [ ] Found in Xuesuan Bitan ( 學算筆談 ). means find positive difference. For example, 5 3 = 3 5 = 2. [ ] Found in Xuesuan Bitan ( 學算筆談 ). means factorial (!). [, ] Found in Duishu Xiangjie ( 對數詳解 ). They are the variants of { and }. [ ] Found in Duishu Xiangjie ( 對數詳解 ). means et cetera ( ). The explanatory notes of it enumerated this symbol particularly, for it has not been used before. [, ] Found in Weiji Suyuan ( 微積溯源 ). means differential (d), and means integral ( ). Considering that and would grow much larger than surrounding letters and be used symbolically (Fig.28 to Fig.30), they should be encoded separately as mathematical operators and cannot be unified with the Kangxi radicals and. Some of the text examples reflect complex notation, which will need higher level representation. Here are the example. Figure 29. Example from Hua Hengfang s ( 華蘅芳 ) book Xuesuan Bitan ( 學算筆談 ) vol.11 p.19.

4 惟因故可令天角 = 人則天 = 人角. 而二二二二二天二角天角亢 =( 天角 ) 亢. 二二 ( 天角 ) 亢 = ( 吇天吜 ) 天二二人亢 ( 吇人吇角吜 ) 人二二人亢 = 吇人人二人亢吜人二其吜以代常數吜吇角也. 求其第一項二二人亢吇人人二二二之積分. 因可令人亢 = 戌則人人 = 一戌所以求得二二人亢一戌二 = = 吇訥戌 = 吇訥吇人人吇戌一二二人亢一一項求微分. 惟因二二午一 ( 人亢 ) 二二 = 人 ( 人亢 ) 午一人所以二二 ( 人亢 ) 午一二二 =( 午一 )( 人亢 ) 午二人人, ( 人 )= 人. 而 ( 二二午一人亢 ) 二二 = 人 ( 午一 )( 人亢 ) 午二二二人人 ( 人亢 ) 午一人人所以二二二二二午 =[ ( 午一 ) 二人 ( 人亢 )] 人 ( 人亢 ). 二二午 ( 人亢 ) = 人 [( 午一 ) 二人二二午 ( 人亢 ) 二 ( 人二亢二 )] 人二二午一 ( 人亢 ) 㖕. 人 3. Character Data 3.1 Character position and name Combining Diacritical Marks Extended (U+1AB0 - U+1AFF) 1AC0 1AC1 1AC2 COMBINING CHINESE PRIME COMBINING CHINESE DOUBLE PRIME COMBINING CHINESE TRIPLE PRIME Combining Diacritical Marks for Symbols (U+20D0 - U+20FF) 20F1 COMBINING ENCLOSING CUT-CORNER RECTANGLE

5 Ancient Chinese Mathematical Symbols (U+1EF00 - U+1EF3F) 1EF00 1EF01 1EF02 1EF03 1EF04 1EF05 1EF06 CHINESE PLUS SIGN CHINESE MINUS SIGN CHINESE PLUS-OR-MINUS SIGN CHINESE VARIANT PLUS SIGN CHINESE VARIANT MINUS SIGN CHINESE POSITIVE DIFFERENCE SIGN CHINESE FACTORIAL SIGN 1EF07 CHINESE LEFT CURLY BRACKET 1EF08 CHINESE RIGHT CURLY BRACKET 1EF09 1EF0A 1EF0B CHINESE ELLIPSIS CHINESE DIFFERENTIAL SIGN CHINESE INTEGRAL SIGN Enclosed Ideographic Supplement (U+1F200 - U+1F2FF) 1F23C 1F23D 1F23E 1F23F 1F252 1F253 1F254 1F255 1F256 SQUARED CJK UNIFIED IDEOGRAPH-554F SQUARED CJK UNIFIED IDEOGRAPH-9700 SQUARED CJK UNIFIED IDEOGRAPH-8A1F SQUARED CJK UNIFIED IDEOGRAPH-5E2B CIRCLED CJK UNIFIED IDEOGRAPH-7532 CIRCLED CJK UNIFIED IDEOGRAPH-4E59 CIRCLED CJK UNIFIED IDEOGRAPH-4E19 CIRCLED CJK UNIFIED IDEOGRAPH-4E01 CIRCLED CJK UNIFIED IDEOGRAPH-620A

6 1F257 1F258 1F259 1F25C 1F25D 1F25E 1F25F 1F260 1F261 1F262 1F263 1F264 1F265 1F266 1F267 1F268 1F269 1F26A 1F26B 1F26C 1F26D 1F26E 1F26F CIRCLED CJK UNIFIED IDEOGRAPH-5DF1 CIRCLED CJK UNIFIED IDEOGRAPH-5E9A CIRCLED CJK UNIFIED IDEOGRAPH-8F9B CIRCLED CJK UNIFIED IDEOGRAPH-89D2 CIRCLED CJK UNIFIED IDEOGRAPH-4EA2 CIRCLED CJK UNIFIED IDEOGRAPH-6C10 CIRCLED CJK UNIFIED IDEOGRAPH-623F CIRCLED CJK UNIFIED IDEOGRAPH E00 CIRCLED CJK UNIFIED IDEOGRAPH E8C CIRCLED CJK UNIFIED IDEOGRAPH E09 CIRCLED CJK UNIFIED IDEOGRAPH DB CIRCLED CJK UNIFIED IDEOGRAPH E94 CIRCLED CJK UNIFIED IDEOGRAPH D CIRCLED CJK UNIFIED IDEOGRAPH E03 CIRCLED CJK UNIFIED IDEOGRAPH B CIRCLED CJK UNIFIED IDEOGRAPH E5D CIRCLED CJK UNIFIED IDEOGRAPH-58F9 CIRCLED CJK UNIFIED IDEOGRAPH-8CB3 CIRCLED CJK UNIFIED IDEOGRAPH-53C1 CIRCLED CJK UNIFIED IDEOGRAPH-5343 CIRCLED CJK UNIFIED IDEOGRAPH-5929 CIRCLED CJK UNIFIED IDEOGRAPH-5730 CIRCLED CJK UNIFIED IDEOGRAPH-4EBA

7 1F270 1F271 1F272 1F273 1F274 1F275 1F276 1F277 1F278 1F279 1F27B 1F27C 1F27D 1F280 1F281 1F282 1F283 1F284 1F285 1F286 CIRCLED CJK UNIFIED IDEOGRAPH-5B50 CIRCLED CJK UNIFIED IDEOGRAPH-4E11 CIRCLED CJK UNIFIED IDEOGRAPH-5BC5 CIRCLED CJK UNIFIED IDEOGRAPH-536F CIRCLED CJK UNIFIED IDEOGRAPH-8FB0 CIRCLED CJK UNIFIED IDEOGRAPH-5DF3 CIRCLED CJK UNIFIED IDEOGRAPH-5348 CIRCLED CJK UNIFIED IDEOGRAPH-672A CIRCLED CJK UNIFIED IDEOGRAPH-7533 CIRCLED CJK UNIFIED IDEOGRAPH-9149 CIRCLED CJK UNIFIED IDEOGRAPH-4EA5 CIRCLED CJK UNIFIED IDEOGRAPH-8853 CIRCLED CJK UNIFIED IDEOGRAPH-53C8 CIRCLED CJK UNIFIED IDEOGRAPH-5477 CIRCLED CJK UNIFIED IDEOGRAPH-20B99 CIRCLED CJK UNIFIED IDEOGRAPH-20C33 CIRCLED CJK UNIFIED IDEOGRAPH-53EE CIRCLED CJK UNIFIED IDEOGRAPH-NNNNN CIRCLED CJK UNIFIED IDEOGRAPH-NNNNN CIRCLED CJK UNIFIED IDEOGRAPH-NNNNN 1F287 CIRCLED CJK UNIFIED IDEOGRAPH F28A CIRCLED CJK UNIFIED IDEOGRAPH-4E8C F28B CIRCLED CJK UNIFIED IDEOGRAPH-4E8C 9149

8 1F28C CIRCLED CJK UNIFIED IDEOGRAPH-4E8C 4EA5 1F28D CIRCLED CJK UNIFIED IDEOGRAPH-4E8C F28E 1F28F 1F290 1F291 1F292 1F293 1F294 1F295 1F296 1F297 1F298 1F299 1F2A0 1F2A1 1F2A2 1F2A3 1F2A4 1F2A5 1F2A6 1F2A7 1F2A9 CIRCLED CJK UNIFIED IDEOGRAPH E8C CIRCLED CJK UNIFIED IDEOGRAPH-4E59 4E8C CIRCLED CJK UNIFIED IDEOGRAPH-4E19 4E8C CIRCLED CJK UNIFIED IDEOGRAPH-4E01 4E8C CIRCLED CJK UNIFIED IDEOGRAPH-620A 4E8C CIRCLED CJK UNIFIED IDEOGRAPH-5DF3 4E8C CIRCLED CJK UNIFIED IDEOGRAPH-5E9A 4E8C CIRCLED CJK UNIFIED IDEOGRAPH-8F9B 4E8C CIRCLED CJK UNIFIED IDEOGRAPH-5B50 4E8C CIRCLED CJK UNIFIED IDEOGRAPH-4E11 4E8C CIRCLED CJK UNIFIED IDEOGRAPH-5BC5 4E8C CIRCLED CJK UNIFIED IDEOGRAPH-536F 4E8C SQUARED IDEOGRAPHIC NUMBER ZERO SQUARED CJK UNIFIED IDEOGRAPH-56DB SQUARED CJK UNIFIED IDEOGRAPH-4E94 SQUARED CJK UNIFIED IDEOGRAPH-516D SQUARED CJK UNIFIED IDEOGRAPH-4E03 SQUARED CJK UNIFIED IDEOGRAPH-516B SQUARED CJK UNIFIED IDEOGRAPH-4E5D SQUARED CJK UNIFIED IDEOGRAPH-5341 SQUARED CJK UNIFIED IDEOGRAPH E8C

9 1F2AB 1F2AD 1F2AE 1F2AF 1F2B0 1F2B1 1F2B2 1F2B3 1F2B4 1F2B5 1F2B6 1F2B7 SQUARED CJK UNIFIED IDEOGRAPH DB SQUARED CJK UNIFIED IDEOGRAPH D SQUARED CJK UNIFIED IDEOGRAPH E03 SQUARED CJK UNIFIED IDEOGRAPH-4E7E SQUARED CJK UNIFIED IDEOGRAPH-5426 SQUARED CJK UNIFIED IDEOGRAPH-5C65 SQUARED CJK UNIFIED IDEOGRAPH-5C6F SQUARED CJK UNIFIED IDEOGRAPH-6B65 SQUARED CJK UNIFIED IDEOGRAPH-6BD4 SQUARED CJK UNIFIED IDEOGRAPH-6CF0 SQUARED CJK UNIFIED IDEOGRAPH-4749 SQUARED CJK UNIFIED IDEOGRAPH-96A8 is different from it in the evidence figures, because there were mistakes in books in the process of transcribing. According to the Earthly Branches order, the correct character should be 己. The NNNNN in the names of means that the characters in the circle have not been included in the UCS yet: 口己 was in Extension B. VNPF decided to change it into 口巳 in IRGN2240, though Eiso Chan mentioned that the original Unihan property information for it can be moved to the new code point in the feedback. 口戊 (UK-10022) and 口庚 (UK-10023) have been included in WS Blank codes are set to be filled in the future Character properties 1AC0;COMBINING CHINESE PRIME;Mn;230;NSM;;;;;N;;;;; 1AC1;COMBINING CHINESE DOUBLE PRIME;Mn;230;NSM;;;;;N;;;;; 1AC2;COMBINING CHIENSE TRIPLE PRIME;Mn;230;NSM;;;;;N;;;;; 20F1;COMBINING ENCLOSING CUT-CORNER RECTANGLE;Me;0;NSM;;;;;N;;;;; 1EF00;CHINESE PLUS SIGN;Sm;0;L;;;;;N;;;;; 1EF01;CHINESE MINUS SIGN;Sm;0;L;;;;;N;;;;; 1EF02;CHINESE PLUS-OR-MINUS SIGN;Sm;0;L;;;;;N;;;;; 1EF03;CHINESE VARIANT PLUS SIGN;Sm;0;L;;;;;N;;;;; 1EF04;CHINESE VARIANT MINUS SIGN;Sm;0;L;;;;;N;;;;; 1EF05;CHINESE POSITIVE DIFFERENCE SIGN;Sm;0;L;;;;;N;;;;; 1EF06;CHINESE FACTORIAL SIGN;Mn;230;NSM;;;;;N;;;;; 1EF07;CHINESE LEFT CURLY BRACKET;Sm;0;L;;;;;N;;;;; 1EF08;CHINESE RIGHT CURLY BRACKET;Sm;0;L;;;;;N;;;;;

10 1EF09;CHINESE ELLIPSIS;Sm;0;L;;;;;N;;;;; 1EF0A;CHINESE DIFFERENTIAL SIGN;Sm;0;L;;;;;N;;;;; 1EF0B;CHINESE INTEGRAL SIGN;Sm;0;L;;;;;N;;;;; 1F23C;SQUARED CJK UNIFIED IDEOGRAPH-554F;So;0;L;<square> 554F;;;;N;;;;; 1F23D;SQUARED CJK UNIFIED IDEOGRAPH-9700;So;0;L;<square> 9700;;;;N;;;;; 1F23E;SQUARED CJK UNIFIED IDEOGRAPH-8A1F;So;0;L;<square> 8A1F;;;;N;;;;; 1F23F;SQUARED CJK UNIFIED IDEOGRAPH-5E2B;So;0;L;<square> 5E2B;;;;N;;;;; 1F252;CIRCLED CJK UNIFIED IDEOGRAPH-7532;So;0;L;<circle> 7532;;;;N;;;;; 1F253;CIRCLED CJK UNIFIED IDEOGRAPH-4E59;So;0;L;<circle> 4E59;;;;N;;;;; 1F254;CIRCLED CJK UNIFIED IDEOGRAPH-4E19;So;0;L;<circle> 4E19;;;;N;;;;; 1F255;CIRCLED CJK UNIFIED IDEOGRAPH-4E01;So;0;L;<circle> 4E01;;;;N;;;;; 1F256;CIRCLED CJK UNIFIED IDEOGRAPH-620A;So;0;L;<circle> 620A;;;;N;;;;; 1F257;CIRCLED CJK UNIFIED IDEOGRAPH-5DF1;So;0;L;<circle> 5DF1;;;;N;;;;; 1F258;CIRCLED CJK UNIFIED IDEOGRAPH-5E9A;So;0;L;<circle> 5E9A;;;;N;;;;; 1F259;CIRCLED CJK UNIFIED IDEOGRAPH-8F9B;So;0;L;<circle> 8F9B;;;;N;;;;; 1F25C;CIRCLED CJK UNIFIED IDEOGRAPH-89D2;So;0;L;<circle> 89D2;;;;N;;;;; 1F25D;CIRCLED CJK UNIFIED IDEOGRAPH-4EA2;So;0;L;<circle> 4EA2;;;;N;;;;; 1F25E;CIRCLED CJK UNIFIED IDEOGRAPH-6C10;So;0;L;<circle> 6C10;;;;N;;;;; 1F25F;CIRCLED CJK UNIFIED IDEOGRAPH-623F;So;0;L;<circle> 623F;;;;N;;;;; 1F260;CIRCLED CJK UNIFIED IDEOGRAPH E00;So;0;L;<circle> E00;;;;N;;;;; 1F261;CIRCLED CJK UNIFIED IDEOGRAPH E8C;So;0;L;<circle> E8C;;;;N;;;;; 1F262;CIRCLED CJK UNIFIED IDEOGRAPH E09;So;0;L;<circle> E09;;;;N;;;;; 1F263;CIRCLED CJK UNIFIED IDEOGRAPH DB;So;0;L;<circle> DB;;;;N;;;;; 1F264;CIRCLED CJK UNIFIED IDEOGRAPH E94;So;0;L;<circle> E94;;;;N;;;;; 1F265;CIRCLED CJK UNIFIED IDEOGRAPH D;So;0;L;<circle> D;;;;N;;;;; 1F266;CIRCLED CJK UNIFIED IDEOGRAPH E03;So;0;L;<circle> E03;;;;N;;;;; 1F267;CIRCLED CJK UNIFIED IDEOGRAPH B;So;0;L;<circle> B;;;;N;;;;; 1F268;CIRCLED CJK UNIFIED IDEOGRAPH E5D;So;0;L;<circle> E5D;;;;N;;;;; 1F269;CIRCLED CJK UNIFIED IDEOGRAPH-58F9;So;0;L;<circle> 58F9;;;;N;;;;; 1F26A;CIRCLED CJK UNIFIED IDEOGRAPH-8CB3;So;0;L;<circle> 8CB3;;;;N;;;;; 1F26B;CIRCLED CJK UNIFIED IDEOGRAPH-53C1;So;0;L;<circle> 53C1;;;;N;;;;; 1F26C;CIRCLED CJK UNIFIED IDEOGRAPH-5343;So;0;L;<circle> 5343;;;;N;;;;; 1F26D;CIRCLED CJK UNIFIED IDEOGRAPH-5929;So;0;L;<circle> 5929;;;;N;;;;; 1F26E;CIRCLED CJK UNIFIED IDEOGRAPH-5730;So;0;L;<circle> 5730;;;;N;;;;; 1F26F;CIRCLED CJK UNIFIED IDEOGRAPH-4EBA;So;0;L;<circle> 4EBA;;;;N;;;;; 1F270;CIRCLED CJK UNIFIED IDEOGRAPH-5B50;So;0;L;<circle> 5B50;;;;N;;;;; 1F271;CIRCLED CJK UNIFIED IDEOGRAPH-4E11;So;0;L;<circle> 4E11;;;;N;;;;; 1F272;CIRCLED CJK UNIFIED IDEOGRAPH-5BC5;So;0;L;<circle> 5BC5;;;;N;;;;; 1F273;CIRCLED CJK UNIFIED IDEOGRAPH-536F;So;0;L;<circle> 536F;;;;N;;;;; 1F274;CIRCLED CJK UNIFIED IDEOGRAPH-8FB0;So;0;L;<circle> 8FB0;;;;N;;;;; 1F275;CIRCLED CJK UNIFIED IDEOGRAPH-5DF3;So;0;L;<circle> 5DF3;;;;N;;;;; 1F276;CIRCLED CJK UNIFIED IDEOGRAPH-5348;So;0;L;<circle> 5348;;;;N;;;;; 1F277;CIRCLED CJK UNIFIED IDEOGRAPH-672A;So;0;L;<circle> 672A;;;;N;;;;; 1F278;CIRCLED CJK UNIFIED IDEOGRAPH-7533;So;0;L;<circle> 7533;;;;N;;;;; 1F279;CIRCLED CJK UNIFIED IDEOGRAPH-9149;So;0;L;<circle> 9149;;;;N;;;;; 1F27B;CIRCLED CJK UNIFIED IDEOGRAPH-4EA5;So;0;L;<circle> 4EA5;;;;N;;;;; 1F27C;CIRCLED CJK UNIFIED IDEOGRAPH-8853;So;0;L;<circle> 8853;;;;N;;;;; 1F27D;CIRCLED CJK UNIFIED IDEOGRAPH-53C8;So;0;L;<circle> 53C8;;;;N;;;;; 1F280;CIRCLED CJK UNIFIED IDEOGRAPH-5477;So;0;L;<circle> 5477;;;;N;;;;; 1F281;CIRCLED CJK UNIFIED IDEOGRAPH-20B99;So;0;L;<circle> 20B99;;;;N;;;;; 1F282;CIRCLED CJK UNIFIED IDEOGRAPH-20C33;So;0;L;<circle> 20C33;;;;N;;;;; 1F283;CIRCLED CJK UNIFIED IDEOGRAPH-53EE;So;0;L;<circle> 53EE;;;;N;;;;; 1F284;CIRCLED CJK UNIFIED IDEOGRAPH-NNNNN;So;0;L;<circle> NNNNN;;;;N;;;;; 1F285;CIRCLED CJK UNIFIED IDEOGRAPH-NNNNN;So;0;L;<circle> NNNNN;;;;N;;;;; 1F286;CIRCLED CJK UNIFIED IDEOGRAPH-NNNNN;So;0;L;<circle> NNNNN;;;;N;;;;; 1F287;CIRCLED CJK UNIFIED IDEOGRAPH-3595;So;0;L;<circle> 3595;;;;N;;;;; 1F28A;CIRCLED CJK UNIFIED IDEOGRAPH-4E8C 7533;So;0;L;<circle> 4E8C 7533;;;;N;;;;; 1F28B;CIRCLED CJK UNIFIED IDEOGRAPH-4E8C 9149;So;0;L;<circle> 4E8C 9149;;;;N;;;;; 1F28C;CIRCLED CJK UNIFIED IDEOGRAPH-4E8C 4EA5;So;0;L;<circle> 4E8C 4EA5;;;;N;;;;; 1F28D;CIRCLED CJK UNIFIED IDEOGRAPH-4E8C 5929;So;0;L;<circle> 4E8C 5929;;;;N;;;;; 1F28E;CIRCLED CJK UNIFIED IDEOGRAPH E8C;So;0;L;<circle> E8C;;;;N;;;;; 1F28F;CIRCLED CJK UNIFIED IDEOGRAPH-4E59 4E8C;So;0;L;<circle> 4E59 4E8C;;;;N;;;;; 1F290;CIRCLED CJK UNIFIED IDEOGRAPH-4E19 4E8C;So;0;L;<circle> 4E19 4E8C;;;;N;;;;;

11 1F291;CIRCLED CJK UNIFIED IDEOGRAPH-4E01 4E8C;So;0;L;<circle> 4E01 4E8C;;;;N;;;;; 1F292;CIRCLED CJK UNIFIED IDEOGRAPH-620A 4E8C;So;0;L;<circle> 620A 4E8C;;;;N;;;;; 1F293;CIRCLED CJK UNIFIED IDEOGRAPH-5DF3 4E8C;So;0;L;<circle> 5DF3 4E8C;;;;N;;;;; 1F294;CIRCLED CJK UNIFIED IDEOGRAPH-5E9A 4E8C;So;0;L;<circle> 5E9A 4E8C;;;;N;;;;; 1F295;CIRCLED CJK UNIFIED IDEOGRAPH-8F9B 4E8C;So;0;L;<circle> 8F9B 4E8C;;;;N;;;;; 1F296;CIRCLED CJK UNIFIED IDEOGRAPH-5B50 4E8C;So;0;L;<circle> 5B50 4E8C;;;;N;;;;; 1F297;CIRCLED CJK UNIFIED IDEOGRAPH-4E11 4E8C;So;0;L;<circle> 4E11 4E8C;;;;N;;;;; 1F298;CIRCLED CJK UNIFIED IDEOGRAPH-5BC5 4E8C;So;0;L;<circle> 5BC5 4E8C;;;;N;;;;; 1F299;CIRCLED CJK UNIFIED IDEOGRAPH-536F 4E8C;So;0;L;<circle> 536F 4E8C;;;;N;;;;; 1F2A0;SQUARED IDEOGRAPHIC NUMBER ZERO;So;0;L;<square> 3007;;;;N;;;;; 1F2A1;SQUARED CJK UNIFIED IDEOGRAPH-56DB;So;0;L;<square> 56DB;;;;N;;;;; 1F2A2;SQUARED CJK UNIFIED IDEOGRAPH-4E94;So;0;L;<square> 4E94;;;;N;;;;; 1F2A3;SQUARED CJK UNIFIED IDEOGRAPH-516D;So;0;L;<square> 516D;;;;N;;;;; 1F2A4;SQUARED CJK UNIFIED IDEOGRAPH-4E03;So;0;L;<square> 4E03;;;;N;;;;; 1F2A5;SQUARED CJK UNIFIED IDEOGRAPH-516B;So;0;L;<square> 516B;;;;N;;;;; 1F2A6;SQUARED CJK UNIFIED IDEOGRAPH-4E5D;So;0;L;<square> 4E5D;;;;N;;;;; 1F2A7;SQUARED CJK UNIFIED IDEOGRAPH-5341;So;0;L;<square> 5341;;;;N;;;;; 1F2A9;SQUARED CJK UNIFIED IDEOGRAPH E8C;So;0;L;<square> E8C;;;;N;;;;; 1F2AB;SQUARED CJK UNIFIED IDEOGRAPH DB;So;0;L;<square> DB;;;;N;;;;; 1F2AD;SQUARED CJK UNIFIED IDEOGRAPH D;So;0;L;<square> D;;;;N;;;;; 1F2AE;SQUARED CJK UNIFIED IDEOGRAPH E03;So;0;L;<square> E03;;;;N;;;;; 1F2AF;SQUARED CJK UNIFIED IDEOGRAPH-4E7E;So;0;L;<square> 4E7E;;;;N;;;;; 1F2B0;SQUARED CJK UNIFIED IDEOGRAPH-5426;So;0;L;<square> 5426;;;;N;;;;; 1F2B1;SQUARED CJK UNIFIED IDEOGRAPH-5C65;So;0;L;<square> 5C65;;;;N;;;;; 1F2B2;SQUARED CJK UNIFIED IDEOGRAPH-5C6F;So;0;L;<square> 5C6F;;;;N;;;;; 1F2B3;SQUARED CJK UNIFIED IDEOGRAPH-6B65;So;0;L;<square> 6B65;;;;N;;;;; 1F2B4;SQUARED CJK UNIFIED IDEOGRAPH-6BD4;So;0;L;<square> 6BD4;;;;N;;;;; 1F2B5;SQUARED CJK UNIFIED IDEOGRAPH-6CF0;So;0;L;<square> 6CF0;;;;N;;;;; 1F2B6;SQUARED CJK UNIFIED IDEOGRAPH-4749;So;0;L;<square> 4749;;;;N;;;;; 1F2B7;SQUARED CJK UNIFIED IDEOGRAPH-96A8;So;0;L;<square> 96A8;;;;N;;;;; Script: Common 3. References 刘鐸辑. 古今算學叢書 ( 据微波榭本等石印 ). 上海 : 算學書局, 光緒二十四年 (1898). 劉永錫, ( 美 ) Calvin Wilson Mateer. 形學備旨 ( 十卷 ). 重校本. 葉耀元. 形學補編 ( 一卷 ). 原稿本. 吳嘉善. 平三角術 ( 一卷 ). 白芙堂叢書本. ( 英 ) John Fryer. 三角須知 ( 一卷 ). 原刊本. 左潛. 綴術釋明附刊誤 ( 二卷 ). 白芙堂叢書本. 曾紀鴻, 左潛, 黃宗憲. 圓率考真圖解附刊誤 ( 一卷 ). 白芙堂叢書本. 黃宗憲, 左潛. 求一術通解 ( 二卷 ). 白芙堂叢書本. 戴煦. 對數簡法附刊誤 ( 二卷 ) 續對數簡法附刊誤 ( 一卷 ). 小萬卷樓叢書本. 曾紀鴻, 丁取忠. 對數詳解附刊誤 ( 五卷 ). 白芙堂叢書本. 李善蘭, ( 附卷 ) 王季同. 測圓海鏡圖表附九容公式 ( 一卷 ). 原稿本. 李冶, ( 校 ) 李銳. 益古演段 ( 三卷 ). 白芙堂叢書本. 朱世傑, ( 細草 ) 羅士琳. 四元玉鑑細草 ( 二十四卷 ). 觀我生室彙稿本. 華蘅芳, ( 英 ) John Fryer. 代數術附刊誤 ( 二十五卷 ). 江南製造局本. [ 第一百十四款, 補劉彝程沈善蒸崔朝慶算式 ] 鄒立文, 生福維. 代數備旨 ( 六卷 ). 重校本. 李善蘭, ( 英 ) Alexander Wylie, ( 注 ) 湯金鑄, 李鳳苞, 華蘅芳. 代微積拾級注 ( 十八卷 ). 墨海刊本. 附三家注原稿本. 華蘅芳, ( 英 ) John Fryer. 微積溯源 ( 六卷 ). 江南製造局本. 秦九韶, ( 附卷 ) 宋景昌, ( 校 ) 鄒安鬯. 數書九章十八卷附札記 ( 四卷 ). 宜稼堂叢書本校注原稿本.

12 ( 第一卷 ) 丁取忠, 左潛, 曾紀鴻, 吳嘉善, 李善蘭, ( 第二卷 ) 鄒伯奇, 丁取忠, 左潛, ( 補卷 ) 丁取忠. 粟布演草 ( 二卷 ) 補 ( 一卷 ). 白芙堂叢書本. 方中通. 珠算 ( 一卷 ). 隨衍室本. 徐建寅, ( 英 ) John Fryer. 運規約指 ( 三卷 ). 江南製造局本. 華蘅芳. 學算筆談 ( 十二卷 ). 原刻本. (There are also 75 books collected in the series but not put to use for examples) 4. Acknowledgement This proposal is improved with great help of Eduardo Marin, Andrew West and Eiso Chan. The glyphs of the symbols are modified from Symbola and Sursong. 5. Figures Figure 1. Example from Qin Jiushao s ( 秦九韶 ) book Shushu Jiuzhang ( 數書九章 ) vol.12 p.19 and p.24 (Shanghai: Arithmetic Publishing House ( 算學書局 ), 1898).

13 Figure 2. Example from Qin Jiushao s ( 秦九韶 ) book Shushu Jiuzhang ( 數書九章 ) vol.12 p.22 and p.24 (Shanghai: Arithmetic Publishing House ( 算學書局 ), 1898).

14 Figure 3. Example from Huang Zongxian s ( 黃宗憲 ) book Qiuyishu Tongjie ( 求一術通解 ) vol.2 p.7 (Shanghai: Arithmetic Publishing House ( 算學書局 ), 1898), showing, and in text. Figure 4. Example from Zhu Shijie s ( 朱世傑 ) book Siyuan Yujian ( 四元玉鑑 ) vol.1.2 p.11 (Shanghai: Arithmetic Publishing House ( 算學書局 ), 1898), showing in text.

15 Figure 5. Example from Wu Jiashan s ( 吳嘉善 ) book Pingsanjiao Bianjiao Huqiushu ( 平三角邊角互求術 ) p.1 and p.2 (Shanghai: Arithmetic Publishing House ( 算學書局 ), 1898), showing,,,, and in text. Figure 6. Example from Hua Hengfang s ( 華蘅芳 ) book Weiji Suyuan ( 微積溯源 ) vol.6 p.19, p.44 and p.45 (Shanghai: Arithmetic Publishing House ( 算學書局 ), 1898), showing,,, and in text.

16 Figure 7. Example from Hua Hengfang s ( 華蘅芳 ) book Daishushu ( 代數術 ) vol.7 p.7 (Shanghai: Arithmetic Publishing House ( 算學書局 ), 1898), showing and in text. * Figure 8. Example from Huang Zongxian s ( 黃宗憲 ) book Qiuyishu Tongjie ( 求一術通解 ) vol.2 p.7 (Shanghai: Arithmetic Publishing House ( 算學書局 ), 1898), showing,, and in text. * The dots are punctuations. The usage of them is like. or,. In the green box these are counting rods. means

17 Figure 9. Example from Huang Zongxian s ( 黃宗憲 ) book Qiuyishu Tongjie ( 求一術通解 ) vol.2 p.12 (Shanghai: Arithmetic Publishing House ( 算學書局 ), 1898), showing,,,, and in text. Figure 10. Example from Zeng Jihong s ( 曾紀鴻 ) book Duishu Xiangjie ( 對數詳解 ) vol.4 p.3 and p.4 (Shanghai: Arithmetic Publishing House ( 算學書局 ), 1898), showing, and in text.

18 Figure 11. Example from Hua Hengfang s ( 華蘅芳 ) book Daishushu ( 代數術 ) vol.8 p.10; vol.24 p.13, p.15, p.19 (Shanghai: Arithmetic Publishing House ( 算學書局 ), 1898), showing,,,,, and in text. Figure 12. Example from Hua Hengfang s ( 華蘅芳 ) book Daishushu ( 代數術 ) vol.24 p.22, p.26 (Shanghai: Arithmetic Publishing House ( 算學書局 ), 1898), showing and in text.

19 Figure 13. Example from Hua Hengfang s ( 華蘅芳 ) book Daishushu ( 代數術 ) vol.24 p.27, p.29, p.31, p.32, p.33, p.34 (Shanghai: Arithmetic Publishing House ( 算學書局 ), 1898), showing,,,,,,, and in text. Figure 14. Example from Hua Hengfang s ( 華蘅芳 ) book Daishushu ( 代數術 ) vol.24 p.35, p.37, p.39, p.40 (Shanghai: Arithmetic Publishing House ( 算學書局 ), 1898), showing,,, and in text.

20 Figure 15. Example from Hua Hengfang s ( 華蘅芳 ) book Daishushu ( 代數術 ) vol.25 p.6, p.7, p.8, p.17, p.19 (Shanghai: Arithmetic Publishing House ( 算學書局 ), 1898), showing,,,,, and in text. Figure 16. Example from Hua Hengfang s ( 華蘅芳 ) book Daishushu ( 代數術 ) vol.25 p.22, p.25 (Shanghai: Arithmetic Publishing House ( 算學書局 ), 1898), showing,, and in text. 餘弦甲一 means cos a+ i, where i is the imaginary unit.

21 Figure 17. Example from Fang Zhongtong s ( 方中通 ) book Zhusuan ( 珠算 ) p.5 (Shanghai: Arithmetic Publishing House ( 算學書局 ), 1898), showing, and in text. Figure 18. Example from Zeng Jihong s ( 曾紀鴻 ) book Yuanlü Kaozhen Tujie ( 圓率攷眞圖解 ) p.13 (Shanghai: Arithmetic Publishing House ( 算學書局 ), 1898), showing,, and in text.

22 Figure 19. Example from Zou Liwen s ( 鄒立文 ) book Daishu Beizhi ( 代數備旨 ) vol.3 p.13 (Shanghai: Arithmetic Publishing House ( 算學書局 ), 1898), showing in text. Figure 20. Example from Zeng Jihong s ( 曾紀鴻 ) book Subu Yancao ( 粟布演草 ) vol.1 p.3 (Shanghai: Arithmetic Publishing House ( 算學書局 ), 1898), showing, and in text.

23 Figure 21. Example from Zeng Jihong s ( 曾紀鴻 ) book Duishu Xiangjie ( 對數詳解 ) vol.2 p.7, p.8 and p.10 (Shanghai: Arithmetic Publishing House ( 算學書局 ), 1898), showing,,,, and in text. Figure 22. Example from Zeng Jihong s ( 曾紀鴻 ) book Duishu Xiangjie ( 對數詳解 ) vol.3 p.1, p.2 and p.3 (Shanghai: Arithmetic Publishing House ( 算學書局 ), 1898), showing,, and in text.

24 Figure 23. Example from Zeng Jihong s ( 曾紀鴻 ) book Duishu Xiangjie ( 對數詳解 ) vol.4 p.2, p.3, p.4 and p.6 (Shanghai: Arithmetic Publishing House ( 算學書局 ), 1898), showing,,,, and in text. Figure 24. Example from Alexander Wylie and Li Shanlan s ( 李善蘭 ) book Daiweiji Sheji Zhu ( 代微積拾級注 ) vol.1 p.10 (Shanghai: Arithmetic Publishing House ( 算學書局 ), 1898), showing,, and in text.

25 Figure 25. Example from Zou Liwen s ( 鄒立文 ) book Xingxue Beizhi ( 形學備旨 ) vol.1 p.11 and Daishu Beizhi ( 代數備旨 ) vol.1 p.19 (Shanghai: Arithmetic Publishing House ( 算學書局 ), 1898), showing and in text. Figure 26. Example from Hua Hengfang s ( 華蘅芳 ) book Xuesuan Bitan ( 學算筆談 ) vol.8 p.1 and p.4 (Shanghai: Arithmetic Publishing House ( 算學書局 ), 1898), showing, in text.

26 Figure 27. Example from Zeng Jihong s ( 曾紀鴻 ) book Duishu Xiangjie ( 對數詳解 ) vol.1 p.2 and p.3 (Shanghai: Arithmetic Publishing House ( 算學書局 ), 1898), showing, and in text. Figure 28. Example from Hua Hengfang s ( 華蘅芳 ) book Weiji Suyuan ( 微積溯源 ) vol.6 p.36 (Shanghai: Arithmetic Publishing House ( 算學書局 ), 1898), showing and in text.

27 Figure 29. Example from Hua Hengfang s ( 華蘅芳 ) book Xuesuan Bitan ( 學算筆談 ) vol.11 p.19 (Shanghai: Arithmetic Publishing House ( 算學書局 ), 1898), showing in text.

28 Figure 30. Example from Hua Hengfang s ( 華蘅芳 ) book Xuesuan Bitan ( 學算筆談 ) vol.11 p.32 (Shanghai: Arithmetic Publishing House ( 算學書局 ), showing in text.

Daiweiji Shiji ( 代微積拾級 ). For saving the space, the and usually closed to the characters narrowly. For example a + b would be represented as 甲乙. So t

Daiweiji Shiji ( 代微積拾級 ). For saving the space, the and usually closed to the characters narrowly. For example a + b would be represented as 甲乙. So t Proposal to encode Ancient Chinese Mathematical Symbols Kushim Jiang ( 姜兆勤 ) (kushim_jiang@outlook.com) July 12, 2017 1. Introduction of the new block - Ancient Chinese Mathematical Symbols. Because Chinese