The word "algebra" is derived from the Arabic word ????? al-jabr, and this comes from the treatise written in the year 830 by the medieval Persian mathematician, Muhammad ibn Mūsā al-Khwārizmī, whose Arabic title, Kitāb al-mu?ta?ar fī ?isāb al-?abr wa-l-muqābala, can be translated as The Compendious Book on Calculation by Completion and Balancing. The treatise provided for the systematic solution of linear and quadratic equations. According to one history, "[i]t is not certain just what the terms al-jabr and muqabalah mean, but the usual interpretation is similar to that implied in the previous translation. The word 'al-jabr' presumably meant something like 'restoration' or 'completion' and seems to refer to the transposition of subtracted terms to the other side of an equation; the word 'muqabalah' is said to refer to 'reduction' or 'balancing'—that is, the cancellation of like terms on opposite sides of the equation. Arabic influence in Spain long after the time of al-Khwarizmi is found in Don Quixote, where the word 'algebrista' is used for a bone-setter, that is, a 'restorer'."[1] The term is used by al-Khwarizmi to describe the operations that he introduced, "reduction" and "balancing", referring to the transposition of subtracted terms to the other side of an equation, that is, the cancellation of like terms on opposite sides of the equation.[2]
The subject matter of Book II is usually called "geometric algebra." The first ten propositions of Book II can be easily interpreted in modern algebraic notation. Of course, in doing so the geometric flavor of the propositions is lost. Nonetheless, restating them algebraically can aid in understanding them. The equations are all quadratic equations since the geometry is plane geometry.
“代数”一词来自阿拉伯语单词 ????? al-jabr，这来自中世纪波斯数学家Muhammad ibn Mūsā al-Khwārizmī在830年写的论文，其阿拉伯语标题Kitāb al-mu?ta?ar fī ?isāb al-?a该论文提供了线性方程和二次方程的系统解。根据一段历史，“还不确定al-jabr和muqabalah这两个术语的含义，但通常的解释与之前翻译中暗示的解释相似。“Al-jabr”一词可能意味着类似“恢复”或“完成”的东西，似乎指的是将减去的项转换到方程的另一侧；“muqabalah”一词据说是指“减少”或“平衡”——即在方程的两侧取消类似项。在al-Khwarizmi时代很久之后，阿拉伯语在西班牙的影响就出现在《堂吉诃德》中，其中“algebrista”一词用于骨架，即“修复者”。1]该术语被al-Khwarizmi用来描述他引入的操作，“还原”和“平衡”，指的是将减去的项移至方程的另一侧，即方程两侧的类似项的抵消。[2]
(原文）：
The word "algebra" is derived from the Arabic word ????? al-jabr, and this comes from the treatise written in the year 830 by the medieval Persian mathematician, Muhammad ibn Mūsā al-Khwārizmī, whose Arabic title, Kitāb al-mu?ta?ar fī ?isāb al-?abr wa-l-muqābala, can be translated as The Compendious Book on Calculation by Completion and Balancing. The treatise provided for the systematic solution of linear and quadratic equations. According to one history, "[i]t is not certain just what the terms al-jabr and muqabalah mean, but the usual interpretation is similar to that implied in the previous translation. The word 'al-jabr' presumably meant something like 'restoration' or 'completion' and seems to refer to the transposition of subtracted terms to the other side of an equation; the word 'muqabalah' is said to refer to 'reduction' or 'balancing'—that is, the cancellation of like terms on opposite sides of the equation. Arabic influence in Spain long after the time of al-Khwarizmi is found in Don Quixote, where the word 'algebrista' is used for a bone-setter, that is, a 'restorer'."[1] The term is used by al-Khwarizmi to describe the operations that he introduced, "reduction" and "balancing", referring to the transposition of subtracted terms to the other side of an equation, that is, the cancellation of like terms on opposite sides of the equation.[2]
”和算术说数学，秀才遇见兵“
中国古代为什么没科学，一言以蔽之：只在乎实用的技术，只知其然，不深究，不知其所以然。
说：13世纪之前，在西方能够乘、除大数的人被视若数学专家。而在同时代的中国，一个十来岁的孩童就可以完成。“九九乘法表”这一伟大发明赋予了几乎所有中国人出色的基础计算能力。“九九乘法表”13世纪才传入西方国家，而且还是大学级别的学术部门才能学到。
问：既然如此，那为啥几乎所有的数学定理都是西方人发明的？
公元前200多年，中国人发明了99表，那么同时代的西方人只有大数学家才会乘法，他们整天都在为9x9等于几伤脑筋吗？
看看同时期或更早的西方人在做什么？
这是一块被称为普林顿 322的古巴比伦泥板，现在收藏于哥伦比亚大学。经测试，它诞生于公元前1800，是一个三角函数平方表。（靠掰手指头算乘法的人居然弄出了三角函数平方！）
比普林斯顿322断代更早的莫斯科纸草书（古埃及），显示了计算锥台面积的方法：“如果你知道一个截断的角锥，高为4，底边为4，顶边为2。你需要先计算4的平方，得16， 然后乘以4，得8。计算2的平方，得4。然后把16、8、4加起来，等于28。计算6的三分之一，等于2。将28翻倍，等于56。因此，答案是56，这就是正确的答案。”
公元前2000-1800年的莱因德数学纸草书，包含了面积公式、乘法除法的计算方法和分数的知识，甚至包括素数和合数，代数平均数、几何平均数以及调和平均数，同时也展示了如何求解一阶线性方程，以及代数和几何数列，还有对π的简单计算，所得值为3.1605。
公元前1800年的柏林纸草书6619显示了如何求解二次代数方程。
在古希腊，毕达哥拉斯创立毕达哥拉斯定理；欧多克索斯发展了穷竭法，也就四积分法的前身；欧几里得写下《几何原本》……
这些，都在一个不知道9x9如何计算的地方，难道古希腊，古埃及，包括巴比伦的整个历史真的都是伪造的不成？
中国孩子的数学真是厉害，几乎每年奥数金牌都拿到手发软，那这些金牌获得者至今有人成为数学大师吗？为什么呢？
拿不出一个原创的数学定理却大肆吹嘘早就被计算器抛在后面的乘法口诀，正好比站在一台庞大的超级电脑前说：老祖宗的算盘多简单实用啊。
一般数学的基础是十进制，位值。希腊数学没有二进制，没有十进制，没有位值，数字与字母用同一套符号，不能运算圆周，认为几何学来自希腊人欧几里得是没有根据，不能成立的。
太好玩了吧！
几何学来自哪里呢？
你说二进制，十进制，十六进制，六十进制是算术。可一般数学的基础是十进制，位值。希腊数学没有二进制，没有十进制，等，没有位值，数字与字母用同一套符号，不能运算圆周，认为几何学来自希腊人欧几里得是没有根据的，根本不能成立的。
请教大师，太好玩了！
好玩不？
人工智能基于二进制，四则算术基于十进制、位值，希腊、拉丁数字结构不符合十进制，没有位值，整个数字系统架构不能支持算法。
太好玩了！
代数”一词来自阿拉伯文，为什么不是希腊文？因为希腊字母与数字用一样的符号，不能直接写公式。另外加标签，还是会眼花缭乱。代数的字源推翻了源自希腊的数学，既然没有代数，几何也不能做。欧几里得几何原本之说，大有问题。
代数”与“阿拉伯数字”，欧洲人认为是Khwarizmi 花剌子米在九世纪创造的。以前阿拉伯人几千年用什么数字？为什么不用阿拉伯所在地巴比伦的数字？因为巴比伦文字/数字不先进，被淘汰了。
维基百科：
The word "algebra" is derived from the Arabic word ????? al-jabr, and this comes from the treatise written in the year 830 by the medieval Persian mathematician, Muhammad ibn Mūsā al-Khwārizmī, whose Arabic title, Kitāb al-mu?ta?ar fī ?isāb al-?abr wa-l-muqābala, can be translated as The Compendious Book on Calculation by Completion and Balancing. The treatise provided for the systematic solution of linear and quadratic equations. According to one history, "[i]t is not certain just what the terms al-jabr and muqabalah mean, but the usual interpretation is similar to that implied in the previous translation. The word 'al-jabr' presumably meant something like 'restoration' or 'completion' and seems to refer to the transposition of subtracted terms to the other side of an equation; the word 'muqabalah' is said to refer to 'reduction' or 'balancing'—that is, the cancellation of like terms on opposite sides of the equation. Arabic influence in Spain long after the time of al-Khwarizmi is found in Don Quixote, where the word 'algebrista' is used for a bone-setter, that is, a 'restorer'."[1] The term is used by al-Khwarizmi to describe the operations that he introduced, "reduction" and "balancing", referring to the transposition of subtracted terms to the other side of an equation, that is, the cancellation of like terms on opposite sides of the equation.[2]
十进制能证明所有同底等高三角形的面积都相同吗？
代数的字源推翻了源自希腊的数学，既然没有代数，几何也不能做。欧几里得几何原本之说，问题多啊？
不懂就问，大师。
太好玩了！
可见几何有几何证法，代数有代数证法。并不存在没代数证不了几何。不敢当大师，只是分开学过几何和代数课而已。
代数的字源推翻了源自希腊的数学，
所以古代希腊没有代数，几何也能做。欧几里得几何与代数无关？
俺的大学数学老师大有问题。
五郎是考据大师，从中国古代到现代，从古希腊到现代西方。
五郎重复证明古希腊的神话，俺要破除迷信。
太好玩了。
The subject matter of Book II is usually called "geometric algebra." The first ten propositions of Book II can be easily interpreted in modern algebraic notation. Of course, in doing so the geometric flavor of the propositions is lost. Nonetheless, restating them algebraically can aid in understanding them. The equations are all quadratic equations since the geometry is plane geometry.
怎么证明Algebra 代数是古希腊人的著作？为何不用古希腊语！
我的欧几里得几何学啊，你为何二千年前都不用古希腊语来写代数Algebra 这个词word 啊，是用一个“落后的”,“后来的”阿拉伯语Algebra 来证明？不懂就问。
恐怕没那么简单吧？
太好玩了！
维基百科有吗？整个世界都知道如今代数是Algebra ，不是古希腊词。
而古希腊几何代数那么发达？没有创造出几何这个词吗？而用阿拉伯文字？额的希腊神啊！
太好玩了！
谢谢！欧几里得几何学里有代数？他那个时候“代数Algebra 是什么词？是古希腊词吗？ 回答: 欧几里得几何学里有代数但还不成为代数学，请看下面我对学科的解释 由 波粒子3 于 2023-12-23 14:16:58 维基百科有吗？整个世界都知道如今代数是Algebra ，不是古希腊词。 而古希腊几何代数那么发达？没有创造出几何这个词吗？而用阿拉伯文字？额的希腊神啊！ 太好玩了！ Zzzzzzzzzz 改了： 古希腊几何代数那么发达，为何没有创造出代数这个名词呢？而是用后来的阿拉伯文字呢？请教大师啊，我的希腊神啊！ 太好玩了，继续！
“代数”Algebra 与“阿拉伯数字”，欧洲人认为是Khwarizmi 花剌子米在九世纪创造的。以前阿拉伯人几千年用什么数字？为什么不用阿拉伯所在地巴比伦的数字？因为什么？
以下是代数Algebra 一词的语源学（翻译自维基）：
“代数”一词来自阿拉伯语单词 ????? al-jabr，这来自中世纪波斯数学家Muhammad ibn Mūsā al-Khwārizmī在830年写的论文，其阿拉伯语标题Kitāb al-mu?ta?ar fī ?isāb al-?a该论文提供了线性方程和二次方程的系统解。根据一段历史，“还不确定al-jabr和muqabalah这两个术语的含义，但通常的解释与之前翻译中暗示的解释相似。“Al-jabr”一词可能意味着类似“恢复”或“完成”的东西，似乎指的是将减去的项转换到方程的另一侧；“muqabalah”一词据说是指“减少”或“平衡”——即在方程的两侧取消类似项。在al-Khwarizmi时代很久之后，阿拉伯语在西班牙的影响就出现在《堂吉诃德》中，其中“algebrista”一词用于骨架，即“修复者”。1]该术语被al-Khwarizmi用来描述他引入的操作，“还原”和“平衡”，指的是将减去的项移至方程的另一侧，即方程两侧的类似项的抵消。[2]
(原文）：
The word "algebra" is derived from the Arabic word ????? al-jabr, and this comes from the treatise written in the year 830 by the medieval Persian mathematician, Muhammad ibn Mūsā al-Khwārizmī, whose Arabic title, Kitāb al-mu?ta?ar fī ?isāb al-?abr wa-l-muqābala, can be translated as The Compendious Book on Calculation by Completion and Balancing. The treatise provided for the systematic solution of linear and quadratic equations. According to one history, "[i]t is not certain just what the terms al-jabr and muqabalah mean, but the usual interpretation is similar to that implied in the previous translation. The word 'al-jabr' presumably meant something like 'restoration' or 'completion' and seems to refer to the transposition of subtracted terms to the other side of an equation; the word 'muqabalah' is said to refer to 'reduction' or 'balancing'—that is, the cancellation of like terms on opposite sides of the equation. Arabic influence in Spain long after the time of al-Khwarizmi is found in Don Quixote, where the word 'algebrista' is used for a bone-setter, that is, a 'restorer'."[1] The term is used by al-Khwarizmi to describe the operations that he introduced, "reduction" and "balancing", referring to the transposition of subtracted terms to the other side of an equation, that is, the cancellation of like terms on opposite sides of the equation.[2]
代數學，直譯為完成和平衡計算法概要（阿拉伯語：????????? ???????????? ??? ?????? ???????? ??????????????? , al-Kitāb al-Mukhta?ar fī ?isāb al-Jabr wal-Muqābalah ; 拉丁語：Liber Algebræ et Almucabola )是波斯數學家花拉子米於公元820年左右在巴格達撰寫的關於代數的阿拉伯數學論文。 《代數學》是數學史上具有里程碑意義的著作，將代數確立為一門獨立的學科，並創造了Algebra（代數學）一詞 。
https://zh.wikipedia.org/zh-tw/代数学_(花拉子米)