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krt006 0002.chapter one clearly demonstrates the introduction to wisdom arithmetic the main points of the general chart.g2.0f

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Chinese

上面的关键在于确定为一。然后将十等依次组合上去。进行乘除运算时,从自身的上方开始。如果没有超过,就从上面降下十位。即使这样也没有超过,就从上面降下百位等,依次进行。进行混合相加时,自身位置的个位、十位、百位等。不要弄错,下面的数字。如果超过了,就从上面进位。对此进行详细说明,十以下是基本的数字。九以下是个位数的改变。从一到十,进到上一位。如果出现超过十的余数。就记录在原来的位置上。例如,十位和个位。如果两者都满了九。在个位上加上九。在《工巧明论》中说,二十四个指节为一肘。四个肘为一弓,也就是一寻。一百弓称为“拉瓦”。一千弓为一“疆扎”(རྒྱང་གྲགས།)。两个“疆扎”为一“嘎布提”。两个“嘎布提”为一“帕匝”(དཔག་ཚད།)。这是全知司徒所著的《翻译名义集释》中所说。在《名义集释》中,帕策与时轮历相同。从至尊时轮历来说,两千弓为一“疆”(རྒྱང་།)。四个“疆扎”为一“帕策”(དཔག་ཚད།)。说得非常清楚。这样,三种论典中“疆扎”(རྒྱང་གྲགས།)的说法。名义集和《名义集释》中“帕策”(དཔག་ཚད།)的说法不同,而时轮历中。要知道“帕策”(དཔག་ཚད།)是它的一半。对于其他的物质,四“色朗”(སྲང་།)为一“赛瓦”(སེ་བ།),“丹”(ཌཾ་)和“奥廓”(ཨོ་ཀོར།)。同样,“卡”(ཁལ།)、“扎”(བྲ་)、“普”(ཕུལ།)是份额。“德卡”(འདེགས་ཁལ།)、“尼雅”(ཉག་།)、“色波”(སྤོར།)等份额。从上面降下来,从下面提上去。要了解上面的规则。所有的人间算术。通过理解这个规则,可以轻松阅读。总之,所有要了解的事物都可以计算。要书写的字母和数字有十个。了解它们的乘、除、减、加的关键。就不会对算术感到困惑。如果很好地理解了这个规则。数字的变化和图表的错误。无论多少都会自然地出现在脑海中。要知道那是无边无际的。这里所说的图表的关键。不要弄错词义,以正直的心。在学习计算时,要记住。一定要牢记在心。因此,作为计算的先导,即使命名。也是进入这门学科的门径。省力而意义重大,不可或缺。是非常珍贵的。

English

The key to the top is to determine it as one. Then combine ten, etc., in order upwards. When performing multiplication and division, start from directly above yourself. If it doesn't exceed, drop the tens from above. Even if it doesn't exceed that way, drop the hundreds, etc., from above, and proceed in order. When performing mixing and addition, the places of ones, tens, hundreds, etc., of your own position. Don't make a mistake with the numbers below. If it exceeds, carry over from above. Furthermore, when explaining in detail, below ten are the basic numbers. Below nine, the place of one changes. From one to ten, it carries over to the next place. If there is a remainder of more than ten. Record it in its original place. For example, the places of tens and ones. If both are filled with nine each. Add nine to the place of one. In the "Treatise on Crafts," it says that twenty-four finger widths are one cubit. Four cubits are one bow, which is one fathom. One hundred bows are called "Lawa." One thousand bows are one "gyangdrag" (རྒྱང་གྲགས།). Two "gyangdrag" are one "gabuti." Two "gabuti" are one "pagtsad" (དཔག་ཚད།). This is according to the "Commentary on the Compendium of Nomenclature" translated by the Omniscient Situ. In the "Commentary on the Compendium of Nomenclature," the "pagtsad" is the same as in the Kalachakra system. According to the Supreme Kalachakra, two thousand bows are one "gyang" (རྒྱང་།). Four "gyangdrag" are one "pagtsad" (དཔག་ཚད།). It is stated very clearly. Thus, the term "gyangdrag" (རྒྱང་གྲགས།) in the three treatises. The term "pagtsad" (དཔག་ཚད།) in the Nomenclature and the "Commentary on the Compendium of Nomenclature" are different, while in the Kalachakra system. Know that the "pagtsad" (དཔག་ཚད།) is half of that. For other material objects, four "serang" (སྲང་།) are one "sewa" (སེ་བ།), "dam" (ཌཾ་), and "okor" (ཨོ་ཀོར།). Similarly, "khal" (ཁལ།), "dra" (བྲ་), "pul" (ཕུལ།) are shares. "Dekha" (འདེགས་ཁལ།), "nya" (ཉག་།), "sepor" (སྤོར།), etc., are shares. Descend from above and lift from below. Understand the rules above. All human arithmetic. By understanding this rule, it can be read easily. In short, everything to be known can be calculated. There are ten letters and numbers to be written. Knowing the key to their multiplication, division, subtraction, and addition. You will not be confused about arithmetic. If you understand this rule well. The changes in numbers and the errors in diagrams. No matter how much, it will naturally appear in your mind. Know that it is boundless. The key to the diagrams mentioned here. Don't mistake the meaning of the words, with an upright mind. When learning calculations, remember. Be sure to keep it in mind. Therefore, as a precursor to calculation, even naming. It is also the gateway to entering this discipline. Effortless and meaningful, indispensable. It is very precious.

Tibetan

ན་ངག་ཡིན། །འོན་ཀྱང་བློ་གསལ་བརྩོན་འགྲུས་ཅན། །མཁས་པ་ཡུན་དུ་བསྟེན་བྱས་ནས། །རིག་པ་བློ་ལ་འཛིན་པ་ལ། །ཡི་གེ་འདི་ལྟས་ཅི་ཞིག་བྱ། །དེས་ན་དེ་ལྟར་མགུ་བའི་སྐྱེས། །བདག་གི་བརྗོད་པ་འདི་མི་སེམས། །མ་སྦྱངས་ཤེས་པའི་རྩལ་མ་རྫོགས། །བརྩོན་པའི་ཤུགས་དྲག་མི་ལྡན་བཞིན། །རིག་པ་འདི་ལ་ཞུགས་འདོད་པའི། །རང་འདྲ་རྩིས་པ་གསར་བུ་ལ། །རྟོག་དཔྱོད་དབང་གི་ཡིད་འཁྲུགས་པའི། །ངལ་བ་སྤང་ཞིང་བརྗེད་གསོས་སླད། །རྩིས་མཁན་མཁས་པའི་གསུང་གི་རྒྱུན། །ཡང་ཡང་སྒྲོགས་པའི་དོན་ཇི་བཞིན། །བཀླགས་པ་ཙམ་གྱིས་ཤེས་པའི་གཏམ། །གསལ་བར་བརྗོད་ལ་ཉེས་ཡོད་མིན། །དེ་སྐད་ཚེ་རིང་ལྷ་ལམ་ལས་འོང་པའི། །རྒྱུ་སྐར་དབང་པོ་ཇི་བཞིན་ཆེས་དཀར་རྒྱུར། །ལྷག་བསམ་དག་པའི་ཚིག་གི་ནོར་བུ་འདི། །བཀོད་པའི་དགེ་བས་ཀུན་མཁྱེན་མཆོག་ཐོབ་ཤོག ། ཅེས་པ་རིག་པ་རྩིས་ཀྱི་འཇུག་སྒོ་སྤྱི་དོན་རི་མོའི་གནད་ཤིན་ཏུ་གསལ་བར་བསྟན་པའི་སྐབས་ཏེ་དང་པོའོ། ། སྐབས་དང་པོ། རིག་པ་རྩིས་ཀྱི་འཇུག་སྒོ་སྤྱི་དོན་རི་མོའི་གནད་ཤིན་ཏུ་གསལ་བར་བསྟན་པ།

Chinese

我是那昂(作者名)。然而,对于那些聪慧且勤奋的人,通过长期依止智者,将知识铭记于心的人来说,这本书又能起到什么作用呢?因此,我并不在意那些因此而感到满足的人的想法。对于那些未经学习,知识技能尚未圆满,且不具备强烈精进力的人,以及对于那些想要进入这门学问,像我一样的新手来说,为了消除因思辨而产生的困惑,为了消除疲劳并恢复精神,就像反复宣讲算术大师的教言一样,仅仅通过阅读就能理解的内容,清晰地阐述出来并没有什么过错。如是,从长寿天道而来的,像星宿之王一样洁白的光芒中,以纯洁的意乐所著的这颗语句的宝珠,愿以此功德获得一切智智的果位!这是关于算术入门总纲要义图解之极其清晰的阐释的第一章。 第一章:算术入门总纲要义图解之极其清晰的阐释。

English

I am Na-ngag (author's name). However, what use is this book for those who are intelligent and diligent, who have long relied on wise individuals, and who have memorized knowledge? Therefore, I do not mind the thoughts of those who are satisfied with this. For those who have not studied, whose knowledge and skills are not yet complete, and who do not possess strong diligence, and for those who want to enter this field of study, like me, a novice, in order to eliminate the confusion caused by speculation, to eliminate fatigue and restore the spirit, just as the teachings of arithmetic masters are repeatedly proclaimed, there is no fault in clearly explaining the content that can be understood simply by reading. Thus, from the long-lived celestial path, like the king of stars, in the extremely white light, this jewel of words composed with pure intention, may I attain the supreme omniscience through this merit! This is the first chapter on the extremely clear explanation of the key points of the general outline diagram for the introduction to the science of arithmetic. Chapter One: The Extremely Clear Explanation of the Key Points of the General Outline Diagram for the Introduction to the Science of Arithmetic.

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