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PHILOSOPHY & FUN OF ALGEBRA, Chapter 1, From Arithmetic To Algebra, part 1

Chapter 1, From Arithmetic To Algebra, part 1

Arithmetic means dealing logically with facts which we know (about questions of number). “Logically”; that is to say, in accordance with the “Logos” or hidden wisdom, i.e. the laws of normal action of the human mind. For instance, you are asked what will have to be paid for six pounds of sugar at 3d. a pound. You multiply the six by the three. That is not because of any property of sugar, or of the copper of which the pennies are made. You would have done the same if the thing bought had been starch or apples. You would have done just the same if the material had been tea at 3s. a pound. Moreover, you would have done just the same kind of action if you had been asked the price of seven pounds of tea at 2s. a pound. You do what you do under direction of the Logos or hidden wisdom. And this law of the Logos is made not by any King or Parliament, but by whoever or whatever created the human mind. Suppose that any Parliament passed an act that all the children in the kingdom were to divide the price by the number of pounds; the Parliament could not make the answer come right. The only result of a foolish Act of Parliament like that would be that everybody's sums would come wrong, and everybody's accounts be in confusion, and everybody would wonder why the trade of the country was going to the bad. In former times there were kings and emperors quite stupid enough to pass Acts like that, but governments have grown wiser by experience and found out that, as far as arithmetic goes, there is no use in ordering people to go contrary to the laws of the Logos, because the Logos has the whip hand, and knows its own business, and is master of the situation. Therefore children now are allowed to study the laws of the Logos, whenever the business on hand is finding out how much they are to pay in a shop.

Chapter 1, From Arithmetic To Algebra, part 1 الفصل الأول، من الحساب إلى الجبر، الجزء الأول Kapitel 1, Von der Arithmetik zur Algebra, Teil 1 Capítulo 1, De la aritmética al álgebra, parte 1 1 skyrius, Nuo aritmetikos iki algebros, 1 dalis Capítulo 1, Da aritmética à álgebra, parte 1 Глава 1. От арифметики к алгебре, часть 1 Bölüm 1, Aritmetikten Cebire, kısım 1 Розділ 1, Від арифметики до алгебри, частина 1

Arithmetic means dealing logically with facts which we know (about questions of number). الحساب يعني التعامل بشكل منطقي مع الحقائق التي نعرفها (فيما يتعلق بالأسئلة العددية). La aritmética significa tratar lógicamente con hechos que conocemos (sobre cuestiones de número). Aritmética significa lidar logicamente com fatos que conhecemos (sobre questões de número). Арифметика означает логическое обращение с известными нам фактами (в вопросах числа). Арифметика означає логічне оперування фактами, які ми знаємо (про питання числа). “Logically”; that is to say, in accordance with the “Logos” or hidden wisdom, i.e. "منطقيا"؛ وهذا يعني، وفقًا لـ "اللوجوس" أو الحكمة الخفية، أي “Lógicamente”; es decir, de acuerdo con el “Logos” o sabiduría oculta, es decir, “Logicamente”; isto é, de acordo com o “Logos” ou sabedoria oculta, isto é, "Логически"; то есть в соответствии с «Логосом» или скрытой мудростью, т.е. the laws of normal action of the human mind. قوانين العمل الطبيعي للعقل البشري. las leyes de la acción normal de la mente humana. 人間の心の正常な作用の法則。 as leis da ação normal da mente humana. закони нормальної дії людського розуму. For instance, you are asked what will have to be paid for six pounds of sugar at 3d. على سبيل المثال، يتم سؤالك عن المبلغ الذي يجب دفعه مقابل ستة أرطال من السكر بسعر ثلاثي الأبعاد. Por ejemplo, le preguntan cuánto tendrá que pagar por seis libras de azúcar a 3 peniques. 例えば、6ポンドの砂糖を3ドルで買うとしたらいくらになるかと尋ねられたとする。 Por exemplo, perguntam-lhe o que terá de ser pago por seis libras de açúcar a 3d. Например, вас спрашивают, сколько придется заплатить за шесть фунтов сахара в 3 пенса. Наприклад, вас запитують, скільки доведеться заплатити за шість фунтів цукру за курсом 3. a pound. باوند. una libra. uma libra. You multiply the six by the three. أنت تضرب الستة في الثلاثة. You multiply the six by the three. Multiplicas el seis por el tres. Você multiplica o seis pelo três. That is not because of any property of sugar, or of the copper of which the pennies are made. وليس ذلك من خاصية السكر أو النحاس الذي تصنع منه البنسات. That is not because of any property of sugar, or of the copper of which the pennies are made. Eso no se debe a ninguna propiedad del azúcar o del cobre del que están hechos los centavos. Isso não se deve a nenhuma propriedade do açúcar ou do cobre de que são feitas as moedas. You would have done the same if the thing bought had been starch or apples. وكنت ستفعل الشيء نفسه لو كان الشيء الذي اشتريته نشاءً أو تفاحًا. Hubieras hecho lo mismo si lo comprado hubiera sido almidón o manzanas. Você teria feito o mesmo se a coisa comprada fosse amido ou maçãs. Вы поступили бы точно так же, если бы в качестве товара был куплен крахмал или яблоки. You would have done just the same if the material had been tea at 3s. كنت ستفعل الشيء نفسه لو كانت المادة عبارة عن شاي عند 3 ثوانٍ. You would have done just the same if the material had been tea at 3s. Hubieras hecho lo mismo si el material hubiera sido té a los 3s. Você teria feito o mesmo se o material fosse chá às 3s. a pound. باوند. a pound. uma libra. Moreover, you would have done just the same kind of action if you had been asked the price of seven pounds of tea at 2s. علاوة على ذلك، كنت ستفعل نفس النوع من الإجراء لو طُلب منك سعر سبعة أرطال من الشاي بسعر 2 شلن. Moreover, you would have done just the same kind of action if you had been asked the price of seven pounds of tea at 2s. Además, habrías hecho exactamente el mismo tipo de acción si te hubieran preguntado el precio de siete libras de té a 2 chelines. Além disso, você teria feito exatamente o mesmo tipo de ação se lhe perguntassem o preço de sete libras de chá a 2 xelins. a pound. باوند. una libra. uma libra. You do what you do under direction of the Logos or hidden wisdom. أنت تفعل ما تفعله بتوجيه من اللوغوس أو الحكمة الخفية. You do what you do under direction of the Logos or hidden wisdom. Haces lo que haces bajo la dirección del Logos o sabiduría oculta. Vous faites ce que vous faites sous la direction du Logos ou de la sagesse cachée. Você faz o que faz sob a direção do Logos ou sabedoria oculta. And this law of the Logos is made not by any King or Parliament, but by whoever or whatever created the human mind. وقانون اللوغوس هذا لم يضعه أي ملك أو برلمان، بل أي شخص أو أي شيء خلق العقل البشري. And this law of the Logos is made not by any King or Parliament, but by whoever or whatever created the human mind. Y esta ley del Logos no es hecha por ningún Rey o Parlamento, sino por quienquiera o lo que sea que haya creado la mente humana. Et cette loi du Logos n'est pas faite par un roi ou un parlement, mais par quiconque ou quoi que ce soit qui a créé l'esprit humain. E esta lei do Logos não é feita por nenhum Rei ou Parlamento, mas por quem ou o que quer que tenha criado a mente humana. 徽标的法律不是由任何国王或议会制定的,而是由创造人类思想的任何人或任何人制定的。 Suppose that any Parliament passed an act that all the children in the kingdom were to divide the price by the number of pounds; the Parliament could not make the answer come right. لنفترض أن أي برلمان أصدر قانونًا يقضي بأن يقوم جميع الأطفال في المملكة بتقسيم السعر على عدد الجنيهات؛ ولم يتمكن البرلمان من تقديم الإجابة الصحيحة. Suppose that any Parliament passed an act that all the children in the kingdom were to divide the price by the number of pounds; the Parliament could not make the answer come right. Supongamos que cualquier parlamento aprobara una ley por la que todos los niños del reino tuvieran que dividir el precio por el número de libras; el Parlamento no pudo dar la respuesta correcta. Supposez qu'un Parlement adopte une loi stipulant que tous les enfants du royaume doivent diviser le prix par le nombre de livres ; le Parlement n'a pas pu donner la bonne réponse. Suponha que qualquer Parlamento aprovasse uma lei determinando que todas as crianças do reino deveriam dividir o preço pelo número de libras; o Parlamento não conseguiu dar a resposta correta. 假设任何议会通过一项法案,使王国中的所有孩子都将价格除以磅数;议会无法使答案正确。 The only result of a foolish Act of Parliament like that would be that everybody's sums would come wrong, and everybody's accounts be in confusion, and everybody would wonder why the trade of the country was going to the bad. إن النتيجة الوحيدة لقانون برلماني أحمق كهذا هو أن تخطئ مبالغ الجميع، وتتشوش حسابات الجميع، ويتساءل الجميع عن سبب تدهور تجارة البلاد. The only result of a foolish Act of Parliament like that would be that everybody's sums would come wrong, and everybody's accounts be in confusion, and everybody would wonder why the trade of the country was going to the bad. El único resultado de una tonta Ley del Parlamento como esa sería que las sumas de todos saldrían mal, y las cuentas de todos estarían confundidas, y todos se preguntarían por qué el comercio del país iba tan mal. Le seul résultat d'une loi stupide du Parlement comme celle-là serait que les sommes de tout le monde seraient fausses, et les comptes de tout le monde seraient confus, et tout le monde se demanderait pourquoi le commerce du pays allait mal. O único resultado de uma tola Lei do Parlamento como essa seria que as somas de todos dariam errado, e as contas de todos ficariam confusas, e todos se perguntariam por que o comércio do país estava indo mal. In former times there were kings and emperors quite stupid enough to pass Acts like that, but governments have grown wiser by experience and found out that, as far as  arithmetic goes, there is no use in ordering people to go contrary  to the laws of the Logos, because the Logos has the whip hand, and knows its own business, and is master of the situation. في العصور السابقة، كان هناك ملوك وأباطرة أغبياء بما فيه الكفاية لتمرير مثل هذه القوانين، لكن الحكومات أصبحت أكثر حكمة من خلال التجربة واكتشفت أنه، بقدر ما تذهب الحسابات الحسابية، لا فائدة من إصدار أوامر للناس بمخالفة قوانين الدولة. الشعارات، لأن اللوغوس له اليد السوطية، ويعرف شؤونه الخاصة، وهو سيد الموقف. In former times there were kings and emperors quite stupid enough to pass Acts like that, but governments have grown wiser by experience and found out that, as far as arithmetic goes, there is no use in ordering people to go contrary to the laws of the Logos, because the Logos has the whip hand, and knows its own business, and is master of the situation. En tiempos pasados hubo reyes y emperadores lo suficientemente estúpidos como para aprobar Actos como ese, pero los gobiernos se han vuelto más sabios por experiencia y han descubierto que, en lo que respecta a la aritmética, no sirve de nada ordenar a la gente que actúe en contra de las leyes del país. Logos, porque el Logos tiene el látigo en la mano, y conoce su propio negocio, y es dueño de la situación. Autrefois, il y avait des rois et des empereurs assez stupides pour passer des lois comme celle-là, mais les gouvernements sont devenus plus sages par expérience et ont découvert qu'en ce qui concerne l'arithmétique, il ne sert à rien d'ordonner aux gens d'aller à l'encontre des lois du Logos, parce que le Logos a le fouet, qu'il connaît ses propres affaires et qu'il est maître de la situation. Antigamente havia reis e imperadores bastante estúpidos para aprovar leis como essa, mas os governos tornaram-se mais sábios pela experiência e descobriram que, no que diz respeito à aritmética, não adianta ordenar que as pessoas contrariem as leis do Logos, porque o Logos tem a mão de chicote, conhece seu próprio negócio e é senhor da situação. 在过去,国王和皇帝非常愚蠢,无法通过这样的法案,但各国政府凭经验变得更加明智,并发现,就算术而言,命令人们违背法律是没有用的。徽标,因为徽标拥有鞭子之手,并且了解自己的业务,并且是情况的主人。 Therefore children now are allowed to study the laws of the Logos, whenever the business on hand is finding out how much they are to pay in a shop. ولذلك، يُسمح للأطفال الآن بدراسة قوانين الشعارات، عندما تكتشف الشركة القائمة المبلغ الذي يتعين عليهم دفعه في المتجر. Therefore children now are allowed to study the laws of the Logos, whenever the business on hand is finding out how much they are to pay in a shop. Por lo tanto, a los niños ahora se les permite estudiar las leyes del Logos, siempre que el asunto en cuestión sea averiguar cuánto deben pagar en una tienda. Par conséquent, les enfants sont maintenant autorisés à étudier les lois du Logos, chaque fois que l'affaire en cours découvre combien ils doivent payer dans un magasin. Portanto, as crianças agora podem estudar as leis do Logos, sempre que o negócio em questão estiver descobrindo quanto devem pagar em uma loja. 因此,现在,只要手头的商家发现他们在商店里要付多少钱,现在就可以让孩子们学习徽标的法律。