PHILOSOPHY & FUN OF ALGEBRA, Chapter 1, From Arithmetic To Algebra, part 2

Chapter 1, From Arithmetic To Algebra, part 2

Sometimes your teachers set you more complicated problems than:—What is the price of six pounds of sugar? For instance:—In what proportion must one mix tea bought at 1s. 4d. a pound with tea bought at 1s. 10d. a pound so as to make 5 per cent. proﬁt by selling the mixture at 1s. 9d. a pound?

Arithmetic, then, means dealing logically with certain facts that we know, about number, with a view to arriving at knowledge which as yet we do not possess. When people had only arithmetic and not algebra, they found out a surprising amount of things about numbers and quantities. But there remained problems which they very much needed to solve and could not. They had to guess the answer; and, of course, they usually guessed wrong. And I am inclined to think they disagreed. Each person, of course, thought his own guess was nearest to the truth. Probably they quarrelled, and got nervous and overstrained and miserable, and said things which hurt the feelings of their friends, and which they saw afterwards they had better not have said—things which threw no light on the problem, and only upset everybody's mind more than ever. I was not there, so I cannot tell you exactly what happened; but quarrelling and disagreeing and nerve-strain always do go on in such cases. At last (at least I should suppose this is what happened) some man, or perhaps some woman, suddenly said: “How stupid we've all been! We have been dealing logically with all the facts we knew about this problem, except the most important fact of all, the fact of our own ignorance.

Chapter 1, From Arithmetic To Algebra, part 2 الفصل الأول، من الحساب إلى الجبر، الجزء الثاني Kapitel 1, Von der Arithmetik zur Algebra, Teil 2 Capítulo 1, De la aritmética al álgebra, parte 2 Capitolo 1, Dall'aritmetica all'algebra, parte 2 第1章算数から代数へその2 Rozdział 1, Od arytmetyki do algebry, część 2 Capítulo 1, Da aritmética à álgebra, parte 2 Глава 1. От арифметики к алгебре, часть 2 Bölüm 1, Aritmetikten Cebire, kısım 2

Sometimes your teachers set you more complicated problems than:—What is the price of six pounds of sugar? |||assign|||||||||||||| أحيانًا يطرح عليك معلموك مشاكل أكثر تعقيدًا من: - ما هو سعر ستة أرطال من السكر؟ A veces tus maestros te plantean problemas más complicados que: ¿Cuál es el precio de seis libras de azúcar? Às vezes, seus professores colocam problemas mais complicados do que: — Qual é o preço de seis libras de açúcar? For instance:—In what proportion must one mix tea bought at 1s. |||||必须|||||| على سبيل المثال: - ما هي النسبة التي يجب أن يتم شراء مزيج الشاي منها بسعر 1 شلن؟ Por ejemplo:—¿En qué proporción se debe mezclar té comprado a 1s. Por exemplo:—Em que proporção se deve misturar chá comprado a 1s. 4d. 4 د. 4d. 4d. a pound with tea bought at 1s. تم شراء رطل مع الشاي بسعر 1 ثانية. una libra con té comprado en 1s. uma libra com chá comprada a 1s. 10d. 10 د. 10d. 10d. a pound so as to make 5 per cent. جنيه وذلك لجعل 5 في المائة. una libra para hacer el 5 por ciento. uma libra para fazer 5 por cento. proﬁt by selling the mixture at 1s. 利润|||||| profit|||||| nyereség|||||| الربح عن طريق بيع الخليط بسعر 1 ثانية. ganancia vendiendo la mezcla a 1s. lucro vendendo a mistura a 1s. 9d. 9 د. 9d. a pound? باوند؟ uma libra?

Arithmetic, then, means dealing logically with certain facts that we know, about number, with a view to arriving at knowledge which as yet we do not possess. فالحساب إذن يعني التعامل منطقيا مع بعض الحقائق التي نعرفها، عن العدد، بهدف الوصول إلى المعرفة التي لا نملكها بعد. La aritmética, entonces, significa tratar lógicamente con ciertos hechos que conocemos, sobre el número, con miras a llegar a un conocimiento que aún no poseemos. Aritmética, então, significa lidar logicamente com certos fatos que conhecemos, sobre número, com vistas a chegar a um conhecimento que ainda não possuímos. 那么，算术意味着在逻辑上处理一些我们知道的关于数字的事实，以期得出我们尚不具备的知识。 When people had only arithmetic and not algebra, they found out a surprising amount of things about numbers and quantities. |||||||algebra|||||||||||| عندما كان لدى الناس علم الحساب فقط وليس الجبر، اكتشفوا قدرًا مدهشًا من الأشياء المتعلقة بالأعداد والكميات. Cuando las personas solo tenían aritmética y no álgebra, descubrieron una cantidad sorprendente de cosas sobre números y cantidades. Quando as pessoas tinham apenas aritmética e não álgebra, descobriram uma quantidade surpreendente de coisas sobre números e quantidades. 当人们只有算术而不是代数时，他们发现了数量和数量惊人的事物。 But there remained problems which they very much needed to solve and could not. ولكن ظلت هناك مشاكل كانوا بحاجة ماسة إلى حلها ولم يتمكنوا من حلها. Pero quedaban problemas que necesitaban mucho resolver y no pudieron. Mas restavam problemas que eles precisavam muito resolver e não podiam. 但是仍然存在他们非常需要解决而不能解决的问题。 They had to guess the answer; and, of course, they usually guessed wrong. وكان عليهم أن يخمنوا الجواب؛ وبطبيعة الحال، عادة ما يكون تخمينهم خاطئًا. Tuvieron que adivinar la respuesta; y, por supuesto, por lo general adivinaron mal. Eles tiveram que adivinhar a resposta; e, claro, eles geralmente adivinhavam errado. And I am inclined to think they disagreed. |||tend|||| وأنا أميل إلى الاعتقاد بأنهم اختلفوا. Y me inclino a pensar que no estaban de acuerdo. E estou inclinado a pensar que eles discordaram. 我倾向于认为他们不同意。 Each person, of course, thought his own guess was nearest to the truth. Every|||||||||||| وبطبيعة الحال، كان كل شخص يعتقد أن تخمينه هو الأقرب إلى الحقيقة. Cada persona, por supuesto, pensó que su propia suposición era la más cercana a la verdad. Cada pessoa, é claro, pensou que seu próprio palpite era o mais próximo da verdade. Probably they quarrelled, and got nervous and overstrained and miserable, and said things which hurt the feelings of their friends, and which they saw afterwards they had better not have said—things which threw no light on the problem, and only upset everybody's mind more than ever. |||||||过度紧张||||||||||||||||||||||||||||||||||||||| ||se sont disputés|||||épuisés||||||||||||||||||||||||||||||||||||||| ||argued, fought, disagreed|||||overly stressed|||||||||||||||||later on|||||||||||||||||||||| ||vesztekedtek|||||túlhajszolt||||||||||||||||||||||||||||||||||||||| ربما تشاجروا وشعروا بالتوتر والإرهاق والبؤس، وقالوا أشياء تؤذي مشاعر أصدقائهم، والتي رأوها بعد ذلك كان من الأفضل ألا يقولوها - أشياء لم تلقي أي ضوء على المشكلة، بل أزعجت عقول الجميع أكثر. من أي وقت مضى. Probablemente se pelearon, y se pusieron nerviosos, sobrecargados y miserables, y dijeron cosas que hirieron los sentimientos de sus amigos, y que luego vieron que era mejor no haber dicho, cosas que no arrojaron luz sobre el problema, y solo perturbaron más la mente de todos. que nunca Provavelmente eles brigaram, ficaram nervosos, exaustos e infelizes, e disseram coisas que feriram os sentimentos de seus amigos, e que depois viram que era melhor não terem dito - coisas que não lançaram luz sobre o problema e apenas perturbaram ainda mais a mente de todos. do que nunca. 他们可能吵架，变得紧张，过分紧张和痛苦，并说了伤害朋友感情的事，后来他们最好不要说-那些事情没有解决这个问题，只会让每个人的思想更加沮丧比以往任何时候都好。 I was not there, so I cannot tell you exactly what happened; but quarrelling and disagreeing and nerve-strain always do go on in such cases. I|||||||||||||||||nervous|tension||||||| لم أكن هناك، لذا لا أستطيع أن أخبركم بما حدث بالضبط؛ لكن الشجار والخلاف وتوتر الأعصاب يستمر دائمًا في مثل هذه الحالات. Yo no estaba allí, así que no puedo decirles exactamente lo que pasó; pero las peleas, los desacuerdos y la tensión nerviosa siempre continúan en tales casos. Eu não estava lá, então não posso dizer exatamente o que aconteceu; mas brigas, discordâncias e tensão nervosa sempre acontecem nesses casos. At last (at least I should suppose this is what happened) some man, or perhaps some woman, suddenly said: “How stupid we've all been! ||at last|||||||||||||||||In what way|||| أخيرًا (على الأقل يجب أن أفترض أن هذا ما حدث) قال رجل ما، أو ربما امرأة، فجأة: "كم كنا جميعًا أغبياء! Por fin (al menos debo suponer que esto es lo que sucedió) algún hombre, o tal vez alguna mujer, dijo de repente: “¡Qué estúpidos hemos sido todos! Finalmente (pelo menos eu suponho que foi isso que aconteceu) algum homem, ou talvez alguma mulher, disse de repente: “Como todos nós fomos estúpidos! We have been dealing logically with all the facts we knew about this problem, except the most important fact of all, the fact of our own ignorance. لقد كنا نتعامل بشكل منطقي مع كل الحقائق التي نعرفها حول هذه المشكلة، باستثناء الحقيقة الأكثر أهمية على الإطلاق، وهي حقيقة جهلنا. Hemos estado tratando lógicamente con todos los hechos que conocíamos sobre este problema, excepto el hecho más importante de todos, el hecho de nuestra propia ignorancia. Temos lidado logicamente com todos os fatos que conhecíamos sobre esse problema, exceto o fato mais importante de todos, o fato de nossa própria ignorância. 除了最重要的事实，就是我们自己的无知之外，我们一直在逻辑上处理我们知道的有关该问题的所有事实。