此零非彼O臺灣商務印書館, 2006 - 353 σελίδες |
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Σελίδα 1
... 代數學習>與<數學課程的文化衝擊> (也見《科學月刊》) ,就已經明顯地指向數學教育的實質問題了。所謂 HPM ,是 Relations between History and Pedagogy of Mathematics (數學史與數學教學之關聯)的縮寫,同時,它也代表一個以此為宗旨、且隸屬於國際數學 ...
... 代數學習>與<數學課程的文化衝擊> (也見《科學月刊》) ,就已經明顯地指向數學教育的實質問題了。所謂 HPM ,是 Relations between History and Pedagogy of Mathematics (數學史與數學教學之關聯)的縮寫,同時,它也代表一個以此為宗旨、且隸屬於國際數學 ...
Σελίδα 8
... 代數學習 171 ·圖說一體。不證自明 184 ·中算史中的「張本例」( generic examples ) 190 ·勾股定理的「非常」遐想 194 •數學與人文社會的對話:一個 HPM 的進路 201 ·為教師而寫的溫柔數學史篇 207 · HPM 的法國經驗:在教學中融入古代數學問題... 212 ...
... 代數學習 171 ·圖說一體。不證自明 184 ·中算史中的「張本例」( generic examples ) 190 ·勾股定理的「非常」遐想 194 •數學與人文社會的對話:一個 HPM 的進路 201 ·為教師而寫的溫柔數學史篇 207 · HPM 的法國經驗:在教學中融入古代數學問題... 212 ...
Σελίδα 8
... 代數符號,如此大概就很容易瞭解命題的意思了。假設這兩個「幾何量」(譬如「兩個線段」好了)分別為 a , b , a > b ,那麼,經過「輾轉相減」,得 a = pb + c , b = qc + d , c = rd + e ......等等。如果,此一步驟無法終止,也就是說,餘項始終不為 0 ,那麼,就 ...
... 代數符號,如此大概就很容易瞭解命題的意思了。假設這兩個「幾何量」(譬如「兩個線段」好了)分別為 a , b , a > b ,那麼,經過「輾轉相減」,得 a = pb + c , b = qc + d , c = rd + e ......等等。如果,此一步驟無法終止,也就是說,餘項始終不為 0 ,那麼,就 ...
Σελίδα 8
... 代數教科書中的一個方法,充分反映了本命題及其證明中極為濃厚的「程序性」色彩,令人印象深刻。承英國 Dick Tahta 教授告知, George Chrystal ( 1851-1911 )曾任英國愛丁堡大學數學教授,他編寫的這一本教科書極為成功(第一版 1886 年,再版多次) ,而且影響 ...
... 代數教科書中的一個方法,充分反映了本命題及其證明中極為濃厚的「程序性」色彩,令人印象深刻。承英國 Dick Tahta 教授告知, George Chrystal ( 1851-1911 )曾任英國愛丁堡大學數學教授,他編寫的這一本教科書極為成功(第一版 1886 年,再版多次) ,而且影響 ...
Σελίδα 48
... 代數符號運算引進邏輯推論,為邏輯的形式化奠定了基礎。譬如說,他以 x 代表狗所成的類( class ) ,以 1 代表所有的物體,則 1 - x 代表非狗的物體。如此一來,下列方程式「 x + ( 1 - x ) = 1 」,就可以解讀成為「每一個物體不是狗就是非狗」了。同時,將此一 ...
... 代數符號運算引進邏輯推論,為邏輯的形式化奠定了基礎。譬如說,他以 x 代表狗所成的類( class ) ,以 1 代表所有的物體,則 1 - x 代表非狗的物體。如此一來,下列方程式「 x + ( 1 - x ) = 1 」,就可以解讀成為「每一個物體不是狗就是非狗」了。同時,將此一 ...
Δημοφιλή αποσπάσματα
Σελίδα 289 - That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles...
Σελίδα 220 - FC is equal* to the base GB, and the triangle AFC to the triangle AGB; and the remaining angles of the one are equal * to the remaining angles of the other, each to each, to which the equal sides are opposite; viz. the angle ACF to the angle ABG, and the angle AFC to the angle AGB...
Σελίδα 30 - ... legislation may fitly prescribe; and we must endeavour to persuade those who are to be the principal men of our State to go and learn arithmetic, not as amateurs, but they must carry on the study until they see the nature of numbers with the mind only; nor again, like merchants or...
Σελίδα 289 - Parallel straight lines are straight lines which, being in the same plane and being produced indefinitely in both directions, do not meet one another in either direction.
Σελίδα 244 - ... with a view to buying or selling, but for the sake of their military use, and of the soul herself; and because this will be the easiest way for her to pass from becoming to truth and being.
Σελίδα 223 - PROPOSITION 4 // two triangles have the two sides equal to two sides respectively, and have the angles contained by the equal straight lines equal, they will also have the base equal to the base, the triangle will be equal to the triangle, and the remaining angles will be equal to the remaining angles respectively, namely those which the equal sides subtend.
Σελίδα 221 - CGB, and the remaining angles will be equal to the remaining angles respectively, namely those which the equal sides subtend; therefore the angle FBC is equal to the angle GCB, and the angle BCF to the angle CBG.
Σελίδα 216 - In isosceles triangles, the angles at the base are equal to one another, and, if the equal straight lines be produced further, the angles under the base will be equal to one another.
Σελίδα 291 - Things which are equal to the same thing are equal to one another. 2. If equals be added to equals the wholes are equal. 3. If equals be taken from equals the remainders are equal.
Σελίδα 31 - I was saying, that arithmetic has a very great and elevating effect, compelling the soul to reason about abstract number, and rebelling against the introduction of visible or tangible objects into the argument.