此零非彼O臺灣商務印書館, 2006 - 353 σελίδες |
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Αποτελέσματα 1 - 5 από τα 58.
Σελίδα 8
... 命題:大小兩幾何,輾轉相減,而所餘幾何俱不度原幾何,則為兩無等幾何。( If , when the less of two unequal magnitudes is ... 命題的證明,改寫成代數符號,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 ...
... 命題:大小兩幾何,輾轉相減,而所餘幾何俱不度原幾何,則為兩無等幾何。( If , when the less of two unequal magnitudes is ... 命題的證明,改寫成代數符號,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 ...
Σελίδα 8
... 命題中。不過,在命題一,歐幾里得先說明如何利用「輾轉相減」,以證明兩正整數「互質」( prime to one another )。請看底下的引文:第一題:兩不等數,輾轉相減,餘一而止,則為兩無等數之數。( Proposition 1. Two unequal numbers being set out , and the ...
... 命題中。不過,在命題一,歐幾里得先說明如何利用「輾轉相減」,以證明兩正整數「互質」( prime to one another )。請看底下的引文:第一題:兩不等數,輾轉相減,餘一而止,則為兩無等數之數。( Proposition 1. Two unequal numbers being set out , and the ...
Σελίδα 8
... 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) ,而且影響深遠。現在,讓我們介紹 Chrystal 的 ...
... 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) ,而且影響深遠。現在,讓我們介紹 Chrystal 的 ...
Σελίδα 9
... 命題之證明, Chrystal 先利用「邊」 BC 為「尺」去度量「對角線」 AC ,結果剩下「量不盡」的 CF。其次,再以這一個 CF 為「尺」去度量 BC ,結果去掉 BE 之後,還剩下 CE 「量不盡」。現在,再將這種「輾轉互相度量」的作法,應用在較小正方形 CFEG 的「邊 ...
... 命題之證明, Chrystal 先利用「邊」 BC 為「尺」去度量「對角線」 AC ,結果剩下「量不盡」的 CF。其次,再以這一個 CF 為「尺」去度量 BC ,結果去掉 BE 之後,還剩下 CE 「量不盡」。現在,再將這種「輾轉互相度量」的作法,應用在較小正方形 CFEG 的「邊 ...
Σελίδα 36
... 命題無法「確定」真假。尤其,那麼多傑出的數學家投入由集合論「悖論」引出來的數學基礎研究,卻落得幾乎是一事無成的窘況。這是本書第九至十二章的主要内容。如此一來,「數學的孤立」(第十三章)以及它究竟「何去何從」(第十四章) ,自然是數學家非常關心的 ...
... 命題無法「確定」真假。尤其,那麼多傑出的數學家投入由集合論「悖論」引出來的數學基礎研究,卻落得幾乎是一事無成的窘況。這是本書第九至十二章的主要内容。如此一來,「數學的孤立」(第十三章)以及它究竟「何去何從」(第十四章) ,自然是數學家非常關心的 ...
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.