This text of this version of Euclid’s Elements is similar to Heath's edition which he translated from Heiberg's definitive edition in Greek, but it is slightly less literal to make it more readable.
Heath, Sir Thomas Little (1861-1940) The thirteen books of Euclid's Elements translated from the text of Heiberg with introduction and commentary. Three volumes. University Press, Cambridge, 1908. Second edition: University Press, Cambridge, 1925. Reprint: Dover Publ., New York, 1956. Reviewed: Isis 10 (1928), 60-62.
Heiberg, J. L. (Johan Ludwig) (1854-1928), and H. Menge. Euclidis opera omnia. 8 vol. & supplement, in Greek. Teubner, Leipzig, 1883-1916. Edited by J. L. Heiberg and H. Menge.
Heath's excellent critical commentary is as important as the text itself, and since Heath's edition is in publication (Dover), a purchase of that edition is recommended. The text of Heath's translation of Euclid’s Elements is also available on-line at the Perseus Project at Tuft's University starting with the first definition of book I. Not just Heath's translation, but his commentary as well as the Greek text is available at the Perseus Project. (The figures are not included.)
Other versions of Euclid’s Elements
I have also used other versions of the Elements for this translation including
Peyrard, F. Les Oeuvres d'Euclide, en Grec, en Latin et en Français. Three volumes. M. Patris, Paris, 1814.
Todhunter's edition (1862) of Simson's translation (various editions from 1756-1830) which was published in 1933 by Dent, London, with an introduction by Heath.
公理，假设
1. 直线是均匀向同一方向延长的线
2. 直线没有宽度只有方向
3. 平面是在上面的线能够保持方向不变的面
4. 平面上的两条线会交叉在一点
5. 这个点没有大小因为直线没有宽度
6. 如何知道这个点在平面上那里？
7. 在直线上取任意一点用0表示
8. 再取任意一点用1表示
9. 如果交叉在两点之间取两点中间，这个点对应的数字就是0.5
10. 如此反复下去，交叉点会逐渐接近中间点
11. 运气好的话交叉点与中间点会在一起，就知道交叉点在哪里
结论：点没有大小，一条直线可以对应所有数字。
所以饿死三千万，南京大屠杀三十万数字没有大小。
对以色列来上，巴勒斯坦不是人，所以杀死两万只是一个没有大小的数字，没有意义无足轻重。以色列人是上帝之子，以色列人这个单位非常有意义，因为与上帝连起来了。
学是单位，一门学科。欧几里得没有发明几何，他发明的是几何学，所有学科的祖先。几何学定下了学科的标准：必须consistent，logical。而且从定义假设公理推导出一门学科。
给一条黑线，线中间黑黑的＂东西＂都是＂点＂呢
还是点只在线的两端
注意只能在几何原本的逻辑中思考：）
你还须要证伪 只有线的两端有点：）
Definition 4. A straight line is a line which lies evenly with the points on itself.
Definition 4. A straight line is a line which lies evenly with the points on itself.
英文却可以创造新的字。
我的版本出自
http://aleph0.clarku.edu/~djoyce/java/elements/bookII/bookII.html#props
原始资料出自哪个版本的《几何原本》？
This text of this version of Euclid’s Elements is similar to Heath's edition which he translated from Heiberg's definitive edition in Greek, but it is slightly less literal to make it more readable.
Heath, Sir Thomas Little (1861-1940)The thirteen books of Euclid's Elements translated from the text of Heiberg with introduction and commentary. Three volumes. University Press, Cambridge, 1908. Second edition: University Press, Cambridge, 1925. Reprint: Dover Publ., New York, 1956. Reviewed: Isis 10 (1928), 60-62.
Heiberg, J. L. (Johan Ludwig) (1854-1928), and H. Menge.Euclidis opera omnia. 8 vol. & supplement, in Greek. Teubner, Leipzig, 1883-1916. Edited by J. L. Heiberg and H. Menge.
Heath's excellent critical commentary is as important as the text itself, and since Heath's edition is in publication (Dover), a purchase of that edition is recommended. The text of Heath's translation of Euclid’s Elements is also available on-line at the Perseus Project at Tuft's University starting with the first definition of book I. Not just Heath's translation, but his commentary as well as the Greek text is available at the Perseus Project. (The figures are not included.)
Other versions of Euclid’s ElementsI have also used other versions of the Elements for this translation including
Peyrard, F.Les Oeuvres d'Euclide, en Grec, en Latin et en Français. Three volumes. M. Patris, Paris, 1814.
Todhunter's edition (1862) of Simson's translation (various editions from 1756-1830) which was published in 1933 by Dent, London, with an introduction by Heath.一根线可以分为无数根相连线段
每根两端都是点。
一直分下去, 直到每根线只剩两点
结论: 线是由点构成的。
那位网友根本不懂几何。