论文标题
在Euclid的元素书籍中，在伴随的Reductio Ad Ad荒谬的图表上。查看Hartshorne和Manders
On diagrams accompanying reductio ad absurdum proofs in Euclid's Elements book I. Reviewing Hartshorne and Manders
论文作者
论文摘要
在元素的第1本书中探索选定的还原荒谬的证明，我们表明它们包括未构建的数字。这与Hartshorne声称“在Euclid的几何形状中，只有存在这些几何形象可以用统治者和指南针构建”。我们还提供了图表，质疑Manders在图的精确和共同置换属性之间的区别，特别是半欧几里得几何的模型，该模型满足了线的直率和角度的平等性，并且不满足平行假设。
Exploring selected reductio ad absurdum proofs in Book 1 of the Elements, we show they include figures that are not constructed. It is squarely at odds with Hartshorne's claim that "in Euclid's geometry, only those geometrical figures exist that can be constructed with ruler and compass". We also present diagrams questioning Manders' distinction between exact and co-exact attributes of a diagram, specifically, a model of semi-Euclidean geometry which satisfies straightness of lines and equality of angles and does not satisfy the parallel postulate.
