僕竊不遜，近自託於無能之辭，網羅天下放失舊聞，考之行事，綜其終始，稽其成敗興壞之理，上計軒轅，下至於茲，為十表，本紀十二，書八章，世家三十，列傳七十，凡百三十篇，亦欲以究天人之際，通古今之變，成一家之言。草創未就，適會此禍，惜其不成 ，是以就極刑而無慍色。僕誠已著此書，藏諸名山，傳之其人通邑大都，則僕償前辱之責，雖萬被戮，豈有悔哉！然此可為智者道，難為俗人言也。
司馬遷自稱太史公，在《報任少卿書》中，自言其所著《史記》
藏諸名山，傳之其人
通邑大都也。
歷史回眸總一笑，相逢何必得相識？
文字記載千古傳，前人之事後人知！
莫問
種子入土何時發？逢人遇時自開花！
亞歷山大的帕普斯（古希臘語：Πάππος ὁ Ἀλεξανδρεύς，約290年－約350年）也譯巴普士，是羅馬帝國晚期的偉大的古希臘數學家，著有《數學彙編》（Synagoge）一書，該書記錄了許多重要的古希臘數學成果，在數學史上意義重大。
出生於今埃及亞歷山大港，主要活躍於公元4世紀早期，其生平不詳。根據其著作推斷，帕普斯主要當數學老師。著書甚多，主要作品《數學彙編》成書約340年，全書共有8卷，現今僅存的希臘文版本首尾部分有缺失，僅有第3卷至第7卷及第2卷和第8卷的部分存世。該書經費代里科·科曼迪諾（Federico Commandino）翻譯成拉丁文後開始在歐洲廣為流傳，書中的幾何原理和方法影響了包括勒內·笛卡兒，皮埃爾·德·費馬和艾薩克·牛頓在內的諸多數學家。[1]
Mathematicae collectiones, 1660
啟人無數；
吉拉德·笛沙格
吉拉德·笛沙格（Girard Desargues，1591年2月21日生於法國里昂 ，3月2日受洗，1661年10月卒於里昂），法國數學家和工程師，別名S.G.D.L. ，他署名Sieur Girard Desargues Lyonnois的縮寫。他奠定了射影幾何的基礎。以他命名的事物有笛沙格定理、笛沙格圖、笛沙格平面和月球笛沙格隕石坑。
笛沙格出生於里昂的一個為法國王室服務的家庭。他的父親是皇家公證人。笛沙格於1645開始建築師生涯。在此之前，他是作為一名導師，可能是黎塞留的隨行工程技術顧問。作為建築師，他在巴黎和里昂設計了幾個私人和公共建築；作為工程師，他設計了一個安裝在巴黎附近的提水系統，這個設計基於當時尚不了解的外擺線輪原理。
他的數學著作早在1639年就已問世，其中已有笛沙格定理的描述，並已有了射影幾何的雛形，但沒有引起較大關注。1864年他的作品被重新發現和再版，隨後被收集到L’oeuvre mathématique de Desargues一書中。在他的晚年，笛沙格公開了標有神秘標題「DALG」的文件，對這標題最普遍認可的看法是亨利·布羅卡提出的：Des Argues, Lyonnais, Géometre。
自然生華◎
處中文譯『帕普斯定理』，英文稱
Pappus’s hexagon theorem
In mathematics, Pappus’s hexagon theorem (attributed to Pappus of Alexandria) states that given one set of collinear points A, B, C, and another set of collinear points a, b, c, then the intersection points X, Y, Z of line pairs Ab and aB, Ac and aC, Bc and bC are collinear, lying on the Pappus line. These three points are the points of intersection of the “opposite” sides of the hexagon AbCaBc. It holds in a projective plane over any field, but fails for projective planes over any noncommutative division ring.[1] Projective planes in which the “theorem” is valid are called pappian planes.
The dual of this incidence theorem states that given one set of concurrent lines A, B, C, and another set of concurrent lines a, b, c, then the lines x, y, z defined by pairs of points resulting from pairs of intersections A∩b and a ∩ B, A ∩ c and a ∩ C, B ∩ c and b ∩ C are concurrent. (Concurrent means that the lines pass through one point.)
Pappus’s theorem is a special case of Pascal’s theorem for a conic—the limiting case when the conic degenerates into 2 straight lines. Pascal’s theorem is in turn a special case of the Cayley–Bacharach theorem.
The Pappus configuration is the configuration of 9 lines and 9 points that occurs in Pappus’s theorem, with each line meeting 3 of the points and each point meeting 3 lines. In general, the Pappus line does not pass through the point of intersection of ABC and abc.[2] This configuration is self dual. Since, in particular, the lines Bc, bC, XY have the properties of the lines x, y, z of the dual theorem, and collinearity of X, Y, Z is equivalent to concurrence of Bc, bC, XY, the dual theorem is therefore just the same as the theorem itself. The Levi graph of the Pappus configuration is the Pappus graph, a bipartite distance-regular graph with 18 vertices and 27 edges.
Pappus’s hexagon theorem: Points X, Y and Z are collinear on the Pappus line. The hexagon is AbCaBc.
之際。
當曉『交比』之『原點』乎？★
Origins
In its earliest known form, Pappus’s Theorem is Propositions 138, 139, 141, and 143 of Book VII of Pappus’s Collection.[5] These are Lemmas XII, XIII, XV, and XVII in the part of Book VII consisting of lemmas to the first of the three books of Euclid‘s Porisms.
The lemmas are proved in terms of what today is known as the cross ratio of four collinear points. Three earlier lemmas are used. The first of these, Lemma III, has the diagram below (which uses Pappus’s lettering, with G for Γ, D for Δ, J for Θ, and L for Λ).
Here three concurrent straight lines, AB, AG, and AD, are crossed by two lines, JB and JE, which concur at J. Also KL is drawn parallel to AZ. Then
- KJ : JL :: (KJ : AG & AG : JL) :: (JD : GD & BG : JB).
These proportions might be written today as equations:[6]
- KJ/JL = (KJ/AG)(AG/JL) = (JD/GD)(BG/JB).
The last compound ratio (namely JD : GD & BG : JB) is what is known today as the cross ratio of the collinear points J, G, D, and B in that order; it is denoted today by (J, G; D, B). So we have shown that this is independent of the choice of the particular straight line JD that crosses the three straight lines that concur at A. In particular
- (J, G; D, B) = (J, Z; H, E).
It does not matter on which side of A the straight line JE falls. In particular, the situation may be as in the next diagram, which is the diagram for Lemma X.
Just as before, we have (J, G; D, B) = (J, Z; H, E). Pappus does not explicitly prove this; but Lemma X is a converse, namely that if these two cross ratios are the same, and the straight lines BE and DH cross at A, then the points G, A, and Z must be collinear.
What we showed originally can be written as (J, ∞; K, L) = (J, G; D, B), with ∞ taking the place of the (nonexistent) intersection of JK and AG. Pappus shows this, in effect, in Lemma XI, whose diagram, however, has different lettering:
What Pappus shows is DE.ZH : EZ.HD :: GB : BE, which we may write as
- (D, Z; E, H) = (∞, B; E, G).
The diagram for Lemma XII is:
The diagram for Lemma XIII is the same, but BA and DG, extended, meet at N. In any case, considering straight lines through G as cut by the three straight lines through A, (and accepting that equations of cross ratios remain valid after permutation of the entries,) we have by Lemma III or XI
- (G, J; E, H) = (G, D; ∞ Z).
Considering straight lines through D as cut by the three straight lines through B, we have
- (L, D; E, K) = (G, D; ∞ Z).
Thus (E, H; J, G) = (E, K; D, L), so by Lemma X, the points H, M, and K are collinear. That is, the points of intersection of the pairs of opposite sides of the hexagon ADEGBZ are collinear.
Lemmas XV and XVII are that, if the point M is determined as the intersection of HK and BG, then the points A, M, and D are collinear. That is, the points of intersection of the pairs of opposite sides of the hexagon BEKHZG are collinear.
或可按圖索驥，想像『歷史現場』耶！☆
※ 出處︰ Elena Marchisotto, Apr 03, 2015
The Theorem of Pappus:
A Bridge Between Algebra and Geometry