7th ESHS Conference Prague 2016

Prague, Czech Republic, 22–24 September, 2016
Symposium 38: The Power of the Knowledge of Geometry in the West
and the East
Organizers: Zhigang Ji (Shanghai Jiao Tong University, Shanghai, China), Tatsuhiko Kobayashi
(Yokkaichi University, Yokkaichi, Japan)
Chair: Zhigang Ji (Shanghai Jiao Tong University, Shanghai, China)
On the title page of the On the Revolutions of the Heavenly Spheres (1543), Copernicus wrote:
ἀγεωμέτρητος μηδεὶς εἰσίτω (Let no one ignorant of geometry enter here), that is, according to a 12thc.
Byzantine legend, the sentence inscribed on the entrance to Plato’s academy. This quotation echoes
the impact of Antiquity on Renaissance authors, and it also illustrates the power early modern scholars
associated with geometry. In 1570, Henry Billingsley got the first English translation of Euclid’s Elements
published. Four years later, Christopher Clavius contributed his Latin version of Euclid’s Elements.
The first six volumes of Clavius’ Elements were translated into Chinese in 1607 by Matteo Ricci
and Xu Guangqi. The last nine volumes of Billingsley’s Elements were translated into Chinese in 1857
by Alexander Wylie and Li Shanlan.
In his Mathematical Preface to the Billingsley’s version of the Elements, John Dee wrote: “But, unto
God our Creator, let us all be thankful: for that, as he, of his Goodness, by his Power, and in his
wisdom, have created all things, in Number, Weight, and Measure.” Number, Weight, and Measure
appeared to have been perceived as be the real grounds for the powers of geometry, not only in the
West but also in the East. This is the theme this symposium intends to bring to light.
This symposium consists of the following four papers. Paper one considers the reason why John Dee
chose Euclid's Elements to present his Mathematical Tree, and what role geometry, and more specifically
Euclid's Elements, played in John Dee’s research life. Paper two makes a comparative study of
Commandino’s and Clavius’ Prolegomena to Euclid’s Elements. Paper three relies on a cultural interpretation
of Ricci and Xu’ Prefaces to the Chinese translation under the title Jihe yuanben, to examine
how this knowledge of geometry was transferred to China. Paper four will discuss the transmission
and influence of the Chinese version of Jihe Yuanben in Japan.
Keywords: Elements, knowledge of geometry, John Dee, mathematical tree, Christopher Clavius,
Matteo Ricci, Xu Guangqi, Jihe yuanben, transmission
Why John Dee chose the Elements: A New Discussion on the ‘Mathematical Preface’ of
Henry Billingsley’s Elements of Geometry of Euclid (ID 55)
Jingbo Cao (Shanghai Jiao Tong University, Shanghai, China)
In 1570, Henry Billingsley’s Elements of Geometrie of Euclid of Megara was published as the first
English translation of Euclid’s Elements. The famous Mathematical Preface of this book, completed on
February 9 of the same year by Dee, delivered a full image of mathematics in his Mathematical Tree,
and represented the culmination of Dee’s interest in natural philosophy. This article endeavors to show
the reasons why John Dee chose Euclid's Elements to present his Mathematical Tree, as well as the
roles geometry played in Euclid's Elements through John Dee’s research life.
Besides a brief introduction to Dee’s work in his Preface, this paper will primarily present Dee’s view
of the Power of Mathematics (especially Geometry) and his explanations of the nature of Geometry,
bringing out a detailed table in which various branches of applied mathematics appeared. As he said,
“This Science of Magnitude, its properties, conditions, and appurtenances: commonly, now is, and from
the beginning, has of all Philosophers, been called Geometry.” By means of this branch of mathematics
the Road to Nature could be uncovered—“But, onto God our Creator, let us all be thankful: for that,
As he, of his Goodness, by his Power, and in his wisdom, has Created all things, in Number, Weight,
and Measure”. According to his point of view, these are the Grounds of everything. Mathematics provides
a ladder to a perfect understanding of the universe and all things within it.
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