Astronomical Images : Billingsley instructs readers on interpreting images on a page using pop-up shapes

Euclid

Astronomical Images

<p style='text-align: justify;'>This English translation of Euclid's <i>Elements</i> was composed by Henry Billingsley (d. 1606), a merchant who was educated at St John's College and also Oxford, where he developed an interest in mathematics. Billingsley worked mainly from the Greek text with corrections from Bartolomeo Zamberti's Latin version, and supplemented by earlier editions. This is the first English translation of Euclid's <i>Elements. </i>It contained a preface by John Dee (1527-1608), mathematician, astrologer and philosopher, that extolled the usefulness of mathematics. This edition was evidently intended for novices, as Billingsley often notes how visualising three-dimensional objects from a two-dimensional figure on a page might be difficult. One of his solutions was to paste on additional slips of paper in order to make 'pop-up' figures. Here, on a page where a definition of a pyramid is given, Billingsley writes: 'Although the figure of a Pyramis can not be well expressed in a playne superficies, â?¦ And yet that the reader may more clerely see the forme of a Pyramis, I have here set two sundry Pyramids which will appeare bodilike, if ye erecte the papers wherein are drawen the triangular sides of eche Pyramis, in such sort that the pointes of the angles F of ech triangle may in every Pyramis concurre in one point, and make a solide angle: one of which hath to his base a fower sided figure, and the other a five sided figure [the pop-up shapes at the bottom of the page]. The forme of a triangled Pyramis ye may before beholde in the example of a solide angle [the pop-up shape at the top of the page]. And by these may ye conceave of all other kindes of Pyramids'. The idea is that once the readers have learnt how to visualize these three types of pyramids with the aid of these 'pop-up' figures, they will be able to imagine all other types of pyramids themselves.</p>