Brook Taylor’s elegant but austere treatment of perspective in the first edition of Linear Perspective proved difficult for all but the most determined scholars to absorb. Treating his topic in the most general fashion possible, and largely eschewing examples or particular cases, gave little help for his readers to hold onto. In an attempt to meet his audience part way, Taylor rewrote the book, extending and expanding his explanation and introducing more examples in a largely unsuccessful attempt to make the work more palatable. It is clear from his comments that he was as baffled by the inability of ordinary mortals to read his perfectly clear work, as they were defeated by his uncompromising generality. In the much-expanded preface to the second edition, Taylor laid out his reasoning and articulated his underlying philosophy of education.
The changes began with the title. The first edition had been called, Linear Perspective, and only further down did it mention its novelty, `a new method of representing justly all manner of objects as they appear to the eye’. In the second edition, the novelty was emphasized right from the beginning, the New Principles of Linear Perspective, with the further explanation that the book expounded: `the art of designing on a plane the representations of all sorts of objects, in a more general and simple method than has been done before.’
The preface to the first edition spanned two paragraphs; that of the revised second edition ran twelve pages. The new preface is also much more conventional in beginning with a justification of the new work by declaring all previous treatments to be lacking, while again emphasizing the simplicity of his own approach:
Considering how few, and how simple the Principles are, upon which the whole Art of Perspective depends, and withal how useful, nay how absolutely necessary this Art is to all sorts of Designing; I have often wonder’d, that is has still been left in so low a degree of Perfection, as it is found to be, in the Books that have been hitherto wrote upon it.
Reflecting his own emphasis on the mathematical qualities of generality and elegance, his criticisms of previous authors center on their excessive attention to details:
Some of those Books indeed are very voluminous: but then they are made so, only by long and tedious Discourses, explaining of common things; or by a great number of Examples, which indeed do make some of these Book valuable, by the great Variety of curious Cuts that are in them; but do not at all instruct the Reader, by any Improvements made in the Art it self.
Speaking as a high-level mathematician, Taylor’s specific charge against his predecessors is that while they might have had a lot of experience, they were insufficiently skilled mathematicians.
For it seems that those, who have hitherto treated of this Subject, have been more conversant in the Practice of Designing, than in the Principles of Geometry; and therefore when, in their Practice, the Occasions that have offer’d, have put them upon inventing particular Expedients, they have thought them to be worth communicating to the Public, as Improvements in this Art; but they have not been able to produce any real Improvements in it, for want of a sufficient Fund of Geometry, that might have enabled them to render the Principals of it more universal, and more convenient for Practice.
Taylor now explains what is different about his own text and how in contrasts with earlier treatments of perspective.
In this Book I have endeavour’d to do this; and have done my utmost to render the Principles of the Art as general, and as universal as may be, and to devise such Constructions, as might be the most simple and useful in Practice.
In the preface to the first edition Taylor said that he had found it necessary to ‘lay aside’ such terms as ‘Horizontal Line’ from the study of perspective, but had not troubled the reader with an explanation of why this should be necessary. In the second edition preface, he now uses this very term as an example with an explanation of why he was forced to begin anew. First he reiterates his general point:
In order to this, I found it absolutely necessary to consider this Subject entirely anew, as if it had never been treated of before; the Principles of the old Perspective being so narrow, and so confined, that they could be no use in my Design: And I was forced to invent new Terms of Art, those already in use being so peculiarly adapted to the imperfect Notions that have hitherto been had of this Art, that I could make no use of them in explaining those general Principles I intended to establish.
Following the general criticism, Taylor gives a specific example:
The Term of Horizontal Line, for instance, is apt to confine the Notions of a Learner to the Plane of the Horizon, and to make him imagine, that that Plane enjoys some particular Privileges, which make the Figures in it more easy and more convenient to be described, by the means of that Horizontal Line, than the Figures in any other Plane; as if all other Planes might not as conveniently be handled, by finding other Lines of the same nature belonging to them.
Thus speaks the mathematician.