168. Reception of Desargues's work. Strange to say, Desargues's immortal work was heaped with the most violent abuse and held up to ridicule and scorn! "Incredible errors! Enormous mistakes and falsities! Really it is impossible for anyone who is familiar with the science concerning which he wishes to retail his thoughts, to keep from laughing!" Such were the comments of reviewers and critics. Nor were his detractors altogether ignorant and uninstructed men. In spite of the devotion of his pupils and in spite of the admiration and friendship of men like Descartes, Fermat, Mersenne, and Roberval, his book disappeared so completely that two centuries after the date of its publication, when the French geometer Chasles wrote his history of geometry, there was no means of estimating the value of the work done by Desargues. Six years later, however, in 1845, Chasles found a manuscript copy of the "Bruillon-project," made by Desargues's pupil, De la Hire.
169. Conservatism in Desargues's time. It is not necessary to suppose that this effacement of Desargues's work for two centuries was due to the savage attacks of his critics. All this was in accordance with the fashion of the time, and no man escaped bitter denunciation who attempted to improve on the methods of the ancients. Those were days when men refused to believe that a heavy body falls at the same rate as a lighter one, even when Galileo made them see it with their own eyes at the foot of the tower of Pisa. Could they not turn to the exact page and line of Aristotle which declared that the heavier body must fall the faster! "I have read Aristotle's writings from end to end, many times," wrote a Jesuit provincial to the mathematician and astronomer, Christoph Scheiner, at Ingolstadt, whose telescope seemed to reveal certain mysterious spots on the sun, "and I can assure you I have nowhere found anything similar to what you describe. Go, my son, and tranquilize yourself; be assured that what you take for spots on the sun are the faults of your glasses, or of your eyes." The dead hand of Aristotle barred the advance in every department of research. Physicians would have nothing to do with Harvey's discoveries about the circulation of the blood. "Nature is accused of tolerating a vacuum!" exclaimed a priest when Pascal began his experiments on the Puy-de-Dome to show that the column of mercury in a glass tube varied in height with the pressure of the atmosphere.
170. Desargues's style of writing. Nevertheless, authority counted for less at this time in Paris than it did in Italy, and the tragedy enacted in Rome when Galileo [pg 106] was forced to deny his inmost convictions at the bidding of a brutal Inquisition could not have been staged in France. Moreover, in the little company of scientists of which Desargues was a member the utmost liberty of thought and expression was maintained. One very good reason for the disappearance of the work of Desargues is to be found in his style of writing. He failed to heed the very good advice given him in a letter from his warm admirer Descartes.[8] "You may have two designs, both very good and very laudable, but which do not require the same method of procedure: The one is to write for the learned, and show them some new properties of the conic sections which they do not already know; and the other is to write for the curious unlearned, and to do it so that this matter which until now has been understood by only a very few, and which is nevertheless very useful for perspective, for painting, architecture, etc., shall become common and easy to all who wish to study them in your book. If you have the first idea, then it seems to me that it is necessary to avoid using new terms; for the learned are already accustomed to using those of Apollonius, and will not readily change them for others, though better, and thus yours will serve only to render your demonstrations more difficult, and to turn away your readers from your book. If you have the second plan in mind, it is certain that your terms, which are French, and conceived with spirit and grace, will be better received by persons not preoccupied with those of the ancients.... But, if you have that intention, you should make of it a great [pg 107] volume; explain it all so fully and so distinctly that those gentlemen who cannot study without yawning; who cannot distress their imaginations enough to grasp a proposition in geometry, nor turn the leaves of a book to look at the letters in a figure, shall find nothing in your discourse more difficult to understand than the description of an enchanted palace in a fairy story." The point of these remarks is apparent when we note that Desargues introduced some seventy new terms in his little book, of which only one, involution, has survived. Curiously enough, this is the one term singled out for the sharpest criticism and ridicule by his reviewer, De Beaugrand.[9] That Descartes knew the character of Desargues's audience better than he did is also evidenced by the fact that De Beaugrand exhausted his patience in reading the first ten pages of the book.
171. Lack of appreciation of Desargues. Desargues's methods, entirely different from the analytic methods just then being developed by Descartes and Fermat, seem to have been little understood. "Between you and me," wrote Descartes[10] to Mersenne, "I can hardly form an idea of what he may have written concerning conics." Desargues seems to have boasted that he owed nothing to any man, and that all his results had come from his own mind. His favorite pupil, De la Hire, did not realize the extraordinary simplicity and generality of his work. It is a remarkable fact that the only one of all his associates to understand and appreciate the methods of Desargues should be a lad of sixteen years!
172. Pascal and his theorem. One does not have to believe all the marvelous stories of Pascal's admiring sisters to credit him with wonderful precocity. We have the fact that in 1640, when he was sixteen years old, he published a little placard, or poster, entitled "Essay pour les conique,"[11] in which his great theorem appears for the first time. His manner of putting it may be a little puzzling to one who has only seen it in the form given in this book, and it may be worth while for the student to compare the two methods of stating it. It is given as follows: "If in the plane of M, S, Q we draw through M the two lines MK and MV, and through the point S the two lines SK and SV, and let K be the intersection of MK and SK; V the intersection of MV and SV; A the intersection of MA and SA (A is the intersection of SV and MK), and μ the intersection of MV and SK; and if through two of the four points A, K, μ, V, which are not in the same straight line with M and S, such as K and V, we pass the circumference of a circle cutting the lines MV, MP, SV, SK in the points O, P, Q, N; I say that the lines MS, NO, PQ are of the same order." (By "lines of the same order" Pascal means lines which meet in the same point or are parallel.) By projecting the figure thus described upon another plane he is able to state his theorem for the case where the circle is replaced by any conic section.