no solid parts are added or subtracted, but the disposition and extent of the pores or vacua are altered. But no argument can be drawn from this rough method, for the principles of practice are different from those of science.[430] The latter principles are then applied boldly to geometrical science: thus it is shown that an angle, although it may be multiplied indefinitely, can be divided only into two parts; all its lines, it is understood, consisting of _fila_ or rows of atoms;[431] that the circle has not an infinite number of radii, for from the circumference to the centre only six such lines can be drawn;[432] that not every line can be divided into two equal parts, for the physical line or _filum_ may, naturally, consist of an odd number of atoms;[433] in any case geometrical bisection can at best be a near approximation,--though the two halves be apparently equal, they may really differ by many atoms. On this basis, in the fourth and fifth books of the _De Minimo_, Bruno offers a simplification of the geometry of Euclid. As nature itself is the highest unification of the manifold, and the monad is the unity and essence of all number, so we are taught to pass "from the infinite forms and images of art to the definite forms of nature, which the mind in harmony with nature grasps in a few forms, while the _first mind_ has at once the potentiality and the reality of all particular things in the (simple) monad."[434] In accordance with the method of simplification suggested by this doctrine, Bruno sets himself to show that the greater part of Euclid may be intuitively presented in three complicated figures, named respectively the _Atrium Appollinis_, _Atrium Palladis_, and _Atrium Veneris_. He hoped that by this means, "if not always, for the most part at any rate, without further explanation, the demonstration and the very evidence of the thing might be presented to the senses of all, without numbers,--not after the partial method of others, who in considering a statue take now the foot, now the eyes, now the forehead, now other parts separately,--but explaining all in each and each in all."[435] It is no part of the purpose of this book to go at length into the mathematics of Bruno, which unfortunately have not yet met with a competent exposition. Apart from the difficulty of the matter itself, the poetical form and setting of his theorems is an additional stumbling-block in the way of understanding. Bruno was put to many shifts in order to give a poetical colouring to the most prosaic of subjects.