"For this, to draw a right line from every point, to every point, follows the definition, which says, that a line is the flux of a point, and a right line an indeclinable and inflexible flow." (Proclus Lycaeus, cca 5th century)
"From what we have said it is clear that mathematical science makes a contribution of the greatest importance to philosophy and to its particular branches, which we must also mention. For theology, first of all, mathematics prepares our intellectual apprehension. Those truths about the gods that are difficult for imperfect minds to discover and understand, these the science of mathematics, with the help of likenesses, shows to be trustworthy, evident, and irrefutable." (Proclus Lycaeus, 5th century)
"It is essential that the treatment [of geometry] should be rid of everything superfluous, for the superfluous is an obstacle to the acquisition of knowledge; it should select everything that embraces the subject and brings it to focus, for this is of the highest service to science; it must have great regard both to clearness and to conciseness, for their opposites trouble our understanding; it must aim to generalize its theorems, for the division of knowledge into small elements renders it difficult of comprehension." (Proclus Lycaeus, cca 5th century)
"[...] it is my opinion that this problem is what led the ancients to attempt the squaring of the circle. For if a parallelogram can be found equal to any rectilinear figure, it is worth inquiring whether it is not possible to prove that a rectilinear figure is equal to a circular area. Indeed Archimedes proved that a circle is equal to a right-angled triangle when its radius is equal to one of the sides about the right angle and its perimeter is equal to the base. But of this elsewhere." (Proclus Lycaeus, cca 5th century)
"It is told that those who first brought out the irrationals from concealment into the open perished in a shipwreck, to a man. For the unutterable and the formless must needs be concealed. And those who uncovered and touched this image of life were instantaneously destroyed and shall remain forever exposed to the play of the eternal waves." (Proclus Lycaeus, cca 5th century)
"The mathematician speculates the causes of a certain sensible effect, without considering its actual existence; for the contemplation of universals excludes the knowledge of particulars; and he whose intellectual eye is fixed on that which is general and comprehensive, will think but little of that which is sensible and singular." (Proclus Lycaeus, cca 5th century)
"The Pythagoreans considered all mathematical science to be divided into four parts: one half they marked off as concerned with quantity, the other half with magnitude; and each of these they posited as twofold. A quantity can be considered in regard to its character by itself or in relation to another quantity, magnitudes as either stationary or in motion. Arithmetic, then, studies quantity as such, music the relations between quantities, geometry magnitude at rest, spherics magnitude inherently moving." (Proclus Lycaeus, cca 5th century)
"This, therefore, is mathematics: she reminds you of the invisible form of the soul; she gives to her own discoveries; she awakens the mind and purifies the intellect; she brings light to our intrinsic ideas; she abolishes oblivion and ignorance which are ours by birth." (Proclus Lycaeus, cca 5th century)
"We invoke the imagination and the intervals that it furnishes, since the form itself is without motion or genesis, indivisible and free of all underlying matter, though the elements latent in the form are produced distinctly and individually on the screen of imagination. What projects the images is the understanding; the source of what is projected is the form in the understanding; and what they are projected in is this 'passive nous' that unfolds in revolution about the partlessness of genuine Nous." (Proclus Lycaeus, cca 5th century)
"Wherever there is number, there is beauty." (Proclus Lycaeus, cca 5th century)
"It is told that those who first brought out the irrationals from concealment into the open perished in a shipwreck, to a man. For the unutterable and the formless must needs be concealed. And those who uncovered and touched this image of life were instantaneously destroyed and shall remain forever exposed to the play of the eternal waves." (Proclus Lycaeus, cca 5th century)
"The mathematician speculates the causes of a certain sensible effect, without considering its actual existence; for the contemplation of universals excludes the knowledge of particulars; and he whose intellectual eye is fixed on that which is general and comprehensive, will think but little of that which is sensible and singular." (Proclus Lycaeus, cca 5th century)
"The Pythagoreans considered all mathematical science to be divided into four parts: one half they marked off as concerned with quantity, the other half with magnitude; and each of these they posited as twofold. A quantity can be considered in regard to its character by itself or in relation to another quantity, magnitudes as either stationary or in motion. Arithmetic, then, studies quantity as such, music the relations between quantities, geometry magnitude at rest, spherics magnitude inherently moving." (Proclus Lycaeus, cca 5th century)
"This, therefore, is mathematics: she reminds you of the invisible form of the soul; she gives to her own discoveries; she awakens the mind and purifies the intellect; she brings light to our intrinsic ideas; she abolishes oblivion and ignorance which are ours by birth." (Proclus Lycaeus, cca 5th century)
"We invoke the imagination and the intervals that it furnishes, since the form itself is without motion or genesis, indivisible and free of all underlying matter, though the elements latent in the form are produced distinctly and individually on the screen of imagination. What projects the images is the understanding; the source of what is projected is the form in the understanding; and what they are projected in is this 'passive nous' that unfolds in revolution about the partlessness of genuine Nous." (Proclus Lycaeus, cca 5th century)
"Wherever there is number, there is beauty." (Proclus Lycaeus, cca 5th century)
No comments:
Post a Comment