The Definition in the Elements, according to Clavius, is this: Magnitudes are said to be in the same Reason [ratio], a first to a second, and a third to a fourth, when the Equimultiples of the first and third according to any Multiplication whatsoever are both together either short of, equal to, or exceed the Equimultiples of the second and fourth, if those be taken, which answer one another….
Such is Euclid’s Definition of Proportions; that scare-Crow at which the over modest or slothful Dispositions of Men are generally affrighted: they are modest, who distrust their own Ability, as soon as a Difficulty appears, but they are slothful that will not give some Attention for the learning of Sciences; as if while we are involved in Obscurity we could clear ourselves without Labour. Both
of 300 which Sorts of Persons are to be admonished, that the former be not discouraged, nor the latter refuse a little Care and Diligence when a Thing requires some Study.
I… chose rather to publish… in puris Naturalibus, or as they were produced as first, than be at the Trouble of reducing them into any other Form… I could not bear the Pains of reading over again a great Part of these Things; either from my being tired with them, or not caring to undergo the Pains and Study in new modelling them. But I have done in this as weakly Mothers, who give up their
Offspring to the Care of their Friends, either to Nurse and bring up, or abandon to the wide World. One of which is Mr. Isaac Newton, my Collegue, a Man of great Learning and Sagacity, who revised my Copy and noted such Things as wanted Correction, and even gave me some of his own, which you will see here and there interspersed with mine, not without their due Commendations. The other is Mr. John
Collins (who may be deservedly called the Mersennas of our Nation, Born to promote this Science, both with his own Labours, and those of others. Who with much Trouble took care of the Edition.
#. A primary negative injunction. This may have either of two forms: (a) "Do not do so and so, or I will punish you", or (b) "If you do not do so and so, I will punish you". Here we select a context of learning based on avoidance of punishment rather than a context of reward seeking.
In the last centuries of the empire, educational standards and literacy had fallen. In the dulled heads of the masses, distracted by cheap food and the barbaric spectacles of the coliseums, the values on which Rome had been founded and the ancient rationalism of the Greeks had been replaced by mysticism and superstition. It was—Honorius had explained to his pupil—as if a whole culture was
losing its mind. People were forgetting how to think, and soon they would forget they had forgotten. And, to Honorius’s thinking, Christianity only exacerbated that problem.
You know, Augustine warned us that belief in the old myths was fading—even a century and a half ago, as the dogma of the Christians took root. And with the loss of the myths, so vanishes the learning of a thousand
years, which are codified in those myths, and the monolithic dogmas of the Church will snuff out rational inquiry for ten more centuries. The light is fading, Athalric.”
Just when you think you know something, it gets turned around and challenged in some way. But those changes are welcome because you end up learning more.
One’s ears are weary of the voice of the art teacher who sits like the parrot on his perch, learning the jargon of the studios, making but poor copy and calling it criticism. We have had enough of their omniscience, their parade of technical knowledge, and their predilection for the wrong end of the stick.