A History of Greek Mathematics: From Thales to EuclidClarendon Press, 1921 |
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Frases i termes més freqüents
alphabet Apollonius Archimedes Archytas Arist Aristotle arithmetic astronomy attributed base Book centre circle circumference commensurable conics construction cube curve definition Democritus diameter discovered discovery divided Elements equal equations Euclid Eudemus Eudoxus Eutocius figure follows fractions geometry given straight line gives gnomon Greek Heron Hippocrates Hippocrates's Iamblichus incommensurable indivisible lines inscribed irrational isosceles latter lemma length lune magnitudes mathematician mathematics mean proportionals measure Menaechmus method method of exhaustion motion multiples namely Nicom Nicomachus odd numbers Pappus parallel parallelogram passage plane Plato Plutarch polygon porism problem Proclus on Eucl proof propositions proved pyramid Pythagoras Pythagoreans pythmen quadratrix quadrature radius ratio rectangle rectilineal right angles right-angled triangle says semicircle side similar segments Simplicius solid solution sphere square number square root suppose Thales Theaetetus Theon of Smyrna theorem theory of proportion things tion treatise καὶ
Passatges populars
Pàgina ix - But Greece and her foundations are Built below the tide of war, Based on the crystalline sea Of thought and its eternity; Her citizens, imperial spirits, Rule the present from the past, On all this world of men inherits Their seal is set.
Pàgina 166 - Thus when it is said that the sum of the three angles of any triangle is equal to two right angles, this is a theorem, the truth of which is demonstrated by Geometry.
Pàgina 8 - Hence when all such inventions were already established, the sciences which do not aim at giving pleasure or at the necessities of life were discovered, and first in the places where men first began to have leisure. This is why the mathematical arts were founded in Egypt; for there the priestly caste was allowed to be at leisure.
Pàgina 67 - ... they saw that the modifications and the ratios of the musical scales were expressible in numbers; — since, then, all other things seemed in their whole nature to be modelled on numbers, and numbers seemed to be the first things in the whole of nature, they supposed the elements of numbers to be the elements of all things, and the whole heaven to be a musical scale and a number.
Pàgina 413 - ... that circles are to one another in the duplicate ratio of their diameters, and that spheres are to one another in the triplicate ratio of their diameters...
Pàgina 381 - If from a point within a circle more than two equal straight lines can be drawn to the circumference, that point is the centre of the circle.
Pàgina 366 - ... the fact that the sum of the angles of a triangle is equal to two right angles, when such knowledge is based on the authority of those who know.
Pàgina 276 - ... an equal number of bodies of equal size, passing each other on a race-course as they proceed with equal velocity in opposite directions, the one row originally occupying the space between the goal and the middle point of the course, and the other that between the middle point and the starting-post. This, he thinks, involves the conclusion that half a given time is equal to double that time.
Pàgina 219 - It is practically only in the case of the squaring of the circle that we read of abortive efforts made by ' plane ' methods, and none of these (with the possible exception of Bryson's, if the accounts of his argument are correct) involved any real fallacy. On the other band, the bold pronouncement of Antiphon the Sophist that by inscribing in a circle a series of regular polygons each of which has twice as many sides as the preceding one, we shall use up or exhaust the area of the circle, though...
Pàgina 204 - B. equal in area to the oblongs we called ' roots '(surds), as not being commensurable with the others in length, but only in the plane areas to which their squares are equal.