A History of Greek Mathematics, כרך 1Clarendon Press, 1921 |
מהדורות אחרות - הצג הכל
מונחים וביטויים נפוצים
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 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 theory of proportion things tion treatise καὶ
קטעים בולטים
עמוד 385 - Magnitudes are said to have a ratio to one another which are capable, when multiplied, of exceeding one another. 5. Magnitudes are said to be in the same ratio, the first to the second and the third to the fourth, when, if any equimultiples whatever be taken of the first and third, and any equimultiples whatever of the second and fourth, the former equimultiples alike exceed, are alike equal to, or alike fall short of, the latter equimultiples respectively taken in corresponding order.
עמוד 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.
עמוד 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.
עמוד 357 - Give him threepence, since he must make gain out of what he learns ".' 2 Ancient commentaries, criticisms, and references.
עמוד 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.
עמוד 377 - Any two angles of a triangle are together less than two right angles.
עמוד 413 - The earlier geometers have also used this lemma; for it is by the use of this same lemma that they have shown 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...
עמוד 378 - After remarking that the mathematician positively knows that the sum of the three angles of a triangle is equal to two right angles...
עמוד 202 - Y3 inscribed regular figures of sixteen sides, &r. the preceding process gives the proof that circles are to one another as the squares on their diameters.
עמוד 328 - Two unequal magnitudes being set out, if from the greater there be subtracted a magnitude greater than its half, and from that which is left a magnitude greater than its half, and if this process be repeated continually, there will be left some magnitude which will be less than the lesser magnitude set out?