Euclid, His Life and SystemCharles Scribner's sons, 1902 - 227 σελίδες |
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Αποτελέσματα 1 - 5 από τα 42.
Σελίδα 10
... side of a triangle is less than the sum of the two others . We might go further , and say that 1 " Dublin University Press " Series , Greek Geometry from Thales to Euclid . By George Johnston Allman , LL.D. , D.Sc. , F.R.S. , Pro ...
... side of a triangle is less than the sum of the two others . We might go further , and say that 1 " Dublin University Press " Series , Greek Geometry from Thales to Euclid . By George Johnston Allman , LL.D. , D.Sc. , F.R.S. , Pro ...
Σελίδα 13
... sides of equiangular triangles are proportional . " . ( Euc . VI . 4. ) V. “ A circle is bisected by every diameter . " VI . " The angle subtended by a diameter at any point in the circum- ference is a right angle . " ( Might be a ...
... sides of equiangular triangles are proportional . " . ( Euc . VI . 4. ) V. “ A circle is bisected by every diameter . " VI . " The angle subtended by a diameter at any point in the circum- ference is a right angle . " ( Might be a ...
Σελίδα 14
... sides of equiangular triangles are proportional , is founded on a narrative as to his having measured 1 Mr. Ball elsewhere says , " We possess no copies of the Histories of Mathematics written about 325 B.C. by Eudemus ( who was a pupil ...
... sides of equiangular triangles are proportional , is founded on a narrative as to his having measured 1 Mr. Ball elsewhere says , " We possess no copies of the Histories of Mathematics written about 325 B.C. by Eudemus ( who was a pupil ...
Σελίδα 16
... sides are in the proportion of 3 , 4 , and 5 is right angled ; and we can scarcely imagine that they failed to see that the square on the hypotenuse of such a right - angled triangle is equal to the sum of the squares of its sides ...
... sides are in the proportion of 3 , 4 , and 5 is right angled ; and we can scarcely imagine that they failed to see that the square on the hypotenuse of such a right - angled triangle is equal to the sum of the squares of its sides ...
Σελίδα 17
... side . It seems , then , very probable that the Egyptians , before the sojourn of Thales among them , were aware of the truth of these three cases of what afterwards became Euc . I. 47 , though it is very likely that they had not proved ...
... side . It seems , then , very probable that the Egyptians , before the sojourn of Thales among them , were aware of the truth of these three cases of what afterwards became Euc . I. 47 , though it is very likely that they had not proved ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
Adelard admit Alexandria Alexandrian School algebra Almagest Anaximander Arabic Archytas arithmetic ascertain assumption astronomy attained axiom called Campanus century Christian circle conic sections course cube cultivation defect defined demonstration Descartes diameter discovery doubt Egypt Egyptian elementary equilateral triangle Euclid Euclid's Elements Euclidean Euclidean geometry Eudemus extent fact faculty give given Greek Honain important inference intellect intersecting invention Ionian School knew knowledge Laplace Legendre Leibnitz less lived logarithms logic mathe mathematical science mathematical study mathematician matical matter means measure ment method mind modern Newton optical parallel lines philosophy plane plane geometry Plato position principle probably problem Proclus proof Prop proposition proved Ptolemy Pythagoras question reasoning rectangle referred regarded right angles right-angled triangle seems square statement straight line suppose Tarentum teacher teaching Thales theorem thought tion translation treatise triangle are equal true truth
Δημοφιλή αποσπάσματα
Σελίδα 142 - In them hath he set a tabernacle for the sun, which is as a bridegroom coming out of his chamber, and rejoiceth as a strong man to run a race. His going forth Is from the end of the heaven and his circuit unto the ends of It: and there is nothing hid from the heat thereof.
Σελίδα 174 - Let them praise the name of the Lord: for he commanded, and they were created. He hath also stablished them for ever and ever: he hath made a decree which shall not pass.
Σελίδα 133 - It is true, that a little philosophy inclineth man's mind to atheism; but depth in philosophy bringeth men's minds about to religion: for while the mind of man looketh upon second causes scattered, it may sometimes rest in them, and go no farther; but when it beholdeth the chain of them confederate and linked together, it must needs fly to Providence and Deity.
Σελίδα 133 - Lo, these are parts of his ways: but how little a portion is heard of him? but the thunder of his power who can understand?
Σελίδα 183 - Behold also the ships, which, though they be so great, and are driven of fierce winds, yet are they turned about with a very small helm, whithersoever the governor listeth.
Σελίδα 50 - A mule and a donkey were going to market laden with wheat. The mule said 'If you gave me one measure I should carry twice as much as you, but if I gave you one we should bear equal burdens.
Σελίδα 107 - There is that scattereth, and yet increaseth; and there is that withholdeth more •than is meet, and it tendeth to poverty.
Σελίδα 179 - And he made a molten sea, ten cubits from the one brim to the other : it was round all about, and his height was five cubits : and a line of thirty cubits did compass it round about.
Σελίδα 44 - Pythagoras' theorem states that the square of the length of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the lengths of the other two sides.