Euclid, His Life and SystemCharles Scribner's sons, 1902 - 227 σελίδες |
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Αποτελέσματα 1 - 5 από τα 15.
Σελίδα 50
... axioms , and postulates.1 With his first six pro- positions he had perfectly plain sailing . Having proved the equality of two triangles which have two sides and the contained angle in the one equal to two sides and the contained ...
... axioms , and postulates.1 With his first six pro- positions he had perfectly plain sailing . Having proved the equality of two triangles which have two sides and the contained angle in the one equal to two sides and the contained ...
Σελίδα 58
... axioms and postulates which lay betwixt him and the Pons Asinorum . He therefore asked the professor whether he might not proceed by a shorter and easier way . " Nay , Sire , " was the quick response , " there is no royal road to ...
... axioms and postulates which lay betwixt him and the Pons Asinorum . He therefore asked the professor whether he might not proceed by a shorter and easier way . " Nay , Sire , " was the quick response , " there is no royal road to ...
Σελίδα 87
... Axioms , to which we shall have to refer further on . Meantime we may say that to our thinking it is self - condemned by its title , as geometry or any other science without axioms is an absurdity , a contradiction in terms . << 1 Its ...
... Axioms , to which we shall have to refer further on . Meantime we may say that to our thinking it is self - condemned by its title , as geometry or any other science without axioms is an absurdity , a contradiction in terms . << 1 Its ...
Σελίδα 100
... axiom regarding non - parallel lines , of which we shall have much to say in the sequel . With respect to his " investigation " of this theorem , he makes an admission which , we suppose , is unique in geometrical treatises . " Scholium ...
... axiom regarding non - parallel lines , of which we shall have much to say in the sequel . With respect to his " investigation " of this theorem , he makes an admission which , we suppose , is unique in geometrical treatises . " Scholium ...
Σελίδα 185
... axiom the almost axiomatic Prop . i . 13. Now all this Euclid knew just as well as his improvers . Why did he not adopt their method , which would certainly have resulted in a demonstration somewhat simpler than his ? Mani- festly ...
... axiom the almost axiomatic Prop . i . 13. Now all this Euclid knew just as well as his improvers . Why did he not adopt their method , which would certainly have resulted in a demonstration somewhat simpler than his ? Mani- festly ...
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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.