Euclid, His Life and SystemCharles Scribner's sons, 1902 - 227 σελίδες |
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Αποτελέσματα 1 - 5 από τα 27.
Σελίδα 13
... angles at the base of every isosceles triangle are equal . " Again , under I. 15 , Proclus says , This , therefore , is what the present theorem evinces , that when two right lines mutually cut each other , the vertical angles are equal ...
... angles at the base of every isosceles triangle are equal . " Again , under I. 15 , Proclus says , This , therefore , is what the present theorem evinces , that when two right lines mutually cut each other , the vertical angles are equal ...
Σελίδα 14
... angles is constant , though he may easily have fallen short of the perception that that sum is two right angles . The belief that he knew that the sides of equiangular triangles are proportional , is founded on a narrative as to his ...
... angles is constant , though he may easily have fallen short of the perception that that sum is two right angles . The belief that he knew that the sides of equiangular triangles are proportional , is founded on a narrative as to his ...
Σελίδα 15
... right - angled triangles have one of the acute angles in each equal , and the one triangle be isosceles , the other will also be isosceles . But Plutarch gives the narrative otherwise . According to him , Thales , without reference to ...
... right - angled triangles have one of the acute angles in each equal , and the one triangle be isosceles , the other will also be isosceles . But Plutarch gives the narrative otherwise . According to him , Thales , without reference to ...
Σελίδα 17
... right - angled triangle which has one of its acute angles double of the other , or which has its hypotenuse double of its shorter side . It seems , then , very probable that the Egyptians , before the sojourn of Thales among them , were ...
... right - angled triangle which has one of its acute angles double of the other , or which has its hypotenuse double of its shorter side . It seems , then , very probable that the Egyptians , before the sojourn of Thales among them , were ...
Σελίδα 34
... angles is four right angles . Now the converse of this proposition is that if the sum of the exterior angles made by producing the sides of a rectilineal figure be four right angles , then the recti- lineal figure is a triangle . Now ...
... angles is four right angles . Now the converse of this proposition is that if the sum of the exterior angles made by producing the sides of a rectilineal figure be four right angles , then the recti- lineal figure is a triangle . Now ...
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.