Pure MathematicsCurrent Literature Publishing Company, 1909 - 324 Seiten |
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Seite 77
... theorem leads to the usual method of determining the largest number which is a common factor of two given numbers . The smaller is divided into the larger , the re- mainder from this division into the former divisor . The final ...
... theorem leads to the usual method of determining the largest number which is a common factor of two given numbers . The smaller is divided into the larger , the re- mainder from this division into the former divisor . The final ...
Seite 79
... theorems in the theory of numbers , due to Fermat , concerns the number of primes contained in the form Fn 22 + 1 where n is any number . Fermat believed that every value of n gives a prime and showed this , for n = : 0 , 1 , 2 , 3 , 4 ...
... theorems in the theory of numbers , due to Fermat , concerns the number of primes contained in the form Fn 22 + 1 where n is any number . Fermat believed that every value of n gives a prime and showed this , for n = : 0 , 1 , 2 , 3 , 4 ...
Seite 100
... dimen- sional , and space , which is three - dimensional , has been a source of a great deal of study and involves some of the most important theorems of algebraic analysis . 1 A general equation of the form a x2 +. 100 MATHEMATICS.
... dimen- sional , and space , which is three - dimensional , has been a source of a great deal of study and involves some of the most important theorems of algebraic analysis . 1 A general equation of the form a x2 +. 100 MATHEMATICS.
Seite 101
... theorem of Algebra . Now since the hypothesis is proved , the conclusion that there are n roots is easily proved , such proof being famil- iar to any schoolboy . The next concern is , what is the nature of the roots ? Weierstrass proved ...
... theorem of Algebra . Now since the hypothesis is proved , the conclusion that there are n roots is easily proved , such proof being famil- iar to any schoolboy . The next concern is , what is the nature of the roots ? Weierstrass proved ...
Seite 105
... theorem that the root of an alge- braic equation must be of the form a + bi is that no fur- ther extension can be made and have the numbers still conform to the laws of algebra . In the formation of the complex number there are two ...
... theorem that the root of an alge- braic equation must be of the form a + bi is that no fur- ther extension can be made and have the numbers still conform to the laws of algebra . In the formation of the complex number there are two ...
Häufige Begriffe und Wortgruppen
Algebra Analytic Geometry applied Archimedes arithmetic biplane calculation called cardinal century circle class of points column commutative law computed construction contains coördinates cube cubic curvature curve cylinder denoted determined distance divided division Egyptians equal equation Euclid exponent figure fractions functions geometry Georg Cantor given Greek Hindu hundred hyperbola implies q invention isotropic lines known Law of Cosines letter logarithms machine magic square material implication mathematician mathematics means measure mechanical ment method modern multiplication non-collinear points notation notion number system operation pistoles plane player postulates primitive principle problem Professor projective geometry propositions pseudosphere Pythagoras Pythagorean theorem quipu ratio real numbers relation right angles Roman says screw segment side sphere straight line subtraction surface symbol theorem theory tion transitive relation triangle unit weight wheel whole numbers zero
Beliebte Passagen
Seite 269 - ... of its arc, which is its natural place of rest, but does not fix it there, because the momentum acquired during its fall from one side carries it up to an equal height on the other — so in a watch a spring, generally spiral, surrounding the axis of the balance-wheel, is always pulling this towards a middle position of rest, but does not fix it there, because the momentum acquired during its approach to the middle position...
Seite 65 - My lord, I have undertaken this long journey purposely to see your person, and to know by what engine of wit or ingenuity you came first to think of this most excellent help into astronomy, viz. the logarithms ; but, my lord, being by you found out, I wonder nobody else found it out before, when now known it is so easy.
Seite 269 - ... other side, and the spring has to begin its work again. The balance-wheel at each vibration allows one tooth of the adjoining wheel to pass, as the pendulum does in a clock ; and the record of the beats is preserved by the wheel which follows.
Seite 310 - I was thinking upon the engine at the time and had gone as far as the Herd's house when the idea came into my mind, that as steam was an elastic body it would rush into a vacuum, and if a communication...
Seite 80 - If all points of the straight line fall into two classes such that every point of the first class lies to the left of every point of the second class, then there exists one and only one point which produces this division of all points into two classes, this severing of the straight line into two portions.
Seite 121 - By the grace of God, gentlemen hearers, I have performed my promise. I have redeemed my pledge. I have explained, according to my ability, the definitions, postulates, axioms, and the first eight propositions of the Elements of Euclid. Here, sinking under the weight of years, I lay down my art and my instruments.
Seite 118 - That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.
Seite 14 - ... 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...
Seite 118 - Common Notions 1 Things which are equal to the same thing are also equal to one another. 2 If equals be added to equals, the wholes are equal. 3 If equals be subtracted from equals, the remainders are equal. 4 Things which coincide with one another are equal to one another.
Seite 118 - AXIOM is a self-evident truth ; such as, — 1. Things which are equal to the same thing, are equal to each other. 2. If equals be added to equals, the sums will be equal. 3. If equals be taken from equals, the remainders will be equal. 4. If equals be added to unequals, the sums will be unequal. 5. If equals be taken from unequals, the remainders will be unequal. 6. Things which are double of the same thing, or of equal things, are equal to each other.