Pure MathematicsCurrent Literature Publishing Company, 1909 - 324 Seiten |
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Seite 13
... ratio of their diameters , Archi- medes ultimately finds that the number of grains of sand which the sphere of the universe would hold is less than a thousand myriads or ten millions of the eighth octad . This number would be expressed ...
... ratio of their diameters , Archi- medes ultimately finds that the number of grains of sand which the sphere of the universe would hold is less than a thousand myriads or ten millions of the eighth octad . This number would be expressed ...
Seite 73
... ratio of these two numbers ,, is less than 2 and more than I. This may be put in the form , 1 < < 2 . If 1/10 of AB ... ratios , POWERS OF NUMBERS 73.
... ratio of these two numbers ,, is less than 2 and more than I. This may be put in the form , 1 < < 2 . If 1/10 of AB ... ratios , POWERS OF NUMBERS 73.
Seite 74
Leslie Leland Locke. peculiar device used by him in dealing with ratios , avoid- ed the difficulty . Theodorus ( c ... ratio of the circumference to the diameter of a circle 3.14159 . , & , the base of the Naperian system of logarithms ...
Leslie Leland Locke. peculiar device used by him in dealing with ratios , avoid- ed the difficulty . Theodorus ( c ... ratio of the circumference to the diameter of a circle 3.14159 . , & , the base of the Naperian system of logarithms ...
Seite 108
... ratio of the circumference to the diameter of a circle , usually indicated by π , to be 3.1604 , a value much more nearly correct than those used by many later writers . Another glimpse of Egyptian geometry is given by Democritus ( c ...
... ratio of the circumference to the diameter of a circle , usually indicated by π , to be 3.1604 , a value much more nearly correct than those used by many later writers . Another glimpse of Egyptian geometry is given by Democritus ( c ...
Seite 109
... ratio 3 : 4 : 5 . The triangle thus formed is right - angled . Further , the opera- tion of rope - stretching is mentioned in Egypt , without ex- planation , at an extremely early time ( Amenemhat I ) . If this be the correct ...
... ratio 3 : 4 : 5 . The triangle thus formed is right - angled . Further , the opera- tion of rope - stretching is mentioned in Egypt , without ex- planation , at an extremely early time ( Amenemhat I ) . If this be the correct ...
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 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 projective geometry propositions pseudosphere Pythagoras Pythagorean theorem quipu ratio real numbers relation right angles Roman root says screw segment side sphere square straight line subtraction surface symbol theorem theory tion transitive relation triangle unit wheel whole numbers zero
Beliebte Passagen
Seite 271 - ... 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 67 - 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 271 - ... 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 312 - 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 82 - 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 123 - 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 120 - 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 16 - ... 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 120 - 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 120 - 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.