A Short History of Greek MathematicsUniversity Press, 1884 - 323 σελίδες |
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... produced in F , AC produced in G , and the circle in H , D , is turned about the point D until FH equals DG . The line FHDG is called " Philo's line " in modern geometry , but its author did not know its singular property . TABLE OF ...
... produced in F , AC produced in G , and the circle in H , D , is turned about the point D until FH equals DG . The line FHDG is called " Philo's line " in modern geometry , but its author did not know its singular property . TABLE OF ...
Σελίδα 13
... produces are more readily represented with primitive symbols . Given only the fingers or pebbles , it would puzzle any man to represent directly that fraction of an apple which we call 24ths , but it would not be so difficult to ...
... produces are more readily represented with primitive symbols . Given only the fingers or pebbles , it would puzzle any man to represent directly that fraction of an apple which we call 24ths , but it would not be so difficult to ...
Σελίδα 18
... produces 284. The difference , 144 , between this product and 2 is then separately treated3 . 3 is to be × 11 12 14. After this preliminary practice with fractions , Ahmes proceeds to the solution of simple equations with one unknown ...
... produces 284. The difference , 144 , between this product and 2 is then separately treated3 . 3 is to be × 11 12 14. After this preliminary practice with fractions , Ahmes proceeds to the solution of simple equations with one unknown ...
Σελίδα 19
... produce the requisite sum 100. The difference 51⁄2 must have been found from the equation - : a + ( a - b ) + ( a — 2b ) = 7 -- = - = ( a − 3b ) + ( a − 4b ) , - whence 11 ( a - 4b ) 2b and b = 51 ( a - 4b ) . Ahmes then assumes ( a ...
... produce the requisite sum 100. The difference 51⁄2 must have been found from the equation - : a + ( a - b ) + ( a — 2b ) = 7 -- = - = ( a − 3b ) + ( a − 4b ) , - whence 11 ( a - 4b ) 2b and b = 51 ( a - 4b ) . Ahmes then assumes ( a ...
Σελίδα 40
... . p . 584. ) Such forgeries were , of course , not unusual when a city wished to produce a documentary title to some ancient privilege . merely initial letters of numeral names . Π ( πέντε 40 GREEK CALCULATION . Logistica .
... . p . 584. ) Such forgeries were , of course , not unusual when a city wished to produce a documentary title to some ancient privilege . merely initial letters of numeral names . Π ( πέντε 40 GREEK CALCULATION . Logistica .
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Ahmes Alexandria algebraical Almagest alphabet Apollonius Arabic Archimedes Archytas Aristotle arithmetical astronomical Athens attributed Bisect Bretschneider called Cantor centre century Chasles chord circle circumference cited commentary cone conic conic sections contains cube curve cylinder Delambre described diameter Diophantus Egyptian ellipse equal equations Eratosthenes Eucl Euclid Eudemian summary Eudemus Eudoxus Eutocius extant figure follows fractions Friedlein Geminus given Greek geometry Hankel Heiberg Heron Hipparchus Hippocrates history of geometry Hultsch Iamblichus inscribed invented isosceles later lemmas magnitudes Math mathematicians mathematics means Menaechmus mentioned method method of exhaustion Nesselmann Nicomachus numbers Pappus parabola perpendicular plane Plato Plutarch polygonal numbers porism problem Proclus proof Prop proportion propositions Ptolemy Pythagoras Pythagorean quadrature quoted ratio rectangle rectilineal right angles says segment semicircle shews side similar solution sphere square number straight line symbolism Thales Theon theorem Torelli translation treatise triangle vertex Vorles writers καὶ περὶ
Δημοφιλή αποσπάσματα
Σελίδα 199 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Σελίδα 292 - THE rectangle contained by the diagonals of a quadrilateral inscribed in a circle, is equal to both the rectangles contained by its opposite sides.* Let ABCD be any quadrilateral inscribed in a circle, and join AC, BD ; the.
Σελίδα 292 - The rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equal to the sum of the two rectangles contained by its opposite sides.
Σελίδα 298 - He finds as a general law that a ray, passing from a rarer to a denser medium, is refracted towards the perpendicular : if...
Σελίδα 194 - Give him threepence, since he must make gain out of what he learns.
Σελίδα 56 - IJandnotwith any special problem. course, that most astronomers mean by 'the universe' the sphere of which the centre is the centre of the earth and the radius is a line drawn from the centre of the earth to the centre of the sun.
Σελίδα 145 - At a given point in a given straight line, to make a rectilineal angle equal to a given rectilineal angle. Let AB be the given straight line, and A the given point in, it, and DCE the given rectilineal angle ; it is required to make...
Σελίδα 53 - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.
Σελίδα 176 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.
Σελίδα 133 - Pythagoras changed the study of geometry into the form of a liberal education, for he examined its principles to the bottom and investigated its theorems in an immaterial and intellectual manner.