## A Short History of Greek Mathematics |

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### Vanlige uttrykk og setninger

added Apollonius appear applied Arabic Archimedes arithmetical astronomical attributed base begins calculation called Cantor centre century Chasles chord circle cited common cone conic construction contains curve definitions described determined diameter Diophantus divided division draw drawn early Egyptian Elements equal equations Euclid Eutocius evidence fact figure follows four fractions geometry given gives greater Greek hand Heiberg Heron instance introduced invented kind known later less magnitude mathematics mean measure mentioned method numbers observations original Pappus parallel perhaps plane Plato porisms position practice probably problem Proclus produced proof Prop proportion propositions proved Ptolemy Pythagorean quoted ratio rectangle reference remains right angles rule says seems segment shews side signs similar solution sphere square straight line suggested supposed symbolism taken theorem theory translation treated treatise triangle whole writer

### Populære avsnitt

Side 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...

Side 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.

Side 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.

Side 298 - He finds as a general law that a ray, passing from a rarer to a denser medium, is refracted towards the perpendicular : if...

Side 194 - Give him threepence, since he must make gain out of what he learns.

Side 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.

Side 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...

Side 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.

Side 176 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.

Side 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.