The Thirteen Books of Euclid's Elements |
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Page 2
... Archimedes , On the Sphere and Cylinder 11. 2 , ἡ ΒΕ ἐκ τοῦ κέντρου ἐστὶ τοῦ ... ..κύκλου , ΒΕ is a radius of the circle . DEFINITION 2 . Εὐθεῖα κύκλου ἐφάπτεσθαι λέγεται , ἥτις ἁπτομένη τοῦ κύκλου καὶ ἐκβαλλομένη οὐ τέμνει τὸν κύκλον ...
... Archimedes , On the Sphere and Cylinder 11. 2 , ἡ ΒΕ ἐκ τοῦ κέντρου ἐστὶ τοῦ ... ..κύκλου , ΒΕ is a radius of the circle . DEFINITION 2 . Εὐθεῖα κύκλου ἐφάπτεσθαι λέγεται , ἥτις ἁπτομένη τοῦ κύκλου καὶ ἐκβαλλομένη οὐ τέμνει τὸν κύκλον ...
Page 5
... Archimedes . A wider definition of a sector than that given by Euclid is found in a Greek scholiast ( Heiberg's Euclid , Vol . v . p . 260 ) and in an - Nairizi ( ed . Curtze , p . 112 ) . " There are two varieties of sectors ; the one ...
... Archimedes . A wider definition of a sector than that given by Euclid is found in a Greek scholiast ( Heiberg's Euclid , Vol . v . p . 260 ) and in an - Nairizi ( ed . Curtze , p . 112 ) . " There are two varieties of sectors ; the one ...
Page 40
... Archimedes discovered by Heiberg in 1906 ( Archimedes , ed . Heiberg , Vol . 11. 1913 , p . 430 ; T. L. Heath , The Method of Archimedes , 1912 , p . 13 ) , which says that , though Eudoxus was the first to discover the scientific proof ...
... Archimedes discovered by Heiberg in 1906 ( Archimedes , ed . Heiberg , Vol . 11. 1913 , p . 430 ; T. L. Heath , The Method of Archimedes , 1912 , p . 13 ) , which says that , though Eudoxus was the first to discover the scientific proof ...
Page 65
... Archimedes , which has reached us through the Arabic ( Archimedes , ed . Heiberg , II . pp . 520-521 ) . If two chords AB , CD in a circle intersect at right angles in a point O , then the sum of the squares on AO , BO , CO , DO is ...
... Archimedes , which has reached us through the Arabic ( Archimedes , ed . Heiberg , II . pp . 520-521 ) . If two chords AB , CD in a circle intersect at right angles in a point O , then the sum of the squares on AO , BO , CO , DO is ...
Page 79
... Archimedes or Pappus ) , but , as pointed out on it . Def . 2 , Aristotle uses the compound ἐφάπτεσθαι in this sense . “ Simson proposed to read ἐφάπτηται in the case ( Def . 5 ) where άπτηται means touches . He made the like suggestion ...
... Archimedes or Pappus ) , but , as pointed out on it . Def . 2 , Aristotle uses the compound ἐφάπτεσθαι in this sense . “ Simson proposed to read ἐφάπτηται in the case ( Def . 5 ) where άπτηται means touches . He made the like suggestion ...
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Common terms and phrases
ABCD angle ABC angle BAC antecedent Aristotle base bisected centre circle ABC circumference construction continued proportion corresponding sides cube number definition diameter drawn enunciation equal angles equiangular equimultiples Euclid Eutocius ex aequali four magnitudes geometrical geometrical progression given circle given straight line greater ratio greatest common measure Heiberg hypothesis Iamblichus joined less mean proportional numbers measures the number multiple multitude Nicomachus odd number parallel parallelogram pentagon perpendicular polygon Porism prime number Proclus Prop proper fraction proposition PROPOSITION 13 proved rect rectangle rectangle contained rectilineal figure reductio ad absurdum remaining angle right angles segment semicircle similar and similarly similar plane numbers Simson solid numbers square number subtracted taken Theon Theon of Smyrna theorem touches the circle triangle ABC unit VIII δὲ καὶ πρὸς τὸ τοῦ