Euclid's Elements of Geometry, Books 1-6Henry Martyn Taylor The University Press, 1893 - 504 pages |
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Page 19
... cut the circle in E and I , we can choose either DE or DI as the radius of the circle which we describe with D as centre . There are therefore three steps in the construction , at each of which there is a choice of two alternatives ...
... cut the circle in E and I , we can choose either DE or DI as the radius of the circle which we describe with D as centre . There are therefore three steps in the construction , at each of which there is a choice of two alternatives ...
Page 20
... cut off a part equal to the less . Let AB and CD be the two given straight lines , of which AB is the greater : it ... circle EFG . ( Prop . 2. ) ( Post . 6. ) The circle must intersect AB between A and B , for AB is greater than ...
... cut off a part equal to the less . Let AB and CD be the two given straight lines , of which AB is the greater : it ... circle EFG . ( Prop . 2. ) ( Post . 6. ) The circle must intersect AB between A and B , for AB is greater than ...
Page 38
... cut off CE equal to CD . ( Prop . 3. ) On DE construct an equilateral triangle DFE , ( Prop . 1. ) and draw CF ... circle ( Def . 22 38 BOOK I.
... cut off CE equal to CD . ( Prop . 3. ) On DE construct an equilateral triangle DFE , ( Prop . 1. ) and draw CF ... circle ( Def . 22 38 BOOK I.
Page 60
... cut off CG equal to AB , and DH to EF . ( Prop . 3. ) With C as centre and CG as radius describe the circle GKL , and with D as centre and DH as radius describe the circle HKM . Let these circles intersect in K : Draw CK , DK : then CKD ...
... cut off CG equal to AB , and DH to EF . ( Prop . 3. ) With C as centre and CG as radius describe the circle GKL , and with D as centre and DH as radius describe the circle HKM . Let these circles intersect in K : Draw CK , DK : then CKD ...
Page 182
... circle : it is required to find its centre . CONSTRUCTION . Draw any two chords which are not parallel and which cut the circle in A , B , and in C , D. Bisect AB and CD at E and F ; ( I. Prop . 10. ) and draw EG , FG at right angles ...
... circle : it is required to find its centre . CONSTRUCTION . Draw any two chords which are not parallel and which cut the circle in A , B , and in C , D. Bisect AB and CD at E and F ; ( I. Prop . 10. ) and draw EG , FG at right angles ...
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Common terms and phrases
ABCD AC is equal ADDITIONAL PROPOSITION angle ACB angle BAC angles ABC anharmonic arc ABC bisected centre of similitude chord circle ABC coincide Constr Coroll cut the circle describe a circle diagonal diameter draw equal angles equal circles equal to CD equiangular equimultiples Euclid EXERCISES exterior angle given circle given point given straight line given triangle greater harmonic range hypotenuse inscribed intersect Let ABC meet middle points opposite sides pair parallel parallelogram pencil pentagon perpendicular polygon PROOF Prop PROPOSITION 14 Ptolemy's Theorem quadrilateral radical axis radius rectangle contained required to prove respectively rhombus right angles shew sides BC Similarly square on AC straight line &c straight line drawn straight line joining subtend tangent theorem triangle ABC triangle DEF triangles are equal twice the rectangle vertices Wherefore
Popular passages
Page 59 - Any two sides of a triangle are together greater than the third side.
Page 7 - An angle less than a right angle is called an acute angle; an angle greater than a right angle and less than two right angles is called an obtuse angle.
Page 68 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Page 144 - If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced...
Page 376 - To find a mean proportional between two given straight lines. Let AB, BC be the two given straight lines ; it is required to find a mean proportional between them. Place AB, BC in a straight line, and upon AC describe the semicircle ADC, and from the point B draw (9.
Page 135 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.
Page 76 - ... the same side together equal to two right angles ; the two straight lines shall be parallel to one another.
Page 305 - To inscribe, an equilateral and equiangular pentagon in a given circle. Let ABCDE be the given circle. It is required to inscribe an equilateral...
Page 424 - PROPOSITION 5. The locus of a point, the ratio of whose distances from two given points is constant, is a circle*.
Page 248 - If two straight lines within a circle cut one another, the rectangle contained by the segments of one of them is equal to the rectangle contained by the segments of the other. Let the two straight lines AC, BD, within the circle ABCD, cut one another in the point E : the rectangle contained by AE, EC is equal to the rectangle contained by BE, ED.