A Supplement to the Elements of EuclidJ. Deighton and Sons, Cambridge and G and W. B. Whittaker, Ave-Maria-Lane, 1819 - 410 σελίδες |
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Σελίδα 8
... circumference shall pass through any three given points that are not in the same straight line . 11. THEOREM . PROP . VI . There cannot be drawn more than two equal straight lines , to another straight line , from a given point without ...
... circumference shall pass through any three given points that are not in the same straight line . 11. THEOREM . PROP . VI . There cannot be drawn more than two equal straight lines , to another straight line , from a given point without ...
Σελίδα 34
... circumference of a circle , described from that point as the centre , at a distance equal to the half of one of the hypotenuses . # 41. COR.2 . A circle described from the bisection of the hypotenuse of a right - angled triangle as a ...
... circumference of a circle , described from that point as the centre , at a distance equal to the half of one of the hypotenuses . # 41. COR.2 . A circle described from the bisection of the hypotenuse of a right - angled triangle as a ...
Σελίδα 89
... circumference in D : The square of BD is equal to the excess of the square of AC above the square of BC . For join D , C : And since ( constr . ) the △ B is a right 4 , .. ( E. 47. 1. ) CD2 = CB2 + BD ' i.e. ( E. def . 15. 1. ) AC = CB ...
... circumference in D : The square of BD is equal to the excess of the square of AC above the square of BC . For join D , C : And since ( constr . ) the △ B is a right 4 , .. ( E. 47. 1. ) CD2 = CB2 + BD ' i.e. ( E. def . 15. 1. ) AC = CB ...
Σελίδα 116
... circumference in E ; join K , E ; from E draw EF to KE and let EF meet BD in F : Then is F the point which was to be found . For ( E. 13. 1. ) the KEC , KEF , FED are to- gether equal to two right angles ; as are , also , ( E. 32. 1 ...
... circumference in E ; join K , E ; from E draw EF to KE and let EF meet BD in F : Then is F the point which was to be found . For ( E. 13. 1. ) the KEC , KEF , FED are to- gether equal to two right angles ; as are , also , ( E. 32. 1 ...
Σελίδα 118
... circumference of which shall pass through A and touch XY in B. to XY ; join A , and from D draw From B draw ( E. 11. 1. ) BC B ; bisect ( E. 10. 1. ) AB in D , DK 1 to AB ; .. ( S. 3. 1. cor . 2. ) K is equi- distant from A and B : It ...
... circumference of which shall pass through A and touch XY in B. to XY ; join A , and from D draw From B draw ( E. 11. 1. ) BC B ; bisect ( E. 10. 1. ) AB in D , DK 1 to AB ; .. ( S. 3. 1. cor . 2. ) K is equi- distant from A and B : It ...
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ABCD base BC bisect centre chord circle ABC circle described circumference constr decagon describe a circle describe the circle diameter distance divided double draw a straight draw E equi equiangular equilateral and equiangular F draw find a point finite straight line given circle given finite straight given point given ratio given square given straight line half hypotenuse inscribed isosceles less Let AB Let ABC lines be drawn magnitudes manifest manner meet the circumference number of equal number of sides parallel to BC parallelogram pass perimeter point G polygon PROBLEM produced PROP rectangle contained rectilineal figure remaining sides required to describe required to draw rhombus right angles segment semi-diameter straight line joining tangent THEOREM three given touch the circle trapezium vertex