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 12
... THEOREM . Any side of a triangle is greater than the difference between the other two sides . If , the A be equilateral , or isosceles , the propo- sition is manifestly true . But let it be a scalene A : Then , since ( E. 20. 1. ) any ...
... THEOREM . Any side of a triangle is greater than the difference between the other two sides . If , the A be equilateral , or isosceles , the propo- sition is manifestly true . But let it be a scalene A : Then , since ( E. 20. 1. ) any ...
Σελίδα 13
... THEOREM . The two sides of a triangle are together , greater than the double of the straight line which joins the vertex and the bisection of the base . Let ABC be any given A , and let AD be the B D E straight line joining the vertex A ...
... THEOREM . The two sides of a triangle are together , greater than the double of the straight line which joins the vertex and the bisection of the base . Let ABC be any given A , and let AD be the B D E straight line joining the vertex A ...
Σελίδα 15
... THEOREM . If a trapezium and a triangle stand upon the same base , and on the same side of it , and the one figure fall within the other , that which has the greater surface shall have the greater perimeter . D E F B Let the trapezium ...
... THEOREM . If a trapezium and a triangle stand upon the same base , and on the same side of it , and the one figure fall within the other , that which has the greater surface shall have the greater perimeter . D E F B Let the trapezium ...
Σελίδα 18
... THEOREM . If two right - angled triangles have the three angles of the one equal to the three angles of the other , each to each , and if a side of the one be equal to the perpendicular let fall from the right angle upon the hypotenuse ...
... THEOREM . If two right - angled triangles have the three angles of the one equal to the three angles of the other , each to each , and if a side of the one be equal to the perpendicular let fall from the right angle upon the hypotenuse ...
Σελίδα 20
... same number of sides as the figure ABCDEF . PROP . XVIII . 26. THEOREM . If two opposite sides of a quadri- lateral figure be equal to one another , and the two remaining sides be also equal to one another , the 20 A SUPPLEMENT TO THE.
... same number of sides as the figure ABCDEF . PROP . XVIII . 26. THEOREM . If two opposite sides of a quadri- lateral figure be equal to one another , and the two remaining sides be also equal to one another , the 20 A SUPPLEMENT TO THE.
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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