Geometrical problems deducible from the first six books of Euclid, arranged and solved. To which is added, an appendix containing the elements of plane trigonometryJ. Smith, Printer to the University; and sold by Nicholson & Son, Deighton & Sons, Thorpe, and Newby, Cambridge; and J. Mawman, and F. C. & J. Rivington, London., 1819 - 377 sider |
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Side xxv
... square of the line joining the points of bisection of the diagonals . 38. In any trapezium , if two opposite sides ... given triangle and to each other . 42. If the sides of the square described on the hypothenuse of a right - angled ...
... square of the line joining the points of bisection of the diagonals . 38. In any trapezium , if two opposite sides ... given triangle and to each other . 42. If the sides of the square described on the hypothenuse of a right - angled ...
Side xxvi
Miles Bland. necessary ) of the squares described upon the legs ; they will cut off triangles equiangular and equal to the given triangle . 43. If from the angular points of the squares described upon the sides of a right - angled ...
Miles Bland. necessary ) of the squares described upon the legs ; they will cut off triangles equiangular and equal to the given triangle . 43. If from the angular points of the squares described upon the sides of a right - angled ...
Side xxvii
... given in position , to which lines drawn from two given points may have the greatest difference possible . 3. A ... square of their difference . 7. If a straight line be divided into any two parts ; to produce it so that the rectangle ...
... given in position , to which lines drawn from two given points may have the greatest difference possible . 3. A ... square of their difference . 7. If a straight line be divided into any two parts ; to produce it so that the rectangle ...
Side xxviii
... given line into two such parts , that the square of the one shall be equal to the rectangle contained by the other and a given line . 12. A straight line being given in magnitude and position ; to draw to it , from a given point , two ...
... given line into two such parts , that the square of the one shall be equal to the rectangle contained by the other and a given line . 12. A straight line being given in magnitude and position ; to draw to it , from a given point , two ...
Side xxix
... given square . 23. A given straight line being divided into two parts ; to cut off a part which shall be a mean proportional between the two remaining segments . 24. To draw a straight line making a given angle with one of the sides of a ...
... given square . 23. A given straight line being divided into two parts ; to cut off a part which shall be a mean proportional between the two remaining segments . 24. To draw a straight line making a given angle with one of the sides of a ...
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Almindelige termer og sætninger
ABCD angle ABC angles at F base centre chord circle ABC circles cut circles touch circumference describe a circle divided draw a line Draw the diameter drawn parallel duplicate ratio equal angles equiangular Eucl extremities given angle given circle given in position given line given point given ratio given square given straight line given triangle intercepted isosceles triangle Join AE Join BD Let AB Let ABC let fall line given line joining line required lines be drawn lines drawn mean proportional opposite side parallel to BC parallelogram pendicular perpen point of bisection point of contact point of intersection point required radius rectangle rectangle contained right angles segments semicircle shewn tangent touches the circle trapezium triangle ABC