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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Resultater 1-5 af 79
Side v
... chord ; the point of contact will be the middle point of the arc cut off by that chord . COR . 1. Parallel lines placed in a circle cut off equal parts of the circumference . COR . 2. The two straight lines in a circle which join the ex ...
... chord ; the point of contact will be the middle point of the arc cut off by that chord . COR . 1. Parallel lines placed in a circle cut off equal parts of the circumference . COR . 2. The two straight lines in a circle which join the ex ...
Side vi
... chords be drawn ; the locus of their points of bisection will be a circle . 12. If on the radius of a given semicircle ... chord in a circle perpendi- culars be drawn , meeting a diameter ; the points of intersection are equally distant ...
... chords be drawn ; the locus of their points of bisection will be a circle . 12. If on the radius of a given semicircle ... chord in a circle perpendi- culars be drawn , meeting a diameter ; the points of intersection are equally distant ...
Side vii
... chords so drawn will be equal to the last chord produced to meet a line drawn from the given point through the extremity of the first arc . 28. If the circumference of a semicircle be divided into an odd number of equal parts , and ...
... chords so drawn will be equal to the last chord produced to meet a line drawn from the given point through the extremity of the first arc . 28. If the circumference of a semicircle be divided into an odd number of equal parts , and ...
Side viii
... chord of the equal circles . 32. If two circles touch each other externally or internally ; any straight line drawn ... chords of which are parallel . 34. If two circles touch each other externally or internally ; any two straight lines ...
... chord of the equal circles . 32. If two circles touch each other externally or internally ; any straight line drawn ... chords of which are parallel . 34. If two circles touch each other externally or internally ; any two straight lines ...
Side x
... chords which can be drawn through that point , that is the least which is at right angles to the diameter . 51. If from any point without a circle lines be drawn touching it ; the angle contained by the tangents is double the angle ...
... chords which can be drawn through that point , that is the least which is at right angles to the diameter . 51. If from any point without a circle lines be drawn touching it ; the angle contained by the tangents is double the angle ...
Indhold
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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