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 100
Side ii
... drawn to a straight line given in position ; to determine the locus of the points of section , which divide them in a given ratio . 13. A straight line being drawn parallel to one of the lines con- taining a given angle , and produced ...
... drawn to a straight line given in position ; to determine the locus of the points of section , which divide them in a given ratio . 13. A straight line being drawn parallel to one of the lines con- taining a given angle , and produced ...
Side v
... drawn to touch a circle , and be parallel to a 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 ...
... drawn to touch a circle , and be parallel to a 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 ...
Side vi
... drawn ; the locus of their points of bisection will be a circle . 12. If on ... parallel . 15. Through three given points which are not in the same straight ... drawn , meeting a diameter ; the points of intersection are equally distant ...
... drawn ; the locus of their points of bisection will be a circle . 12. If on ... parallel . 15. Through three given points which are not in the same straight ... drawn , meeting a diameter ; the points of intersection are equally distant ...
Side vii
... parallel to a given straight line . 23. The bases of two given circular segments being in the same straight line ; to determine a point in it such , that a line being drawn through it making a given angle , the part intercepted between ...
... parallel to a given straight line . 23. The bases of two given circular segments being in the same straight line ; to determine a point in it such , that a line being drawn through it making a given angle , the part intercepted between ...
Side viii
... drawn through the point of contact will cut off similar segments . 33. If two circles touch each other externally or internally ; two straight lines drawn through the point of contact will intercept arcs , the chords of which are parallel ...
... drawn through the point of contact will cut off similar segments . 33. If two circles touch each other externally or internally ; two straight lines drawn through the point of contact will intercept arcs , the chords of which are parallel ...
Indhold
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140 | |
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170 | |
36 | |
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295 | |
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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