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 60
Side ii
... proportion , and from that point also a line equal to the mean proportional be inclined at any angle ; the lines joining the extremity of this line and of the proportionals will contain equal angles . 16. To trisect a right angle . 17 ...
... proportion , and from that point also a line equal to the mean proportional be inclined at any angle ; the lines joining the extremity of this line and of the proportionals will contain equal angles . 16. To trisect a right angle . 17 ...
Side viii
... mean proportional between the diameters of the circles . 37. If two circles touch each other externally , and the line join- ing their centres be produced to the circumferences ; and from its middle point as a centre with any radius ...
... mean proportional between the diameters of the circles . 37. If two circles touch each other externally , and the line join- ing their centres be produced to the circumferences ; and from its middle point as a centre with any radius ...
Side ix
... proportional . 40. If three circles , whose diameters are in continued proportion , touch each other internally ... mean proportional between the lines drawn from the point of intersection with the circumference to the extremities of the ...
... proportional . 40. If three circles , whose diameters are in continued proportion , touch each other internally ... mean proportional between the lines drawn from the point of intersection with the circumference to the extremities of the ...
Side x
... mean proportional between its segments . 54. Two circles being given in magnitude and position ; to find a point in the circumference of one of them , to which if a tangent be drawn cutting the circumference of the other , the part of ...
... mean proportional between its segments . 54. Two circles being given in magnitude and position ; to find a point in the circumference of one of them , to which if a tangent be drawn cutting the circumference of the other , the part of ...
Side xii
... mean proportional to two dis- tances from the centre in the same straight line ; the lines drawn from their extremities to any point in the circumference will have the same ratio that the distances of these points from the cireum ...
... mean proportional to two dis- tances from the centre in the same straight line ; the lines drawn from their extremities to any point in the circumference will have the same ratio that the distances of these points from the cireum ...
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