Geometrical Problems Deducible from the First Six Books of Euclid, Arranged and Solved: To which is Added an Appendix Containing the Elements of Plane Trigonometry ...J. Smith, 1819 - 377 sider |
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Side v
... 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 two ...
... 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 two ...
Side viii
... circles cut each other , and from either point of intersection a circle be described cutting them ; the points where ... touch each other externally or internally ; any straight line drawn through the point of contact will cut off similar ...
... circles cut each other , and from either point of intersection a circle be described cutting them ; the points where ... touch each other externally or internally ; any straight line drawn through the point of contact will cut off similar ...
Side ix
... circles ; this diameter and the lines joining the points of intersection and contact are in continued proportion . 41. If a common tangent be drawn to any number of circles which touch each other internally , and from any point in this ...
... circles ; this diameter and the lines joining the points of intersection and contact are in continued proportion . 41. If a common tangent be drawn to any number of circles which touch each other internally , and from any point in this ...
Side x
... circle tangents be drawn ; any other tangent to the circle , terminated by them , is so divided at the point of contact , that the radius of the circle is a mean proportional between its segments . 54. Two circles being given in ...
... circle tangents be drawn ; any other tangent to the circle , terminated by them , is so divided at the point of contact , that the radius of the circle is a mean proportional between its segments . 54. Two circles being given in ...
Side xiii
... circle a per- pendicular be drawn to the diameter which passes through one extremity ; it will bisect the segment of ... touches and the other cuts the circle ; a line drawn from the same point in any direction , equal to the tangent ...
... circle a per- pendicular be drawn to the diameter which passes through one extremity ; it will bisect the segment of ... touches and the other cuts the circle ; a line drawn from the same point in any direction , equal to the tangent ...
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Almindelige termer og sætninger
ABCD angle ABC base bisects the angle centre chord circle ABC circles cut circles touch circumference describe a circle divided draw any line drawn parallel duplicate ratio equal angles equiangular Eucl extremities given angle given circle given in position given line given point given ratio given straight line given triangle inscribed 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 perpendicular be drawn point of bisection point of contact point of intersection quadrant radius rectangle contained right angles right-angled triangle segments semicircle shewn tangent touches the circle trapezium triangle ABC vertex vertical angle
Populære passager
Side 124 - If a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or those sides produced, proportionally; and if the sides, or the sides produced, be cut proportionally, the straight '.line which joint the points of section, shall be parallel to the remaining side of the triangle.
Side xiii - IF from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle,. shall be equal to the square of the line which touches it.
Side 158 - Iff a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other...
Side 160 - Upon a given straight line, to describe a segment of a circle, containing an angle equal to a given angle. Let AB be the given straight line, and C the given angle ; it is required to.
Side 230 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.
Side 157 - AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.
Side 33 - FC ; (ax. 1.) and FA, FB, FC are equal to one another : wherefore the circle described from the centre F, at the distance of one of them, will pass through the extremities of the other two, and be described about the triangle ABC.
Side xxv - ... the squares of the diagonals, is equal to the sum of the squares of the bisected sides together with four times the square of the line joining those points of bisection.
Side 248 - If an equilateral triangle be inscribed in a circle, and the adjacent arcs cut off by two of its sides be bisected, the line joining the points of bisection shall be trisected by the sides.
Side 355 - The sine of an angle is equal to the sine of its supplement. The sine rule Consider fig.