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 σελίδες |
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Σελίδα vi
... greater than the diameter of the circle . 21. From a given point in the diameter of a semicircle produced , to draw a line cutting the semicircle , so that lines drawn from the points of intersection to the extremities of the diameter ...
... greater than the diameter of the circle . 21. From a given point in the diameter of a semicircle produced , to draw a line cutting the semicircle , so that lines drawn from the points of intersection to the extremities of the diameter ...
Σελίδα x
... greater than the diameter of the circle . 48. If from each extremity of any number of equal adjacent arcs in the circumference of a circle , lines be drawn through two given points in the opposite circumference , and produced till they ...
... greater than the diameter of the circle . 48. If from each extremity of any number of equal adjacent arcs in the circumference of a circle , lines be drawn through two given points in the opposite circumference , and produced till they ...
Σελίδα xi
... greater line intercepted between the two circumferences shall be equal to the less of the two lines . 60. If two circles cut each other , so that the circumference of one passes through the centre of the other , and from either point of ...
... greater line intercepted between the two circumferences shall be equal to the less of the two lines . 60. If two circles cut each other , so that the circumference of one passes through the centre of the other , and from either point of ...
Σελίδα xii
... greater than the diameter of the smaller circle . 67. To determine a point in the arc of a quadrant , through which if a tangent be drawn meeting the sides of the quadrant pro- duced , the intercepted parts may have a given ratio .. 68 ...
... greater than the diameter of the smaller circle . 67. To determine a point in the arc of a quadrant , through which if a tangent be drawn meeting the sides of the quadrant pro- duced , the intercepted parts may have a given ratio .. 68 ...
Σελίδα xiii
... greater segment of the chord has to the less . 77. If from the extremities of any chord of a circle , perpen- diculars to it be drawn and produced to cut a diameter ; and from the points of intersection with the diameter lines be drawn ...
... greater segment of the chord has to the less . 77. If from the extremities of any chord of a circle , perpen- diculars to it be drawn and produced to cut a diameter ; and from the points of intersection with the diameter lines be drawn ...
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Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.
Σελίδα 230 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 355 - The sine of an angle is equal to the sine of its supplement. The sine rule Consider fig.