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
... semicircle , another semicircle be described , and from the extremity of the diameters any lines be drawn cutting the circumferences , and produced , so that the part produced may always have a given ratio to the part intercepted ...
... semicircle , another semicircle be described , and from the extremity of the diameters any lines be drawn cutting the circumferences , and produced , so that the part produced may always have a given ratio to the part intercepted ...
Σελίδα vii
... semicircle be divided into an odd number of equal parts , and through the points which are equally distant from the diameter lines be drawn ; the segments of these lines intercepted between radii drawn to the extremities of the most ...
... semicircle be divided into an odd number of equal parts , and through the points which are equally distant from the diameter lines be drawn ; the segments of these lines intercepted between radii drawn to the extremities of the most ...
Σελίδα ix
... semicircle a straight line be drawn in it , equal to the radius , and from the centre a perpendicular let fall upon it and produced to the circumference ; it will be a mean proportional between the lines drawn from the point of ...
... semicircle a straight line be drawn in it , equal to the radius , and from the centre a perpendicular let fall upon it and produced to the circumference ; it will be a mean proportional between the lines drawn from the point of ...
Σελίδα xi
... semicircle be described on the side of a quadrant , and from any point in the quadrantal arc a radius be drawn , the part of this radius intercepted between the quadrant and semicircle , is equal to the perpendicular let fall from the ...
... semicircle be described on the side of a quadrant , and from any point in the quadrantal arc a radius be drawn , the part of this radius intercepted between the quadrant and semicircle , is equal to the perpendicular let fall from the ...
Σελίδα xiv
... semicircle , a per- pendicular be drawn , meeting the circumference , and on it as a diameter a circle be described , to the centre of which a line is drawn from the farther extremity of the diameter of the semicircle , cutting its ...
... semicircle , a per- pendicular be drawn , meeting the circumference , and on it as a diameter a circle be described , to the centre of which a line is drawn from the farther extremity of the diameter of the semicircle , cutting its ...
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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.