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 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 ...
Side 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 ...
Side 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 ...
Side 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 ...
Side 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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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 G draw 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 point of bisection point of contact point of intersection point required radius rectangle right angles segments semicircle shewn tangent touching the circle trapezium triangle ABC
Populære passager
Side 14 - IF a straight line be divided into two equal, and also into two unequal parts ; the squares of the two unequal parts are together double of the square of half the line, and of the square of the line between the points of section.
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 230 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.
Side 327 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds.
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 212 - 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 123 - If from a point, without a parallelogram, there be drawn two straight lines to the extremities of the two opposite sides, between which, when produced, the point does not lie, the difference of the triangles thus formed is equal to half the parallelogram. Ex. 2. The two triangles, formed by drawing straight lines from any point within a parallelogram to the extremities of its opposite sides, are together half of the parallelogram.
Side 305 - Given the vertical angle, the difference of the two sides containing it, and the difference of the segments of the base made by a perpendicular from the vertex ; construct the triangle.
Side 247 - The perpendicular from the vertex on the base of an equilateral triangle is equal to the side of an equilateral triangle inscribed in a circle, whose diameter is the base.
Side 299 - AB be equal to the given bisecting line ; and upon it describe a segment of a circle containing an angle equal to the given angle.