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
... contain the properties of tri- angles described in or about circles ; the 8th those which contain the squares or rectangles of lines connected with circles ; and the 9th the construction of triangles . To these is added an Appendix ...
... contain the properties of tri- angles described in or about circles ; the 8th those which contain the squares or rectangles of lines connected with circles ; and the 9th the construction of triangles . To these is added an Appendix ...
Side iv
... contain a given angle , and meet two lines given in position , so that the parts intercepted between those points and the lines may have a given ratio . 30. The length of one of two lines which contain a given angle being given ; to ...
... contain a given angle , and meet two lines given in position , so that the parts intercepted between those points and the lines may have a given ratio . 30. The length of one of two lines which contain a given angle being given ; to ...
Side vi
... contain a given angle , and be terminated in that line . 17. If from the extremities of any chord in a circle perpendi- culars be drawn , meeting a diameter ; the points of intersection are equally distant from the centre . 18. If from ...
... contain a given angle , and be terminated in that line . 17. If from the extremities of any chord in a circle perpendi- culars be drawn , meeting a diameter ; the points of intersection are equally distant from the centre . 18. If from ...
Side vii
... contained by tangents drawn from that point towards the same parts will be equal to the angle contained by lines drawn to the centres . 26. To determine the Arithmetic , Geometric and Harmonic means between two given straight lines . 27 ...
... contained by tangents drawn from that point towards the same parts will be equal to the angle contained by lines drawn to the centres . 26. To determine the Arithmetic , Geometric and Harmonic means between two given straight lines . 27 ...
Side x
... contained by the tangents is double the angle contained by the line joining the points of contact and the diameter drawn through one of them . 52. If from the extremities of the diameter of a circle tangents be drawn , and produced to ...
... contained by the tangents is double the angle contained by the line joining the points of contact and the diameter drawn through one of them . 52. If from the extremities of the diameter of a circle tangents be drawn , and produced to ...
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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.