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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Resultater 1-5 af 79
Side ii
... determine the locus of the points of section , which divide them in a given ratio . 13. A straight line being drawn parallel to one of the lines con- taining a given angle , and produced to meet the other ; through a given point within ...
... determine the locus of the points of section , which divide them in a given ratio . 13. A straight line being drawn parallel to one of the lines con- taining a given angle , and produced to meet the other ; through a given point within ...
Side iii
... determine another , through which if any straight line be drawn , perpendiculars upon it from two of the former shall together be equal to the perpendicular from the third . 25. From a given point in one of two straight lines given in ...
... determine another , through which if any straight line be drawn , perpendiculars upon it from two of the former shall together be equal to the perpendicular from the third . 25. From a given point in one of two straight lines given in ...
Side iv
... determine a point in one of them , from which if two lines be drawn at given angles to the other two , the two lines so drawn may together be equal to a given line . 33. If from a given point two straight lines be drawn including a ...
... determine a point in one of them , from which if two lines be drawn at given angles to the other two , the two lines so drawn may together be equal to a given line . 33. If from a given point two straight lines be drawn including a ...
Side v
... in the outer ; it will be bisected at the point of contact . 10. If any number of equal straight lines be placed in a circle ; to determine the locus of their points of bisection . 11. If from a point in the circumference of a CONTENTS . y.
... in the outer ; it will be bisected at the point of contact . 10. If any number of equal straight lines be placed in a circle ; to determine the locus of their points of bisection . 11. If from a point in the circumference of a CONTENTS . y.
Side vi
... determine the locus of the points which divide them in a given ratio . 14. Having given the radius of a circle ; to determine its centre when the circle touches two given lines which are not parallel . 15. Through three given points ...
... determine the locus of the points which divide them in a given ratio . 14. Having given the radius of a circle ; to determine its centre when the circle touches two given lines which are not parallel . 15. Through three given points ...
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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.