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 xvii
... right - angled triangle , the straight line joining the right angle and the bisection of the hypothenuse is equal to half the hypothenuse . 3. If from any point within an equilateral triangle perpendiculars be drawn to the sides ; they ...
... right - angled triangle , the straight line joining the right angle and the bisection of the hypothenuse is equal to half the hypothenuse . 3. If from any point within an equilateral triangle perpendiculars be drawn to the sides ; they ...
Side xx
... right angle ; and through the point of intersection a line be drawn from one of the acute angles to the opposite side , and the extremity of this line and of the perpendicular be joined ; the locus of its intersection with the line ...
... right angle ; and through the point of intersection a line be drawn from one of the acute angles to the opposite side , and the extremity of this line and of the perpendicular be joined ; the locus of its intersection with the line ...
Side xxiii
... angles from any point within the figure , except from the intersection of the diagonals . 12. Every trapezium is divided by its diagonals into four tri- angles proportional to each other . 13. If two opposite angles of a trapezium be right ...
... angles from any point within the figure , except from the intersection of the diagonals . 12. Every trapezium is divided by its diagonals into four tri- angles proportional to each other . 13. If two opposite angles of a trapezium be right ...
Side xxiv
... angles formed by these lines are together equal to two right angles . 25. If the sides of an equilateral and equiangular hexagon be pro- duced to meet ; the angles formed by these lines are together equal to four right angles . 26. The ...
... angles formed by these lines are together equal to two right angles . 25. If the sides of an equilateral and equiangular hexagon be pro- duced to meet ; the angles formed by these lines are together equal to four right angles . 26. The ...
Side xxv
... right - angled triangle ; each of the lines joining the acute angles and the opposite angle of the square , will cut off from the triangle an obtuse - angled triangle , which will be equal to that cut off from the square by a line drawn ...
... right - angled triangle ; each of the lines joining the acute angles and the opposite angle of the square , will cut off from the triangle an obtuse - angled triangle , which will be equal to that cut off from the square by a line drawn ...
Indhold
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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.