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 xxiii
... rectangular parallelogram a line be drawn to the opposite side , and from the adjacent angle of the tra- pezium thus formed another be drawn perpendicular to the former ; the rectangle contained by these two lines is equal to the given ...
... rectangular parallelogram a line be drawn to the opposite side , and from the adjacent angle of the tra- pezium thus formed another be drawn perpendicular to the former ; the rectangle contained by these two lines is equal to the given ...
Side xxv
... rectangular parallelogram lines be drawn to the angular points ; the sums of the squares of those which are drawn to ... rectangle contained by its parallel sides . 36. The squares of the diagonals of a trapezium are together double the ...
... rectangular parallelogram lines be drawn to the angular points ; the sums of the squares of those which are drawn to ... rectangle contained by its parallel sides . 36. The squares of the diagonals of a trapezium are together double the ...
Side xxvi
To which is Added an Appendix Containing the Elements of Plane Trigonometry ... Miles Bland. necessary ) of the ... rectangle contained by their segments may be equal . 47. If the sides , or sides produced , of a triangle be cut by ...
To which is Added an Appendix Containing the Elements of Plane Trigonometry ... Miles Bland. necessary ) of the ... rectangle contained by their segments may be equal . 47. If the sides , or sides produced , of a triangle be cut by ...
Side xxvii
... rectangle contained by them may be equal to the square of their difference . 7. If a straight line be divided into any two parts ; to produce it so that the rectangle contained by the whole line so produced and the part produced , may ...
... rectangle contained by them may be equal to the square of their difference . 7. If a straight line be divided into any two parts ; to produce it so that the rectangle contained by the whole line so produced and the part produced , may ...
Side xxviii
... rectangle contained by the other and a given line . 12. A straight line being given in magnitude and position ; to draw to it , from a given point , two lines , whose rectangle shall be equal to a given rectangle , and which shall cut ...
... rectangle contained by the other and a given line . 12. A straight line being given in magnitude and position ; to draw to it , from a given point , two lines , whose rectangle shall be equal to a given rectangle , and which shall cut ...
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Almindelige termer og sætninger
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
Populære passager
Side 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.
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 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 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.
Side 230 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.
Side 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.
Side 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.
Side 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.
Side 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.
Side 355 - The sine of an angle is equal to the sine of its supplement. The sine rule Consider fig.