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 100
Side i
... line possible to a given straight line . 21 . 2. If a perpendicular be drawn bisecting a given straight line , any point in this perpendicular is at equal ... given ratio . a 9. From a given point between two indefinite straight lines.
... line possible to a given straight line . 21 . 2. If a perpendicular be drawn bisecting a given straight line , any point in this perpendicular is at equal ... given ratio . a 9. From a given point between two indefinite straight lines.
Side ii
... straight lines given in position , to draw a line which shall be terminated by the given lines , and bisected in the given point . 10. From a given point without two indefinite straight lines given in position , to draw a line such that ...
... straight lines given in position , to draw a line which shall be terminated by the given lines , and bisected in the given point . 10. From a given point without two indefinite straight lines given in position , to draw a line such that ...
Side iii
... line drawn from the extremity of this proportional will bisect the angle formed by the lines drawn from the extremities of the other two . 21. If a straight line be drawn through any point in the line bisecting a given angle , and ...
... line drawn from the extremity of this proportional will bisect the angle formed by the lines drawn from the extremities of the other two . 21. If a straight line be drawn through any point in the line bisecting a given angle , and ...
Side iv
... given line , and their respective distances from the former points in a given ratio . 28. If a straight line be divided into any two parts and pro- duced , so that the segments may have the same ratio that the whole line produced has to ...
... given line , and their respective distances from the former points in a given ratio . 28. If a straight line be divided into any two parts and pro- duced , so that the segments may have the same ratio that the whole line produced has to ...
Side v
... straight line be drawn to touch a circle , and be parallel to a chord ; the ... given points to meet on the convex circumference of a given circle ; the sum ... a point in the circumference of a CONTENTS , ν.
... straight line be drawn to touch a circle , and be parallel to a chord ; the ... given points to meet on the convex circumference of a given circle ; the sum ... a point in the circumference of a CONTENTS , ν.
Indhold
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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.