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 páginas |
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Página v
... chord ; the point of contact will be the middle point of the arc cut off by that chord . COR . 1. Parallel lines placed in a circle cut off equal parts of the circumference . COR . 2. The two straight lines in a circle which join the ex ...
... chord ; the point of contact will be the middle point of the arc cut off by that chord . COR . 1. Parallel lines placed in a circle cut off equal parts of the circumference . COR . 2. The two straight lines in a circle which join the ex ...
Página vi
... chords be drawn ; the locus of their points of bisection will be a circle . 12. If on the radius of a given semicircle ... chord in a circle perpendi- culars be drawn , meeting a diameter ; the points of intersection are equally distant ...
... chords be drawn ; the locus of their points of bisection will be a circle . 12. If on the radius of a given semicircle ... chord in a circle perpendi- culars be drawn , meeting a diameter ; the points of intersection are equally distant ...
Página vii
... chords so drawn will be equal to the last chord produced to meet a line drawn from the given point through the extremity of the first arc . 28. If the circumference of a semicircle be divided into an odd number of equal parts , and ...
... chords so drawn will be equal to the last chord produced to meet a line drawn from the given point through the extremity of the first arc . 28. If the circumference of a semicircle be divided into an odd number of equal parts , and ...
Página viii
... chord of the equal circles . 32. If two circles touch each other externally or internally ; any straight line drawn ... chords of which are parallel . 34. If two circles touch each other externally or internally ; any two straight lines ...
... chord of the equal circles . 32. If two circles touch each other externally or internally ; any straight line drawn ... chords of which are parallel . 34. If two circles touch each other externally or internally ; any two straight lines ...
Página x
... chords which can be drawn through that point , that is the least which is at right angles to the diameter . 51. If from any point without a circle lines be drawn touching it ; the angle contained by the tangents is double the angle ...
... chords which can be drawn through that point , that is the least which is at right angles to the diameter . 51. If from any point without a circle lines be drawn touching it ; the angle contained by the tangents is double the angle ...
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Términos y frases comunes
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
Pasajes populares
Página 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.
Página 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.
Página 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...
Página 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.
Página 230 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.
Página 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.
Página 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.
Página 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.
Página 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.
Página 355 - The sine of an angle is equal to the sine of its supplement. The sine rule Consider fig.