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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... of the Elements of Plane Trigonometry , as is necessary for understanding those parts of Natural Philosophy which are the common subjects of Lectures in the Uni- versity . The Reader who wishes for farther information ,
... of the Elements of Plane Trigonometry , as is necessary for understanding those parts of Natural Philosophy which are the common subjects of Lectures in the Uni- versity . The Reader who wishes for farther information ,
Página viii
... common chord of the equal circles . 32. If two circles touch each other externally or internally ; any straight line drawn through the point of contact will cut off similar segments . 33. If two circles touch each other externally or ...
... common chord of the equal circles . 32. If two circles touch each other externally or internally ; any straight line drawn through the point of contact will cut off similar segments . 33. If two circles touch each other externally or ...
Página ix
... common diameter be produced to cut the cir- cumferences ; the lines joining the points of intersection and the point of contact are proportional . 40. If three circles , whose diameters are in continued proportion , touch each other ...
... common diameter be produced to cut the cir- cumferences ; the lines joining the points of intersection and the point of contact are proportional . 40. If three circles , whose diameters are in continued proportion , touch each other ...
Página xi
... common chord and the two circumferences will be in continued proportion . 57. If a semicircle be described on the side of a quadrant , and from any point in the quadrantal arc a radius be drawn , the part of this radius intercepted ...
... common chord and the two circumferences will be in continued proportion . 57. If a semicircle be described on the side of a quadrant , and from any point in the quadrantal arc a radius be drawn , the part of this radius intercepted ...
Página xv
... common chord of two intersecting circles , and a line drawn from one extremity of the chord , cutting the two circles ; the part intercepted between the two shall be divided by the semicircle into segments proportional to perpendiculars ...
... common chord of two intersecting circles , and a line drawn from one extremity of the chord , cutting the two circles ; the part intercepted between the two shall be divided by the semicircle into segments proportional to perpendiculars ...
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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.