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 xxiv
... equiangular pentagon be produced to meet ; 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 ...
... equiangular pentagon be produced to meet ; 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 ...
Página xxvi
... equiangular and equal to the given triangle . 43. If from the angular points of the squares described upon the sides of a right - angled triangle perpendiculars be let fall upon the hypothenuse produced ; they will cut off equal ...
... equiangular and equal to the given triangle . 43. If from the angular points of the squares described upon the sides of a right - angled triangle perpendiculars be let fall upon the hypothenuse produced ; they will cut off equal ...
Página xxxii
... equiangular pentagon , and of the same altitude . 6. To describe an equilateral triangle , equal to a given isosceles triangle . 7. To describe a parallelogram , the area and perimeter of which shall be respectively equal to the area ...
... equiangular pentagon , and of the same altitude . 6. To describe an equilateral triangle , equal to a given isosceles triangle . 7. To describe a parallelogram , the area and perimeter of which shall be respectively equal to the area ...
Página xxxiii
... equiangular pentagon , to inscribe a square . 30. In a given triangle , to inscribe a rhombus , one of whose angles shall be in a given point in the side of the triangle . 31. To inscribe a circle in a given quadrant . 32. To describe a ...
... equiangular pentagon , to inscribe a square . 30. In a given triangle , to inscribe a rhombus , one of whose angles shall be in a given point in the side of the triangle . 31. To inscribe a circle in a given quadrant . 32. To describe a ...
Página xxxv
... intercepted between the circumferences which are concave to each other , will be equal respectively to those of the other between the other circumferences . 58. If the diagonals of an equilateral and equiangular pentagon CONTENTS . XXXV.
... intercepted between the circumferences which are concave to each other , will be equal respectively to those of the other between the other circumferences . 58. If the diagonals of an equilateral and equiangular pentagon CONTENTS . XXXV.
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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.