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 σελίδες |
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Σελίδα xvii
... sides ; they are together equal to a perpendicular drawn from any of the angles to the opposite side . 4. If the points of bisection of the sides of a given triangle be joined ; the triangle so formed will be one fourth of the given ...
... sides ; they are together equal to a perpendicular drawn from any of the angles to the opposite side . 4. If the points of bisection of the sides of a given triangle be joined ; the triangle so formed will be one fourth of the given ...
Σελίδα xviii
... sides ; these together shall be equal to a perpendicular drawn from either extremity of the base to the opposite side . 12. Of all triangles having the same vertical angle , and whose bases pass through a given point , the least is that ...
... sides ; these together shall be equal to a perpendicular drawn from either extremity of the base to the opposite side . 12. Of all triangles having the same vertical angle , and whose bases pass through a given point , the least is that ...
Σελίδα xix
... sides about the third angle of the former shall be proportional to those about the interior angle at the base of the latter . 22. In a given triangle to draw a line parallel to one of the sides , so that it may be a mean proportional ...
... sides about the third angle of the former shall be proportional to those about the interior angle at the base of the latter . 22. In a given triangle to draw a line parallel to one of the sides , so that it may be a mean proportional ...
Σελίδα xx
... sides ( produced if necessary ) ; and from any point within , lines be drawn parallel to these , and meeting the sides of the triangle ; these lines will together be equal to the given line . 33. If the sides of a triangle be cut ...
... sides ( produced if necessary ) ; and from any point within , lines be drawn parallel to these , and meeting the sides of the triangle ; these lines will together be equal to the given line . 33. If the sides of a triangle be cut ...
Σελίδα xxi
... sides , and the inter- section of the perpendiculars from the middle of the sides , are all in the same straight line . And the distances of those points from one another are in a given ratio . 43. If straight lines be drawn from the ...
... sides , and the inter- section of the perpendiculars from the middle of the sides , are all in the same straight line . And the distances of those points from one another are in a given ratio . 43. If straight lines be drawn from the ...
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Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.
Σελίδα 230 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 355 - The sine of an angle is equal to the sine of its supplement. The sine rule Consider fig.