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 iii
... meeting the three lines be harmonically divided . 23. If a straight line be divided into two equal and also into two unequal parts , and be produced , so that the part produced may have to the whole line so produced , the same ratio ...
... meeting the three lines be harmonically divided . 23. If a straight line be divided into two equal and also into two unequal parts , and be produced , so that the part produced may have to the whole line so produced , the same ratio ...
Σελίδα iv
... meeting these perpendiculars , will be divided at that point into parts which have the same ratio , that those lines have which are drawn from the extremity of the produced line to the points of intersection with the perpendicular . 29 ...
... meeting these perpendiculars , will be divided at that point into parts which have the same ratio , that those lines have which are drawn from the extremity of the produced line to the points of intersection with the perpendicular . 29 ...
Σελίδα viii
... meeting the circumferences ; the part of it intercepted between the circumferences will be bisected by the circle whose diameter is the common chord of the equal circles . 32. If two circles touch each other externally or internally ...
... meeting the circumferences ; the part of it intercepted between the circumferences will be bisected by the circle whose diameter is the common chord of the equal circles . 32. If two circles touch each other externally or internally ...
Σελίδα xii
... meeting the sides of the quadrant pro- duced , the intercepted parts may have a given ratio . 68. If a tangent be drawn to a circle at the extremity of a chord which cuts the diameter at right angles , and from any point in it a ...
... meeting the sides of the quadrant pro- duced , the intercepted parts may have a given ratio . 68. If a tangent be drawn to a circle at the extremity of a chord which cuts the diameter at right angles , and from any point in it a ...
Σελίδα xiv
... meeting the circumference , and on it as a diameter a circle be described , to the centre of which a line is drawn from the farther extremity of the diameter of the semicircle , cutting its circumference ; and through the point of ...
... meeting the circumference , and on it as a diameter a circle be described , to the centre of which a line is drawn from the farther extremity of the diameter of the semicircle , cutting its circumference ; and through the point of ...
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Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD angle ABC angles at F base centre chord circle ABC circles cut circles touch circumference describe a circle divided draw a line draw the diameter drawn parallel duplicate ratio equal angles equiangular Eucl extremities G draw given angle given circle given in position given line given point given ratio given square given straight line given triangle 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 point of bisection point of contact point of intersection point required radius rectangle right angles segments semicircle shewn tangent touching the circle trapezium triangle ABC
Δημοφιλή αποσπάσματα
Σελίδα 14 - IF a straight line be divided into two equal, and also into two unequal parts ; the squares of the two unequal parts are together double of the square of half the line, and of the square of the line between the points of section.
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 230 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.
Σελίδα 327 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds.
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 212 - 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 123 - If from a point, without a parallelogram, there be drawn two straight lines to the extremities of the two opposite sides, between which, when produced, the point does not lie, the difference of the triangles thus formed is equal to half the parallelogram. Ex. 2. The two triangles, formed by drawing straight lines from any point within a parallelogram to the extremities of its opposite sides, are together half of the parallelogram.
Σελίδα 305 - Given the vertical angle, the difference of the two sides containing it, and the difference of the segments of the base made by a perpendicular from the vertex ; construct the triangle.
Σελίδα 247 - The perpendicular from the vertex on the base of an equilateral triangle is equal to the side of an equilateral triangle inscribed in a circle, whose diameter is the base.
Σελίδα 299 - AB be equal to the given bisecting line ; and upon it describe a segment of a circle containing an angle equal to the given angle.