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, 1827 - 377 sider |
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Side viii
... similar segments . 33. If two circles touch each other externally or internally ; two straight lines drawn through the point of contact will intercept arcs , the chords of which are parallel . 34. If two circles touch each other ...
... similar segments . 33. If two circles touch each other externally or internally ; two straight lines drawn through the point of contact will intercept arcs , the chords of which are parallel . 34. If two circles touch each other ...
Side xxxiii
... similar to that on the base . 18. If an equilateral triangle be inscribed in a circle ; the square described on a ... similar to a given parallelogram . 28. In a given triangle , to inscribe a triangle similar to a given triangle . 29 ...
... similar to that on the base . 18. If an equilateral triangle be inscribed in a circle ; the square described on a ... similar to a given parallelogram . 28. In a given triangle , to inscribe a triangle similar to a given triangle . 29 ...
Side xxxix
... . 18. If on the sides of a triangle segments of circles be described similar to a segment on the base , and from the extremities of the base tangents be drawn intersecting their circumferences ; the points CONTENTS . xxxix.
... . 18. If on the sides of a triangle segments of circles be described similar to a segment on the base , and from the extremities of the base tangents be drawn intersecting their circumferences ; the points CONTENTS . xxxix.
Side xl
... If a triangle be inscribed in a circle , and from its vertex lines be drawn parallel to tangents at the extremities of its base ; they will cut off similar triangles . COR . 1. The rectangle contained by the segments of xl CONTENTS .
... If a triangle be inscribed in a circle , and from its vertex lines be drawn parallel to tangents at the extremities of its base ; they will cut off similar triangles . COR . 1. The rectangle contained by the segments of xl CONTENTS .
Side xlvii
... similar , and in the ratio of four to one . 35. If on any two segments of the diameter of a semicircle semi- circles be described ; the area included between the three circum- ferences will be equal to the area of a circle whose ...
... similar , and in the ratio of four to one . 35. If on any two segments of the diameter of a semicircle semi- circles be described ; the area included between the three circum- ferences will be equal to the area of a circle whose ...
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Vanlige uttrykk og setninger
ABCD angle ABC base bisect the angle centre chord circle ABC circles cut circumference describe a circle divided draw a line 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 intercepted isosceles triangle Join AB Join AE Join BD Let AB Let ABC let fall line given line joining line required lines be drawn lines drawn mean proportional opposite sides parallel to AC parallelogram pendicular point of bisection point of contact point of intersection radius rectangle rectangle contained right angles right-angled triangle segments semicircle shewn tangent touching the circle trapezium triangle ABC whence
Populære avsnitt
Side 10 - 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.
Side xv - 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.
Side xxx - 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.
Side 303 - 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.
Side 140 - 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...
Side 329 - CE is equal to the difference of the segments of the base made by the perpendicular.
Side 109 - 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.
Side 164 - PROPOSITION I. PROBLEM. — To describe an equilateral triangle upon a given finite straight line. Let AB be the given straight line; it is required to describe an equilateral triangle upon it.
Side 281 - 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.
Side 270 - AB describe a segment of a circle containing an angle equal to the given angle, (in.