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, 1821 - 438 sider |
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Side v
... circle , and be parallel to a chord ; the point of contact will be the middle point of the arc cut off by that chord ... given points to meet on the convex circumference of a given circle ; the sum of those two will be the least , which ...
... circle , and be parallel to a chord ; the point of contact will be the middle point of the arc cut off by that chord ... given points to meet on the convex circumference of a given circle ; the sum of those two will be the least , which ...
Side vi
... circumference of a circle any number of chords be drawn ; the locus of their points of bisection will be a circle . 12. If on the radius of a given semicircle , another semicircle be described , and from the extremity of the diameters ...
... circumference of a circle any number of chords be drawn ; the locus of their points of bisection will be a circle . 12. If on the radius of a given semicircle , another semicircle be described , and from the extremity of the diameters ...
Side vii
... given circle , to draw to a straight line given in position , a line which shall be equal and parallel to a given straight line . 23. The bases of two given circular segments being in the same straight line ; to determine a point in it ...
... given circle , to draw to a straight line given in position , a line which shall be equal and parallel to a given straight line . 23. The bases of two given circular segments being in the same straight line ; to determine a point in it ...
Side x
... circle may be equal to a given straight line . 47. Through a given point without a given circle , to draw a straight line to cut the circle , so that the two perpendiculars drawn from the points of intersection to that diameter which ...
... circle may be equal to a given straight line . 47. Through a given point without a given circle , to draw a straight line to cut the circle , so that the two perpendiculars drawn from the points of intersection to that diameter which ...
Side xi
... circle , and from its extremities two straight lines be drawn to any point in the circumference of the semicircle ; the segment of the greater line intercepted between the two ... given point within a given circle to CONTENTS . xi.
... circle , and from its extremities two straight lines be drawn to any point in the circumference of the semicircle ; the segment of the greater line intercepted between the two ... given point within a given circle to CONTENTS . xi.
Indhold
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18 | |
22 | |
49 | |
72 | |
108 | |
142 | |
187 | |
209 | |
227 | |
268 | |
293 | |
399 | |
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Almindelige termer og sætninger
ABCD angle ABC angle equal BC is equal centre chord circle cutting circumference construct the triangle cosecant cosine describe a circle divided equation equiangular Eucl extremities find the value given angle given circle given difference given in position given line given point given ratio given rectangle given square given straight line Hence inscribed intercepted isosceles triangle Join AE least common multiple Let AB Let ABC let fall line given line joining lines be drawn lines drawn mean proportional meeting opposite side parallel to AC parallelogram pendicular point of intersection produced quadrant radius rectangle contained right angles right-angled triangle segments semicircle shewn sine squares of AC tang tangent transposition trapezium triangle ABC triangle required vertex vertical angle whence
Populære passager
Side i - 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 xi - 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 319 - 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 150 - 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 204 - 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.
Side 115 - 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 14 - In one of the given equations obtain the value of one of the unknown quantities in terms of the other unknown quantity; Substitute this value in the other equation and solve.
Side 291 - AB describe a segment of a circle containing an angle equal to the given angle, (in.
Side 297 - 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 90 - If from any point in the base of an isosceles triangle perpendiculars...