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 iii
... produced , so that the part produced may have to the whole line so produced , the same ratio that the unequal segments of the line have to each other ; then shall the distances of the point of unequal section from one extremity of the ...
... produced , so that the part produced may have to the whole line so produced , the same ratio that the unequal segments of the line have to each other ; then shall the distances of the point of unequal section from one extremity of the ...
Side iv
... produced has to the part produced , and from the extremities of the given line perpendiculars be erected ; then any line drawn through the point of section , meeting these perpendiculars , will be divided at that point into parts which ...
... produced has to the part produced , and from the extremities of the given line perpendiculars be erected ; then any line drawn through the point of section , meeting these perpendiculars , will be divided at that point into parts which ...
Side vi
... produced , so that the part produced may always have a given ratio to the part intercepted between the two circumferences ; to determine the locus of the ex- tremities of these lines . 13. If from a given point without a given circle ...
... produced , so that the part produced may always have a given ratio to the part intercepted between the two circumferences ; to determine the locus of the ex- tremities of these lines . 13. If from a given point without a given circle ...
Side viii
... produced to the circumferences ; and from its middle point as a centre with any radius whatever a circle be de ... produced to meet ; the angles formed by these lines will be equal . 39. If two circles touch each other internally , and ...
... produced to the circumferences ; and from its middle point as a centre with any radius whatever a circle be de ... produced to meet ; the angles formed by these lines will be equal . 39. If two circles touch each other internally , and ...
Side ix
... produced , a tangent be drawn ; a perpendicular from the point of contact to the diameter will divide it into segments which have the same ratio that the distances of the point without the circle from each extremity of the diameter ...
... produced , a tangent be drawn ; a perpendicular from the point of contact to the diameter will divide it into segments which have the same ratio that the distances of the point without the circle from each extremity of the diameter ...
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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.