Elements of geometry, containing the first two (third and fourth) books of Euclid, with exercises and notes, by J.H. Smith, Del 21872 |
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Resultat 1-5 av 21
Side 125
... Ex . 1 . Then must CD bisect AB . For : OA = 0B , and OE is common , in the right - angled As AEO , BEO , : . AE = BE , that is , CD bisects AB . I. E. Cor . p . 43 . Q. E. D. Shew that if CD does not cut AB at right angles , it cannot ...
... Ex . 1 . Then must CD bisect AB . For : OA = 0B , and OE is common , in the right - angled As AEO , BEO , : . AE = BE , that is , CD bisects AB . I. E. Cor . p . 43 . Q. E. D. Shew that if CD does not cut AB at right angles , it cannot ...
Side 126
... Q. E. D. Ex . 1. Shew that the locus of the points of bisection of all parallel chords of a circle is a straight line . Ex . 2. Shew that no parallelogram , except those which are rectangular , can be inscribed in a circle . PROPOSITION ...
... Q. E. D. Ex . 1. Shew that the locus of the points of bisection of all parallel chords of a circle is a straight line . Ex . 2. Shew that no parallelogram , except those which are rectangular , can be inscribed in a circle . PROPOSITION ...
Side 127
... Q. E. D. Ex . Two circles , whose centres are A and B , intersect in in C ; through C two chords DCE , FCG are drawn equally inclined to AB and terminated by the circles : prove that DE and FG are equal . Note . Circles which have the ...
... Q. E. D. Ex . Two circles , whose centres are A and B , intersect in in C ; through C two chords DCE , FCG are drawn equally inclined to AB and terminated by the circles : prove that DE and FG are equal . Note . Circles which have the ...
Side 130
... Q. E. D. Ex . 1. If AP be produced to meet the circumference in D , shew that PD is less than any other line that can be drawn from P to the circumference . Ex . 2. Shew that PB continually decreases , as B passes from A to D. Ex . 3 ...
... Q. E. D. Ex . 1. If AP be produced to meet the circumference in D , shew that PD is less than any other line that can be drawn from P to the circumference . Ex . 2. Shew that PB continually decreases , as B passes from A to D. Ex . 3 ...
Side 137
... Q. E. D. Ex . Three circles touch one another externally , whose centres are A , B , C. Shew that the difference between AB great as the difference between the and AC is half as diameters of the circles , whose centres are B and C. 8. E ...
... Q. E. D. Ex . Three circles touch one another externally , whose centres are A , B , C. Shew that the difference between AB great as the difference between the and AC is half as diameters of the circles , whose centres are B and C. 8. E ...
Vanlige uttrykk og setninger
ABCD angular points bisect the angle centre of ADE chord AC circle be described circle described circles cut circles intersect circles touch circumference coincide cutting the circle Describe a circle diagonals diameter draw equal circles equiangular equilateral triangle given circle given line given point given square given straight line isosceles triangle Join OA Let ABC line be drawn line drawn meet the Oce middle points opposite sides parallel parallelogram pass perpendicular point of contact produced prove Q. E. D. Ex Q. E. F. PROPOSITION quadrilateral quadrilateral figure rect rectangle contained reflex angle regular pentagon regular polygon required to inscribe rhombus right angles segment ABC semicircle shew shewn straight line joining subtended sum of 48 tangents THEOREM touch the circle triangle ABC vertex
Populære avsnitt
Side 152 - The opposite angles of any quadrilateral figure inscribed in a circle, are together equal to two right angles.
Side 168 - 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 161 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Side 132 - If a point be taken within a circle, from which there fall more than two equal straight lines to the circumference, that point is the centre of the circle. Let...
Side 163 - IF a straight line touch a circle, and from the point of contact a straight line be drawn at right angles to the touching line, the centre of the circle shall be in that line.
Side 177 - IN a given circle to inscribe a triangle equiangular to a given triangle. Let ABC be the given circle, and DEF the given triangle; it is required to inscribe in the circle ABC a triangle equiangular to the triangle DEF. Draw (1 7. 3.) the straight line G AH touching the circle in the point A, and. at the point A, in the straight line AH, make (23.
Side 184 - ABD is described, having each of the angles at the base double of the third angle.
Side 207 - Upon the same straight line, and upon the same side of it, there cannot be two similar segments of circles, not coinciding with one another. If it be possible. let the two similar segments of circles, viz. ACB' ADB be upon the same side of the same straight line AB, not coinciding with one another.
Side 203 - If a straight line be divided into any two parts, the squares on the whole line, and on one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square on the other part.
Side 183 - To inscribe a circle in a given square. Let ABCD be the given square ; it is required to inscribe a circle in ABCD.