Elements of geometry, containing the first two (third and fourth) books of Euclid, with exercises and notes, by J.H. Smith, Μέρος 21872 |
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Σελίδα 126
... 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 V. THEOREM . If two circles cut one another 126 EUCLID'S ELEMENTS .
... 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 V. THEOREM . If two circles cut one another 126 EUCLID'S ELEMENTS .
Σελίδα 169
... parallelogram , and cutting the four sides , and the points of intersection joined so as to form a hexagon , the straight lines thus drawn shall be parallel to each other . 9. If two circles touch each other externally and any third ...
... parallelogram , and cutting the four sides , and the points of intersection joined so as to form a hexagon , the straight lines thus drawn shall be parallel to each other . 9. If two circles touch each other externally and any third ...
Σελίδα 174
... parallelogram is divided by any line equal to one of its shorter sides . 52. If a parallelogram be described having the diameter of a given circle for one of its sides , and the intersection of its diagonals on the circumference , shew ...
... parallelogram is divided by any line equal to one of its shorter sides . 52. If a parallelogram be described having the diameter of a given circle for one of its sides , and the intersection of its diagonals on the circumference , shew ...
Σελίδα 182
... parallelograms can circles be inscribed ? Ex . 2. If , from any point in the circumference of a circle , straight lines be drawn to the angular points of the inscribed square , the sum of the squares on these four lines will be double ...
... parallelograms can circles be inscribed ? Ex . 2. If , from any point in the circumference of a circle , straight lines be drawn to the angular points of the inscribed square , the sum of the squares on these four lines will be double ...
Σελίδα 194
... parallelogram will be divided into four equal parts . In what case will the diagonal bisect the angle of a parallelogram ? III . 15. Shew that all equal straight lines in a circle will be touched by another circle . III . 20. If two ...
... parallelogram will be divided into four equal parts . In what case will the diagonal bisect the angle of a parallelogram ? III . 15. Shew that all equal straight lines in a circle will be touched by another circle . III . 20. If two ...
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 152 - The opposite angles of any quadrilateral figure inscribed in a circle, are together equal to two right angles.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.
Σελίδα 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.
Σελίδα 184 - ABD is described, having each of the angles at the base double of the third angle.
Σελίδα 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.
Σελίδα 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.
Σελίδα 183 - To inscribe a circle in a given square. Let ABCD be the given square ; it is required to inscribe a circle in ABCD.