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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Αποτελέσματα 1 - 4 από τα 4.
Σελίδα 177
... Q. E. F. Ex . If an equilateral triangle be inscribed in a circle , prove that the radii , drawn to the angular points , bisect the angles of the triangle . PROPOSITION III . PROBLEM . About a given circle to BOOK IV . PROP . II . 177.
... Q. E. F. Ex . If an equilateral triangle be inscribed in a circle , prove that the radii , drawn to the angular points , bisect the angles of the triangle . PROPOSITION III . PROBLEM . About a given circle to BOOK IV . PROP . II . 177.
Σελίδα 193
... equilateral triangle , inscribed in the other . 17. Construct a square , having given the sum , or the difference , of the diagonal and the side . 18. If from O , the centre of the circle inscribed in a triangle ABC , OD , OE , OF be ...
... equilateral triangle , inscribed in the other . 17. Construct a square , having given the sum , or the difference , of the diagonal and the side . 18. If from O , the centre of the circle inscribed in a triangle ABC , OD , OE , OF be ...
Σελίδα 196
... Triangles are described on the same base and having the difference of the squares on the other sides constant : shew that the vertex of any triangle is in one or other of two fixed straight lines . IV . 3. Two equilateral triangles are ...
... Triangles are described on the same base and having the difference of the squares on the other sides constant : shew that the vertex of any triangle is in one or other of two fixed straight lines . IV . 3. Two equilateral triangles are ...
Σελίδα 204
... triangle inscribed in a circle , be equal , prove that either the angles are equal , or the third angle is equal to the angle of an equilateral triangle . 1868. 1. 41. OKBM and OLDN are parallelograms about the diameter of a ...
... triangle inscribed in a circle , be equal , prove that either the angles are equal , or the third angle is equal to the angle of an equilateral triangle . 1868. 1. 41. OKBM and OLDN are parallelograms about the diameter of a ...
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD base Book centre chord circles intersect circles touch circumference coincide common construction cutting the circle Describe a circle described diagonals diameter difference distance divided double draw equal equal circles equiangular extremities fall figure Find formed four given circle given point given straight line greater Hence hexagon inscribed join less Let ABC lies line be drawn locus meet middle points NOTE opposite sides parallel parallelogram pass perpendicular point of contact PROBLEM produced PROPOSITION prove Q. E. D. Ex quadrilateral radius rect regular pentagon required to inscribe respectively right angles segment semicircle shew shewn sides Similarly square subtended sum of 48 tangents THEOREM third touch touch the circle triangle triangle ABC twice
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.