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 10
Side 151
... extremities are in the circumference of a circle cut one another , the triangles formed by joining their extremities are equiangular to each other . PROPOSITION XXII . THEOREM . The opposite angles of any BOOK III . PROP . XXI . 151.
... extremities are in the circumference of a circle cut one another , the triangles formed by joining their extremities are equiangular to each other . PROPOSITION XXII . THEOREM . The opposite angles of any BOOK III . PROP . XXI . 151.
Side 153
... equiangular . Ex . 3. Shew that a circle cannot be described about a rhombus . Ex . 4. The lines , bisecting any angle of a quadrilateral figure inscribed in a circle and the opposite exterior angle , meet in the circumference of the ...
... equiangular . Ex . 3. Shew that a circle cannot be described about a rhombus . Ex . 4. The lines , bisecting any angle of a quadrilateral figure inscribed in a circle and the opposite exterior angle , meet in the circumference of the ...
Side 169
... equiangular , 4. If a circle be described round the triangle ABC , and a straight line be drawn bisecting the angle BAC and cutting the circle in D , shew that the angle DCB will equal half the angle BAC . 5. One angle of a ...
... equiangular , 4. If a circle be described round the triangle ABC , and a straight line be drawn bisecting the angle BAC and cutting the circle in D , shew that the angle DCB will equal half the angle BAC . 5. One angle of a ...
Side 170
... equiangular to the triangle EAB . 17. Two equal circles cut one another in the points A , B ; BC is a chord equal to AB ; shew that AC is a tangent to the other circle . 18. In any two circles , which cut one another , the straight line ...
... equiangular to the triangle EAB . 17. Two equal circles cut one another in the points A , B ; BC is a chord equal to AB ; shew that AC is a tangent to the other circle . 18. In any two circles , which cut one another , the straight line ...
Side 177
... equiangular to △ DEF , and it is inscribed in the ABC . 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 ...
... equiangular to △ DEF , and it is inscribed in the ABC . 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 ...
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.