Elements of geometry, containing the first two (third and fourth) books of Euclid, with exercises and notes, by J.H. Smith, Del 21872 |
Inni boken
Resultat 1-5 av 9
Side 166
... , which intersect one another , there be drawn any two other chords , one in each circle , their four extremities shall all lie in the circumference of a circle . PROPOSITION XXXVI . THEOREM . If , from any point 166 EUCLID'S ELEMENTS .
... , which intersect one another , there be drawn any two other chords , one in each circle , their four extremities shall all lie in the circumference of a circle . PROPOSITION XXXVI . THEOREM . If , from any point 166 EUCLID'S ELEMENTS .
Side 169
... 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 circle touch both , prove that 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 circle touch both , prove that the ...
Side 181
... about the Q. E. F. Ex . In a given circle inscribe four circles , equal to each other , and in mutual contact with each other and with the given circle . . PROPOSITION VIII PROBLEM . To inscribe a circle in a BOOK IV . PROP . VII . 181.
... about the Q. E. F. Ex . In a given circle inscribe four circles , equal to each other , and in mutual contact with each other and with the given circle . . PROPOSITION VIII PROBLEM . To inscribe a circle in a BOOK IV . PROP . VII . 181.
Side 182
... straight lines be drawn to the angular points of the inscribed square , the sum of the squares on these four lines will be double of the square on the diameter . PROPOSITION IX . PROBLEM . To describe a circle about 182 EUCLID'S ELEMENTS .
... straight lines be drawn to the angular points of the inscribed square , the sum of the squares on these four lines will be double of the square on the diameter . PROPOSITION IX . PROBLEM . To describe a circle about 182 EUCLID'S ELEMENTS .
Side 194
... 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 straight lines AEB , CED in a circle ...
... 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 straight lines AEB , CED in a circle ...
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.