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 - 5 από τα 11.
Σελίδα 147
... double of the angle at the circumference , subtended by the same arc . Let ABC be a O , O the centre , BC any arc , A any pt . in the Oce . Then must / BOC = twice △ BAC . First , suppose to be in one of the lines containing the L BAC ...
... double of the angle at the circumference , subtended by the same arc . Let ABC be a O , O the centre , BC any arc , A any pt . in the Oce . Then must / BOC = twice △ BAC . First , suppose to be in one of the lines containing the L BAC ...
Σελίδα 150
... double of the angle at the circumference , subtended by the same arc , A B B In the ACBD , let the angles AOB ( not less than two right angles ) at the centre , and ADB at the circumference , be subtended by the same arc ACB . Then must ...
... double of the angle at the circumference , subtended by the same arc , A B B In the ACBD , let the angles AOB ( not less than two right angles ) at the centre , and ADB at the circumference , be subtended by the same arc ACB . Then must ...
Σελίδα 160
... to the bisection of the circumference , and the other at right angles to the diameter , the squares on these two lines are together double of the square on the radius . PROPOSITION XXXI . THEOREM . In a circle , the 160 EUCLID'S ELEMENTS .
... to the bisection of the circumference , and the other at right angles to the diameter , the squares on these two lines are together double of the square on the radius . PROPOSITION XXXI . THEOREM . In a circle , the 160 EUCLID'S ELEMENTS .
Σελίδα 162
... double of the angle contained by the line joining the points of contact , and the diameter drawn through one of them . Ex . 4. The vertical angle of any oblique - angled triangle inscribed in a circle is greater or less than a right ...
... double of the angle contained by the line joining the points of contact , and the diameter drawn through one of them . Ex . 4. The vertical angle of any oblique - angled triangle inscribed in a circle is greater or less than a right ...
Σελίδα 174
... double the diameter of the first . 53. One diagonal of a quadrilateral inscribed in a circle is fixed , and the other of constant length . Shew that the sides will meet if produced on the circumference of a fixed circle . BOOK IV ...
... double the diameter of the first . 53. One diagonal of a quadrilateral inscribed in a circle is fixed , and the other of constant length . Shew that the sides will meet if produced on the circumference of a fixed circle . BOOK IV ...
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.