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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Side 123
Euclides James Hamblin Smith. PROPOSITION I. THEOREM . The line , which bisects a chord of a circle at right angles , must contain the centre . F D B Let ABC be the given O. Let the st . line CE bisect the chord AB at rt . angles in D ...
Euclides James Hamblin Smith. PROPOSITION I. THEOREM . The line , which bisects a chord of a circle at right angles , must contain the centre . F D B Let ABC be the given O. Let the st . line CE bisect the chord AB at rt . angles in D ...
Side 125
Euclides James Hamblin Smith. PROPOSITION III . THEOREM . If a straight line , drawn through the centre of a circle ... given point within a circle , which is not the centre , draw a chord which shall be bisected in that point ...
Euclides James Hamblin Smith. PROPOSITION III . THEOREM . If a straight line , drawn through the centre of a circle ... given point within a circle , which is not the centre , draw a chord which shall be bisected in that point ...
Side 142
... given length in a given circle , which shall be bisected by a given chord ... straight line is said to be a TANGENT to , or to touch , a circle , when it ... line joining two points in the circumference is , being produced , a secant ...
... given length in a given circle , which shall be bisected by a given chord ... straight line is said to be a TANGENT to , or to touch , a circle , when it ... line joining two points in the circumference is , being produced , a secant ...
Side 144
Euclides James Hamblin Smith. PROPOSITION XVII . PROBLEM . To draw a straight line from a given point , either WITH- OUT or on the circumference , which shall touch a given circle . Let A be the given pt . , without the © BCD . Let O be ...
Euclides James Hamblin Smith. PROPOSITION XVII . PROBLEM . To draw a straight line from a given point , either WITH- OUT or on the circumference , which shall touch a given circle . Let A be the given pt . , without the © BCD . Let O be ...
Side 149
... right angles : and we now proceed to shew how the Definition given in that Note may be extended , so as to embrace angles greater than two right angles . ने Let WQ be a straight line , and QE its continuation . Then , by the ...
... right angles : and we now proceed to shew how the Definition given in that Note may be extended , so as to embrace angles greater than two right angles . ने Let WQ be a straight line , and QE its continuation . Then , by the ...
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.