Elements of geometry, containing the first two (third and fourth) books of Euclid, with exercises and notes, by J.H. Smith, 第 2 部1872 |
多く使われている語句
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
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152 ページ - The opposite angles of any quadrilateral figure inscribed in a circle, are together equal to two right angles.
168 ページ - 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.
161 ページ - 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.
132 ページ - 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...
163 ページ - 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.
177 ページ - 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.
184 ページ - ABD is described, having each of the angles at the base double of the third angle.
207 ページ - 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.
203 ページ - 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.
183 ページ - To inscribe a circle in a given square. Let ABCD be the given square ; it is required to inscribe a circle in ABCD.