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 152
Euclides James Hamblin Smith. PROPOSITION XXII . THEOREM . The opposite angles of any quadrilateral figure ... opposite s be together equal to two rt . LS . Draw the diagonals AC , BD ... side of a quadrilateral figure 152 EUCLID'S ELEMENTS .
Euclides James Hamblin Smith. PROPOSITION XXII . THEOREM . The opposite angles of any quadrilateral figure ... opposite s be together equal to two rt . LS . Draw the diagonals AC , BD ... side of a quadrilateral figure 152 EUCLID'S ELEMENTS .
Side 153
... opposite exterior angle , meet in the circumference of the circle . Ex . 5. AB , a chord of a circle , is the base of an isosceles triangle , whose vertex C is without the circle , and whose equal sides meet the circle in D , E : shew ...
... opposite exterior angle , meet in the circumference of the circle . Ex . 5. AB , a chord of a circle , is the base of an isosceles triangle , whose vertex C is without the circle , and whose equal sides meet the circle in D , E : shew ...
Side 165
... side of a triangle , its vertical angle , and the radius of the circumscribing circle : construct the triangle . Ex . 3. Given the base , vertical angle , and the perpen- dicular from the extremity of the base on the opposite side ...
... side of a triangle , its vertical angle , and the radius of the circumscribing circle : construct the triangle . Ex . 3. Given the base , vertical angle , and the perpen- dicular from the extremity of the base on the opposite side ...
Side 169
... sides , shew that the sum of their squares is equal to twice the square of the radius . 6. AB is the diameter of a ... opposite angles of a parallelogram , and cutting the four sides , and the points of intersection joined so as to form ...
... sides , shew that the sum of their squares is equal to twice the square of the radius . 6. AB is the diameter of a ... opposite angles of a parallelogram , and cutting the four sides , and the points of intersection joined so as to form ...
Side 171
... opposite sides , shew that the sum of the squares of the sides of the triangle is equal to twice the sum of the rectangles contained by the perpendiculars and that part of each intercepted between the angles of the triangles and the ...
... opposite sides , shew that the sum of the squares of the sides of the triangle is equal to twice the sum of the rectangles contained by the perpendiculars and that part of each intercepted between the angles of the triangles and 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.