A Supplement to the Elements of EuclidG. and W. B. Whittaker, 1819 - 410 σελίδες |
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Σελίδα 108
... chord which shall be bisected in that point . Let A be a given point within the circle BCD : It is required to draw , through A , a chord of the circle BCD , which shall be bisected in the point A. Find ( E. 1.3 . ) the centre K of ...
... chord which shall be bisected in that point . Let A be a given point within the circle BCD : It is required to draw , through A , a chord of the circle BCD , which shall be bisected in the point A. Find ( E. 1.3 . ) the centre K of ...
Σελίδα 110
... chords of a circle which cut a diameter in the same point and at equal angles , are equal to one another . Let any two chords AB , CD of the circle ADBC E A C G M L D B K F cut a diameter EF in the same point G , and make with it the ...
... chords of a circle which cut a diameter in the same point and at equal angles , are equal to one another . Let any two chords AB , CD of the circle ADBC E A C G M L D B K F cut a diameter EF in the same point G , and make with it the ...
Σελίδα 111
... chords , making with one another an angle equal to a given rectili- neal angle . Let G be a given point in the circle ADBC , A C G Z X D B K H and XHY a given rectilineal angle : It is required to draw through G two equal chords of ...
... chords , making with one another an angle equal to a given rectili- neal angle . Let G be a given point in the circle ADBC , A C G Z X D B K H and XHY a given rectilineal angle : It is required to draw through G two equal chords of ...
Σελίδα 112
... chord AB = chord CD . PROP . VI . 7. THEOREM . If the diameters of two circles are in the same straight line , and have a common ex- tremity , the two circles shall touch one another . For since ( hyp . ) the two diameters are in the ...
... chord AB = chord CD . PROP . VI . 7. THEOREM . If the diameters of two circles are in the same straight line , and have a common ex- tremity , the two circles shall touch one another . For since ( hyp . ) the two diameters are in the ...
Σελίδα 138
... chord , the angle which the one makes with any perpendicular to the chord , shall be equal to the angle which the other makes with the diameter of the circle that passes through the given point . Let C be a given point in the ...
... chord , the angle which the one makes with any perpendicular to the chord , shall be equal to the angle which the other makes with the diameter of the circle that passes through the given point . Let C be a given point in the ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
base BC bisect centre chord circle ABC circle described circumference constr decagon describe a circle describe the circle diameter distance divided double draw a straight draw E equi equiangular equilateral and equiangular F draw find a point finite straight line given circle given figure given finite straight given point given ratio given square given straight line half hypotenuse inscribed isosceles less Let AB Let ABC lines be drawn magnitudes manifest manner meet the circumference number of equal number of sides opposite sides parallel to BC parallelogram pass perimeter polygon PROBLEM produced PROP rectangle contained remaining sides required to describe required to draw rhombus right angles segment semi-diameter straight line joining subtend tangent THEOREM three given touch the circle trapezium vertex
Δημοφιλή αποσπάσματα
Σελίδα 310 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Σελίδα 198 - If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced, together with the square...
Σελίδα 366 - If from the vertical angle of a triangle a straight line be drawn perpendicular to the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the perpendicular and the diameter of the circle described about the...
Σελίδα 92 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.
Σελίδα 284 - And if the first have a greater ratio to the second, than the third has to the fourth, but the third the same ratio to the fourth, which the fifth has to the sixth...
Σελίδα 349 - Divide a straight line into two parts such that the rectangle contained by the whole line and one of the parts shall be equal to the square on the other part.
Σελίδα 288 - Convertendo, by conversion ; when there are four proportionals, and it is inferred, that the first is to its excess above the second, as the third to its excess above the fourth.
Σελίδα 296 - ... line and the extremities of the base have the same ratio which the other sides of the triangle have to one...
Σελίδα 367 - Wherefore, in equal circles &c. QED PROPOSITION B. THEOREM If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Σελίδα 104 - In every triangle, the square of the side subtending any of the acute angles is less than the squares of the sides containing that angle by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fall upon it from the opposite angle, and the acute angle. Let ABC be any triangle, and the angle at B one of its acute angles, and upon BC, one of the sides containing it, let fall the perpendicular...