 | Henry Parr Hamilton - Conic sections - 1834 - 240 pages
...circle ; and if the values of y be imaginary, the straight line falls entirely without the circle. Hence a straight line cannot cut a circle in more than two points. 40. To find the equation to a straight line touching a circle in a given point. Let x, y be the co-ordinates... | |
 | Henry Parr Hamilton - Mathematics - 1834 - 272 pages
...circle ; and if the values of y be imaginary, the straight line falls entirely without the circle. Hence a straight line cannot cut a circle in more than two points. 40. To fold the equation to a straight line touching « circle in a given point, Let x, y' be the co-ordinates... | |
 | Euclid, James Bryce, David Munn (F.R.S.E.) - Geometry - 1874 - 236 pages
...the centre of the circle; at right angles to the chord. PROP. II.— THEOREM. (Euc. III. 2, in Part.) A straight line cannot cut a circle in more than two points; and any point of the line between the points of intersection lies within the circle. If possible suppose... | |
 | Francis Cuthbertson - Euclid's Elements - 1874 - 400 pages
...the ©. Similarly it may be shewn that it does not fall on the Oce; .-. it falls within the ©. COR. A straight line cannot cut a circle in more than two points. PROPOSITION II. The straight line drawn through the middle point of a chord of a circle and the centre... | |
 | Palaestra Oxoniensis - 1884 - 204 pages
...parts without the circle are equal to one another 8. Prove the corollaries (5), (6), in Question 2. 4. A straight line cannot cut a circle in more than two points. From which proposition does this follow ? в. In what case can two chords in a circle bisect one another... | |
 | John Stuart Mill, Alfred Henry Killick - Logic - 1888 - 288 pages
...Inductions." This process is of this kind : After having proved separately the following Propositions — (1.) A straight line cannot cut a circle in more than two points. (2.) A straight line cannot cut an ellipse in more than two points. Similarly of the parabola and hyperbola... | |
 | Euclid - Geometry - 1892 - 460 pages
...Describe a circle that shall pass through two given points, and have a given radius. ON PROPOSITION 2. 7. A straight line cannot cut a circle in more than two points. ON PROPOSITION 3. 8. Through a given point within a circle draw a chord which shall be bisected at... | |
 | Euclid, Henry Sinclair Hall, Frederick Haller Stevens - Euclid's Elements - 1900 - 330 pages
...pass through two given points, and have a given radius. When is this impossible ? ON PROPOSITION 2. 7. A straight line cannot cut a circle in more than two points. ON PROPOSITION 3. 8. Through a given point within a circle draw a chord which shall be bisected at... | |
 | Charles Godfrey, Arthur Warry Siddons - Geometry - 1903 - 384 pages
...the radius ; it will lie inside the circle if the distance < the radius. Straight line and circle. A straight line cannot cut a circle in more than two points. In fact, an unlimited straight line may (i) cut a circle in two points, eg AB or CD in fig. 213. In... | |
 | Euclid - Mathematics, Greek - 1908 - 456 pages
...proposition) and can alternatively be proved by means of i. 7, as shown above in the note on i. i 2. It follows that A straight line cannot cut a circle in more than two points : a proposition which De Morgan would introduce here after in. 2. The proof given does not apply to... | |
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Straight line and circle. A straight line cannot cut a circle in more than two points. In fact, an unlimited straight line may (i) cut a circle in two points, eg AB or CD in fig. 
