 | Euclides - 1660 - 368 pages
...femicircle B Al. which was to be Dem. Cut-oil. Hence, A "ght line drawn from the extremity of ,. ,„ th« diameter of a circle, and at right angles, is a tangent to the faid circle. From this propofiticm are gathered many paradox and; wotiderfull confedlaries , which you may •iiect with in... | |
 | Euclid, Isaac Barrow - Geometry - 1714 - 536 pages
...angle of a femicircle BAL Winch-vat to be dem. Coroll. Hence, A right line drawn from the extra? aiity of the diameter of a circle, and at right angles, is a tangent to the faid circle. From this Proportion are gathered many P*. radox and wonderful Gonfedtaries, which you may meet -with in the... | |
 | John Keill - Logarithms - 1723 - 444 pages
...is a Right Angle. Wherefore EBA is alfo a Right Angle, and EB is a Line drawn from the Center; but a Right Line drawn from the Extremity of the Diameter of a Circle at Right Angles:): to it, touches the Circle. Wherefore AB touches the Circle; which was to be done.... | |
 | Euclid, John Keill - Geometry - 1733 - 444 pages
...EA; fmce the Angles at G, H, K, L, M, are Right Angles: For if it does not touch them, but cuts them, a Right Line drawn from the Extremity of the Diameter of a Circle at Right Angles to the Diameter, will fall within the Circle ; which is f abfurd. Therefore a Circle... | |
 | Euclid - Euclid's Elements - 1751 - 420 pages
...acute-angle BAL is lefs than the angle of a femicirde BAI. Which was to, be dem. ^ Hence, a right-line drawn from the extremity of the diameter of a circle, and at right-angles, is a tangent to the faid circle. Prom this propoiition are gathered many paradoxes, and... | |
 | Rev. John Allen - Astronomy - 1822 - 508 pages
...right line can be drawn between AE and the circle, so as not to cut it. Cor.—Hence it appears, that a right line, drawn from the extremity of the diameter of a circle, at right angles to it, touches the circle (Def. 1. 3), and that it touches it only in one point. PROP.... | |
 | Euclides - 1826 - 226 pages
...But DBF is a right angle; wherefore also DBF is a right angle, and the diameter FB is drawn. But the right line drawn from the extremity of the diameter of a circle at right angles touches the circle ; b wherefore DB must touch the circle ABC. If, therefore, any point,... | |
 | Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 542 pages
...the angle HAB diminishes the perpendicular CI will also diminish. PROPOSITION XVI. THEOREM. (846) The right line drawn from the extremity of the diameter of a circle perpendicular to it falls without the circle. And if any right line be drawn from a point within that... | |
 | Euclides - 1833 - 304 pages
...on which the lesser perpendicular falls (by the foregoing case) ; .-., &c. &c. PROP. 16. THEOR. The right line, drawn from the extremity of the diameter of a circle perpendicular to it, falls without the circle. And if any right line be drawn from any point within... | |
 | Euclides - 1840 - 82 pages
...and, conversely, the greater line is nearer to the centre than the less. PROP. XVI. THEOR. A straight line drawn from the extremity of the diameter of a circle, and perpendicular to it, is a tangent to the circle: and through the same point there cannot be drawn another... | |
| |
Hence, a right line drawn from the extremity of the .diameter of a circle, and at right -angles, is a tangent to the faid circle. From this propofition are gathered many paradoxes, and wonderful confecbtries, which you may meet with in the interpreters. 