| Euclid - Euclid's Elements - 1789 - 272 pages
...three equal parts, by any known method, which is purely geometrical. PROP. _J PROP. XXIV. THEOREM. **The angle formed by a tangent to a circle and a chord drawn from the point of** contacTr, is equal to the angle in the alterr nate fegment. Let EC be a tangent to the circle AFDE,... | |
| John Bonnycastle - Euclid's Elements - 1803 - 279 pages
...divided into three equal parts, by any known method, which is purely geometrical. PROP. XXIV. THEOREM. **The angle formed by a tangent to a circle and a chord...of contact, is equal to the angle in the alternate** fegment. Let BC be a tangent to the circle AFDE, and AB a chord drawn from the point of contaft ; then... | |
| Charles Hutton - Mathematics - 1811
...measure of a right angle (corol. 4, th. 6 ; or corol. 2, th. 48). Therefore the angle D is a right angle. **THEOREM THEOREM LIII. The Angle formed by a Tangent...Circle, and a Chord drawn from the Point of Contact,** ia Equal to the Angle . in the Alternate Segment. IF AB be a tangent, and AC a chord, and D any angle... | |
| Encyclopaedia Perthensis - 1816
...tothe three anpk-s BDC, DBC and DCB, that is to two *-ipht angles. (Th-. ta ) THEOR. XXIV. fa. 50. **The angle formed by a tangent to a circle, and a chord drawn** to the point of contatt, is equal to the angle in the alternate fegment of the circle Let AB be a tangent,... | |
| Charles Hutton - Mathematics - 1822 - 618 pages
...th. 6 ; or eorol. 2, th. 48), ;iogle ii it a right angle. B Therefore the THEOREM 312 THEOREM Lin. **THE Angle formed by a Tangent to a Circle, and a Chord...chord, and D any angle in the alternate segment ADC** ; then will the angle D be equal to the angle BAG made by the tangent and chord, of the arc AEC. For... | |
| George Lees - 1826
...therefore, AD touches the circlee : and because the angle which the chord makes with the tangent at **the point of contact, is equal to the angle in the alternate segment** of the circlef ; therefore, the angle BAD is equal to the angle in the alternate segment AHB ; but... | |
| John Radford Young - Euclid's Elements - 1827 - 208 pages
...include the same portion of the circumference. PROPOSITION XV. THEOREM. a The angle formed by a tangent, **and a chord drawn from the point of contact, is equal to** an angle in the alternate segment of the circle ; that is, to an inscribed angle subtended by the arc... | |
| William Grier - Mechanical engineering - 1832 - 300 pages
...or ADC be a semicircle ; then any angle D in that semicircle, is a right angle. — (Fig. 45.) 51. **If AB be a tangent, and AC a chord, and D any angle in the alternate segment ADC** ; then will the angle D be equal to the angle BAC made by the tangent and chord of the arc AEC —... | |
| William Grier - Mechanical engineering - 1836 - 344 pages
...angle C. 50. If ABC or ADC be a semicircle ; then any angle D in that semicircle, is a right angle. 51. **If AB be a tangent, and AC a chord, and D any angle in the alternate segment ADC** ; then will the angle D be equal to the angle BAC made by the tangent and chord of the arc AEC. 52.... | |
| Andrew Bell - Euclid's Elements - 1837 - 240 pages
...adjacent angles are equal, they are right angles. PROPOSITION XXXII. THKOREM. The angles contained **by a tangent to a circle, and a chord drawn from the point of contact,** are equal to the angles in the alternate segments of the circleLet EF be a tangent to the circle ABCD,... | |
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