| William Grier - 1842 - 308 sider
...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. 53. If the side AB, of the... | |
| 1845
...contact. PLANE GEOMETRY. PROPOSITION LV — THEOREM. The angle ABD, formed by a tangent AB, and a chord DB **drawn from the point of contact, is equal to the angle in the alternate segment** BED, and is measured by half the intercepted arc BD. For (figure last Prop.), let DE be || to AB, then... | |
| George Roberts Perkins - 1847 - 308 sider
...half the entire circumference, which is the measure of two right angles. PROPOSITION IX. THEOEEM. The **angle formed by a tangent to a circle, and a chord...angle in the alternate segment. If AB be a tangent,** AC a chord, and D any angle in the alternate segment ADC ; then will the angle D be equal to the angle... | |
| George Roberts Perkins - 1850 - 320 sider
...entire circumference, which is the measure of two right-angles. PROPOSITION VIII. If AB be a tangent, **AC a chord, and D any angle in the alternate segment ADC; then will the angle** D be equal to the angle B AC made by the tangent and the chord of the arc AFC. For the angle D at the... | |
| Euclides - 1860
...adjacent angles are equal, they are right angles. PROPOSITION XXXII. THEOREM. 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 circle. Given EF a tangent to the circle ABCD,... | |
| Charles Hutton - 1860 - 895 sider
...(cor. 4, th, 6; or cor. 2, th. 48). Therefore iliu angle 1) is a right angle. 384 THEOREM LUI. The **angle formed by a tangent to a circle, and a chord drawn** fftm the pat of contact, is equal to the angle in the alternate segment. If AB be a ¿angent, and AC... | |
| William Grier - 1861 - 305 sider
...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 A.DC ; then will the angle** D be equal to the angle BAG made by the tangent and chord of the arc AEG. 52. Let ABCD be any quadrilateral... | |
| w.j.golbourn - 1866
...possess ? HIGHER MATHEMATICS. 1. Inscribe a circle in a given sector of a circle. 2. 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 circle. 3. To describe a square that shall... | |
| Gerardus Beekman Docharty - 1867 - 283 sider
...angle (Cor. 4, th. 6 ; or Cor. 2, th. 8). Therefore the angle D is a right angle. THEOREM XIII. The **angle formed by a tangent to a circle, and a chord...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. For the angle D, at the circumference,... | |
| The Owens College - 1872
...the outer circle. 8. Define a tangent. Show that the angle contained between a tangent and the chord **from the point of contact is equal to the angle in the alternate segment** of the circle. 9. Divide a given straight line into two parts, so that the squai'cs on the whole line... | |
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