| Euclides - 1874
...is a right angle, an angle in a segment less than a semicircle is greater than a right angle, and an **angle in a segment greater than a semicircle is less than a right angle.** For the angle AOB at the centre may be increased till it becomes two right angles (I. Def. 9), then... | |
| Edward J. Cowling Welch - 1875 - 283 páginas
...stated in the enunciation to be, that " in a circle the angle in a semicircle is a right angle ; but **the angle in a segment greater than a semicircle is...less than a semicircle is greater than a right angle"** is the basis upon which the system, applied in the following pages, is directly founded : and it is... | |
| Edward Atkins - 1876 - 119 páginas
...bisected in DQEF Proposition 31. — Theorem. In a circle, the angle in a semicircle is a right angle; but **the angle in a segment greater than a semicircle is...semicircle is greater than a right angle. Let ABC be a** circle, of which BC is a diameter, and E the centre; and draw CA, dividing the circle into the segments... | |
| Education Department,London - 1876
...in the circumference. SECTION III. 1. In a circle, the angle in a semicircle is a right angle ; but **the angle in a segment greater than a semicircle is...less than a semicircle is greater than a right angle.** The greatest rectangle that can be inscribed in a circle is a square. Divide a circle into two segments,... | |
| Robert Potts - 1876 - 403 páginas
...the angle in a lemicircle i3 a right angle ; but the angle in a segment greater than a semicircle ii **less than a right angle ; and the angle in a segment...than a semicircle is greater than a right angle. Let** ABCD be a circle, of which the diameter isBC, and center E, and let CA be drawn, dividing the circle... | |
| Richard Wormell - 1876
...angle in a semicircle is a right angle ; the angle in a segment less than a semicircle is greater than **a right angle ; and the angle in a segment greater than a semicircle is less than a right angle.** Let А В be a diameter and А С a chord of a circle, ADBE ; then Л А С В in the semicircle AC... | |
| 1876
...Give the algebraical equivalent of this proposition. 6. The angle in a semi-circle is a right angle, **the angle in a segment greater than a semi-circle is less than a right angle, and** in a segment less than a semi-circle it is greater than a right angle. Show how this follows from the... | |
| 1877
...each other. Describe a circle passing through two given points, and touching a given circle. 7. In any **circle, the angle in a semicircle is a right angle,...less than a semicircle is greater than a right angle.** The sides of two acute-angled triangles inscribed in the same circle cannot intersect in fewer than... | |
| Samuel H.. Winter - 1877
...Prove by means of the equation to a circle that the angle in a semicircle is a right angle, and that **the angle in a segment greater than a semicircle is less than a right angle.** 13. Find the equation to the tangent of an ellipse; prove that from a given point two tangents can... | |
| Āryabhaṭa - 1878
...if the centre falls without the triangle, the angle opposite to the side beyond which it is, being **in a segment less than a semicircle, is greater than a right angle** (24. cor.}. Conversely, if the given trwngle le acute-angled, tht centre of the circle falls within... | |
| |