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" ... a circle. The angle in a semicircle is a right angle: the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle. "
A Collection of Problems and Examples Adapted to the "Elementary Course of ... - Page 144
by Harvey Goodwin - 1851 - 173 pages
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1806 - 546 pages
...was to be clone. C PROP. XXXI. THEOR. 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. Let ABCD be a circle, of which the diameter is BC, and 'centre E; and draw CA dividing the circle into...
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A Treatise of Practical Surveying: Which is Demonstrated from Its First ...

Robert Gibson - Surveying - 1806 - 486 pages
...angle ADB is less than half a semicircle, and consequently less than a right angle, fig. 26. Cor. 4. An angle in a segment less than a semicircle, is greater than a right angle, for since the arc AEC is greater than a semicircle, its half, which is the measure of the angle ABC,...
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A Treatise of Practical Surveying, ...

Robert Gibson - 1808 - 482 pages
...angle ADB is less than half a semicircle, and consequently less than a right angle, fig. 26. Cor. 4. An angle in a segment less than a semicircle, is greater than a right angle, for since the arc AEC is greater than a semicircle, 'its half, which is the measure of the angle ABC,...
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The Theory and Practice of Surveying: Containing All the Instructions ...

Robert Gibson - Surveying - 1811 - 580 pages
...angle ADB is less than half a semicircle, and consequently less than a right angle. Fig. sr. Cor. 4 An angle in a segment less than a semicircle, is greater than a right angle, for since the arc AEC is greater than a semicircle, its half, which is the measure of the angle ABC,...
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Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1813 - 714 pages
...into two equal parts. Prop. XXXI. Theor. 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. Prop. XXXII. Theor. If a straight line touches я circle, an J from the point of contact a straight...
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The Theory and Practice of Surveying: Containing All the Instructions ...

Robert Gibson - Surveying - 1814 - 558 pages
...angle ADBis less than half a semicircle, and consequently less than a right angle. Fig. У!. Cor. 4. An angle in a segment less than a semicircle, is greater than a right angle, for since the arc AEC is greater than a semicircle, its half, which is the measure of the angle ABC,...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 588 pages
...Which was to be done. PROP. XXXI. THEOR. 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. Let ABCD be a circle, of which the diameter is BC, and centre E; and draw CA, dividing the circle into...
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A Treatise on Practical Surveying: Which is Demonstrated from Its First ...

Robert Gibson - Surveying - 1818 - 502 pages
...angle ADB is less than half a semicircle, and consequently less than a right angle. fig. 26. Cor. 4. An angle in a segment less than a semicircle, is greater than a right angle, for since the arc AEC is greater than a semicircle, its half which is the measure of the angle ABC,...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 354 pages
...Which was to be done. PROP. XXXI. THEOR. 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. Let ABCD be a cir.de, of which the diameter is BC, and centre E ; draw CA dividing the circle into...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Circle-squaring - 1819 - 350 pages
...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 Wherefore, if the given triangle be acute angled, the ceatre of Ihe circle falls within it : if it...
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