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" 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. "
The Theory and Practice of Surveying: Containing All the Instructions ... - Page 38
by Robert Gibson - 1811 - 508 pages
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A Compleat Treatise of Practical Navigation Demonstrated from It's First ...

Archibald Patoun - Navigation - 1734 - 414 pages
...Corollary they _ are all meafured by the fame Arc, viz. half the Arc AB which each of them fubtends. Cor. 3. Hence an Angle in a Segment greater than a Semicircle is lefs than a right Angle ; thus if ADB be a Segment, greater than a Semicircle, (fee the laft Figure)...
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A Treatise of Practical Surveying: Which is Demonstrated from Its First ...

Robert Gibson - Surveying - 1795 - 319 pages
...they are all meafured by half the Arc they ftand on, viz. by half the Arc AB. Fig. 26. Cor. Plate I. Cor. 3. Hence an Angle in a Segment greater than a Semicircle is lefs than a right Angle ; thus ADB is meafured by half the Arc AB, but as the Arc AB is lefs than a...
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A Treatise of Practical Surveying: Which is Demonstrated from Its First ...

Robert Gibson - Surveying - 1806 - 452 pages
...for they are all measured by half the arc they stand on. viz. bv half the arc AB. ftg. 26. . Plate I. Cor. 3. Hence an angle in a segment greater than a...the arc AB is less than a semicircle, therefore half the arc AB, or the angle ADB is less than half a semicircle, and consequently less than a right angle,...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1806 - 518 pages
...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 right angle ; and the angle in a segment less than a semicircle is greater than a right angle. Let ABCD be a circle,...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1806 - 311 pages
...to be done. Book in PROP. XXXI. THEOR. IN 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 Jess than a semicircle is greater than a right angle. Let ABCD be a circle,...
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A Treatise of Practical Surveying, ...

Robert Gibson - 1808 - 440 pages
...for they are all measured by half the arc they stand on* viz. by half the arc AB. fig. 26. Plate I. Cor. 3. Hence an angle in a segment greater than a...the arc AB is less than a semicircle, therefore half the arc AB, or the angle ADB is less than half a semicircle, and consequently less than a right angle,...
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Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1813
...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 right angle; and the angle in a segment less than a semicircle is greater than a right angle. Prop. XXXII. Theor....
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The Theory and Practice of Surveying: Containing All the Instructions ...

Robert Gibson - Electronic books - 1814 - 508 pages
...to each other, for they are all measured by balf the arc they stand on, viz. by half the arc AB. l Fig. 26. Cor. 3. Hence an angle in a segment greater...measured by half the arc AB, but as the arc AB is less thai* a semicircle, therefore half the arc AB, от the angle ADBis less than half a semicircle, and...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 528 pages
...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 right angle ; and the angle in a segment less than a semicircle is greater than a right angle. Let ABCD be a circle,...
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A Treatise on Practical Surveying: Which is Demonstrated from Its First ...

Robert Gibson - Surveying - 1818 - 478 pages
...AB, are equal to each other, for they are all measured by half the arc they stand on, viz. by half the arc AB. fig. 26. Cor. 3. Hence an angle in a segment...the arc AB is less than a semicircle, therefore half the arc AB. or the angle ADB is less than half a semicircle, and consequently less than a right angle....
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