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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. "
Euclid's Elements [book 1-6] with corrections, by J.R. Young - Page 105
by Euclides - 1838
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A Treatise of Practical Surveying, ...

Robert Gibson - 1808 - 482 pages
...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 semicircle is less than a right angle ; thus ADB is measured by half the arc AB, but as the arc AB is less than a semicircle, therefore half...
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The Theory and Practice of Surveying: Containing All the Instructions ...

Robert Gibson - Surveying - 1811 - 580 pages
...are all measured by half the arc they stand on, viz. by hall the arc AB. fig. 26. Cor. 3. Hence an angle in a segment greater than a semicircle is less than a right angle ; thus ADB is measured by half the arc AB, but as the arc AB is less than a semicircle, therefore half...
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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 Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1814 - 560 pages
...bisected in the point D. 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...angle. Let ABCD be a circle, of which the diameter is EC, and centre E; and draw CA, dividing the circle into the segments ABC, ADC, and join BA, AD, DC;...
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The Theory and Practice of Surveying: Containing All the Instructions ...

Robert Gibson - Surveying - 1814 - 558 pages
...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 than a semicircle is less than a right angle ; thus ADB is measured by half the arc AB, but as the arc AB is less thai* a semicircle, therefore...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 588 pages
...AD, DC ; the angle in the semicircle BAC is a right angle; and the angle in the segment ABC, which is greater than a semicircle, is less than a right angle ; and the angle in the segment ADC, which is less than a semicircle, is greater than a right angle. Join AE, and produce...
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A Treatise on Practical Surveying: Which is Demonstrated from Its First ...

Robert Gibson - Surveying - 1818 - 502 pages
...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 greater than a semicircle is less than a right angle ; thus ADB is measured by half the arc AB, but as the arc AB is less than a semicircle, therefore half...
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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...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 the segments ABC,...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Circle-squaring - 1819 - 350 pages
...DC ; the angle in the semicircle BAC is a right angle ; and the angle in the segment ABC, which is greater than a semicircle, is less than a right angle ; and the angle in the segment ADC, which is less than a semicircle, is greater than a right angle. Join AE, and produce...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - Geometry - 1821 - 514 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...diameter is BC, and centre E; and draw CA, dividing thf circle into the segments ABC, ADC, and join BA, AD, DC; the angle in the semicircle BAC is a right...
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