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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 of geometry, books i. ii. iii. iv - Seite 99
von Euclides - 1862
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A Treatise of Practical Surveying: Which is Demonstrated from Its First ...

Robert Gibson - 1806 - 452 Seiten
...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 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 Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1806 - 518 Seiten
...AD, DC; the angle in the semicircle BAC la a right angle ; and the angle in the segment ABO, 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 an^le. Join AE, and produce...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1806 - 311 Seiten
...AD, DC ; the angle in the semicircle BAG is a right angle ; 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 semiciriite is greater than a right angle. Join £iE, and produce...
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A Treatise of Practical Surveying, ...

Robert Gibson - 1808 - 440 Seiten
...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 - 1811 - 508 Seiten
...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) cyclopædia, by J.M. Good, O. Gregory ..., Band 5

John Mason Good - 1813
...Prob. To bisect a given circumference, that is, to divide it into two equal parts. Prop. XXXI. Theor. In a circle, the angle in a semicircle is a right...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 - 1814 - 508 Seiten
...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 - 528 Seiten
...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 - 1818 - 478 Seiten
...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 - 317 Seiten
...arch DB : and therefore the given arch ADB is bisected in D. Which was to be done. PROP. XXXI. THEOR. In a circle, the angle in a semicircle is a right...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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