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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. "
Elements of Geometry: Containing Books 1. to Vi. and Portions of Books Xi ... - Página 176
por Euclides, James Hamblin Smith - 1879 - 349 páginas
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Mathematical Problems and Examples, Arranged According to Subjects, from the ...

1836 - 335 páginas
...right angles to the same plane. 3. In a circle the angle in a semicircle is a right angle, but 1829 the angle in a segment greater than a semicircle is...less than a semicircle is greater than a right angle. 4. If two triangles have the sides about equal angles reciprocally proportional, they are equal. 5....
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A System of Popular Geometry: Containing in a Few Lessons So Much of the ...

George Darley - 1836 - 128 páginas
...two right angles, (ART. 37,) ADC must be equal to one right angle. This, &c. [See NOTE Z.] ART. 73. The angle in a segment greater than a semicircle is less than a right angle. Let ABC be a segment greater than a semicircle. Then ADC is less than a right angle. DEM. Draw the...
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

1836 - 472 páginas
...circle, the angle in a simicircle is a right angle ; but the angle in a segment greater than a simicircle is less than a right angle; and the angle in a segment less than a simicircle is greater than a right angle. Cor. From this it is manifest, that if one angle of a triangle...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1836 - 311 páginas
...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 hi the segment ADC, which is less than a semicircle, is greatef than a right angle. Join AE, and produce...
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A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - 1837 - 88 páginas
...AD — DB. PROPOSITION XXXI. Theorem. 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. Steps of the Demonstration to Part 1st, That the Z in ^ 0 is a right Z1. Prove that Z EAB = Z ABE ;...
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Elements of Plane Geometry According to Euclid

Andrew Bell - 1837 - 240 páginas
...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 Bf angle. the two angles...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1837 - 318 páginas
...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 centre of the circle falls within it ; if it...
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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838
...Which was to be done.PROP. XXXI. THEOR. In a circle, the angle in a semicircle is a right angle; tut the angle in a segment greater than a semicircle is...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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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Euclid, Robert Simson - 1838 - 416 páginas
...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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Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ...

Euclides - 1840
...Z. ABD is less than a right angle a Prop. 32). But L ABD=Z. AFD (m. Prop. 2i) ; therefore Z. AFD or the angle in a segment greater than a semicircle is...less than a right angle. And the angle in a segment AGD less than a semicircle, is greater than a right angle. For take any point G in the segment, and...
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