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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. "
A Treatise of Practical Surveying: Which is Demonstrated from Its First ... - Σελίδα 40
των Robert Gibson - 1806 - 452 σελίδες
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 513 σελίδες
...III. 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,...

Library of Useful Knowledge: Geometry, plane, solid, and spherical [by ...

1835
...semi-circum•ference, that is, by a quadrant. Cor. -2. (Eue. iii. 31. second part of.) The angle, which is in a segment greater than a semicircle, is less than a right angle ; and the angle, which is in a segment less than a semicircle, is greater than a • From the Latin...

Mathematical Problems and Examples, Arranged According to Subjects, from the ...

1836 - 335 σελίδες
...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 right angle, and the angle in a segment less than a semicircle is greater than a right angle. 4. If two triangles...

A System of Popular Geometry: Containing in a Few Lessons So Much of the ...

George Darley - 1836 - 128 σελίδες
...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...

The Element of Geometry

John Playfair - 1836 - 114 σελίδες
...was to be done. PROP. XXII. THEOR. In a circle, the angles 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,...

A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - 1837 - 88 σελίδες
...— 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 right angle; and the angle in a segment less than a semicircle is greater than a right angle. Steps of the Demonstration...

Elements of Plane Geometry According to Euclid

Andrew Bell - 1837 - 240 σελίδες
...in D. 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 right angle ; and the angle in a segment less than a semicircle is greater than a right angle. Let ABCD be a circle,...

Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838
...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 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,...

Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ...

Euclides - 1840
...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...

The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841 - 351 σελίδες
...Which was to be done. PROP. XXXI. THEOR. In, a circle, the angle in a semicircle is a rig hi 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. Let ABCD be a circle,...




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