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" BAC, inscribed in a segment greater than a semicircle, is an acute angle ; for it is measured by half of the arc BOC, less than a semicircumference. "
Elements of Plane and Solid Geometry - Page 95
by George Albert Wentworth - 1877 - 398 pages
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New Elementary Geometry: With Practical Applications ; a Shorter Course Upon ...

Benjamin Greenleaf - Geometry - 1873 - 202 pages
...semi-circumference, BOD; that is, by the fourth part of the whole circumference. 163. COT.. 3. Every angle, BAC, inscribed in a segment greater than a semicircle, is an acute angle ; for it is measured by the half of the arc BOC, less than a semi-circumference. And every angle, BOC, inscribed in a segment...
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New Elementary Geometry: With Practical Applications : a Shorter Course Upon ...

Benjamin Greenleaf - Geometry - 1874 - 206 pages
...semi-circumference, BOD ; that is, by the fourth part of the whole circumference. 163. Cor. 3. Every angle, BAC, inscribed in a segment greater than a semicircle, is an acute angle ; for it is measured by the half of the arc BOC, less than a semi-circumference. And every angle, BOG, inscribed in a. segment...
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Euclid simplified. Compiled from the most important French works, approved ...

John Reynell Morell - 1875 - 220 pages
...for it has as measure half the semicircumference, or a quadrant. COROLLARY III. — Every angle BAC inscribed in a segment greater than a semi-circle is an acute angle, for it has for measure half the are BOC, less than a semi-circumference ; and every angle BOC inscribed in...
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Elements of Geometry with Exercises for Students: An an Introduction to ...

Aaron Schuyler - Geometry - 1876 - 384 pages
...one-half of a semi-circumference ; that is, by a quadrant which is the measure of a right angle. 3. Any angle inscribed in a segment greater than a semicircle is an acute angle. (?) 4. An angle inscribed in a segment tea than a semicircle is an dbtuse angle. (?) ~>. Two inscribed...
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Elements of Geometry and the First Principles of Modern Geometry

Wm. H. H. Phillips - Geometry - 1878 - 236 pages
...is a right angle ; an angle inscribed in a segment less than a semicircle is an obtuse angle ; and an angle inscribed in a segment greater than a semicircle is an acute angle. COR. 4. In an inscribed quadrilat- j eral, ABCD, two opposite angles, A and C, are together equal to...
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Elements of Geometry

George Albert Wentworth - 1881 - 266 pages
...I.) .-.Z PBF- РПA is measured by (arc PF— arc PA). .-. ZABF is measured by arc A F. QED 204. COROLLARY 1. An angle inscribed in a semicircle...angle inscribed in a segment less than a semicircle is an obtuse angle, for it is measured by an arc greater than one-half a semi-circumference ; ie by...
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Elements of Geometry, After Legendre, with a Selection of Geometrical ...

Charles Scott Venable - 1881 - 380 pages
...by a reference to the Theorem 33, Exercises on Book I. COR. 3. Every angle, BAC (See Fig., Cor. 1), inscribed in a segment greater than a semi-circle is an acute angle, for it is measured by the half of the arc BOC, less than a semi-circumference. And every angle, BOC, inscribed in a segment...
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Elements of Geometry

George Albert Wentworth - Geometry, Modern - 1879 - 262 pages
...is measured by\pne-half a semi-circumference, or by 90. Ljf) 205. COR. 2. An angle inscribe?R*rra segment greater than a semicircle is an acute angle...angle inscribed in a segment less than a semicircle is an obtuse angle, for it is measured by an arc greater than one-half a semi-circumference ; ie by...
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A Text-book of Geometry

George Albert Wentworth - Geometry - 1888 - 264 pages
...inscribed in a semicircle is a right angle. For it is measured by one-half a semi-circumference. 265. COR. 2. An angle inscribed in a segment greater than...acute angle. For it is measured by an arc less than half a semi-circumference ; as, Z CAD. Fig. 2. 266. COR. 3. An angle inscribed in a segment less than...
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The Elements of Plane and Solid Geometry: With Numerous Exercises

Edward Albert Bowser - Geometry - 1890 - 420 pages
...measured by one-half a semi-circumference, or by a quad- A rant. (237) 241. COR. 3. Every angle BAC, inscribed in a segment greater than a semicircle, is an acute angle; for it is measured by one-half the arc BDC, which is less than a quadrant. Every angle BDC, inscribed in a segment less than...
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