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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. "
The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... - Page 79
by Euclides - 1816 - 528 pages
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The New American Practical Navigator: Being an Epitome of Navigation ...

Nathaniel Bowditch - Nautical astronomy - 1826 - 617 pages
....N equal to each other ; for they are all measured by the same arch, viz. half the arch AB. XLII. An angle in a segment greater than a semicircle is less than a right angle. Thus if ABC be a segment greater than a semicircle, the arch AC on which it stands must be less than...
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The New American Practical Navigator: Being an Epitome of Navigation ...

Nathaniel Bowditch - Nautical astronomy - 1826 - 617 pages
...arch DKF, that is, by half a semicircle or by rt quadrant ; therefore the angle DEF is a right one. An angle in a segment less than a semicircle is greater than a right angle. ' J* Thus if GHI be a segment less than a semicircle, the arch GLI on which it stands must be greater...
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Euclid's Elements of geometry, transl. To which are added, algebraic ...

Euclides - 1826
...COROLLARY. Hence it is manifest, when the centre of the circle falls within the triangle, the angle BAC, in a segment greater than a semicircle, is less than a right angle; but when the centre falls on the right line в с, the angle BAC, in a semircircle, is a right angle;...
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Elements of Geometry, Containing the First Six Books of Euclid

Euclid - 1826 - 180 pages
...COROLLARY. Hence it is manifest, when the centre of the circle falls within the triangle, the angle BAC, in a segment greater than a semicircle, is less than a right angle ; but when the centre falls on the right line вс, the angle BAC, in a semrrcircle, is a right angle;...
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - Geometry - 1830 - 272 pages
...semi-circumference, 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 and let the diameters A Qj, QQ, be...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1833 - 333 pages
...centre (Cor. 1.3.); wherefore the arch AD is equal to the arch DB ; and therefore the given arch ADB is bisected in D. Which was to be done. PROP. XXXI....ABCD be a circle, of which the diameter is BC, and fcentre E ; draw CA dividing the circle into the segments ABC, ADC, and join BA, AD, DC ; the angle...
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The Elements of geometry [Euclid book 1-3] in general terms, with notes &c ...

Euclides - 1833
...angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is an acute angle ; and the angle in a segment less than a semicircle is obtuse. PART 1. The angle in a semicircle is a right angle. Draw a diameter connecting the extremities...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1834
...Ihe angle in a semicircle is a right angle ; but the angle in a segment greater than a semicircle, ii less than a right angle ; and the angle in a segment less litan a semicircle, is greater than a right angle. Let ABCD be a circle, of which the diameter is BC,...
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Library of Useful Knowledge: Geometry, plane, solid, and spherical [by ...

Mathematics - 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 word цгайчии,...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 513 pages
...AD, DC; the angle in the semicircle BAG 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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