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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 the First Six Books of Euclid with a ... - Strona 80
autor: John Playfair - 1855 - Liczba stron: 318
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Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Tom 5

John Mason Good - 1819
...circumference, ili;ii is, to divide it into two equal parts. Prop. XXXI. Theor. In a circle, theanglein* semicircle is a right angle; but the angle in a segment...less than a semicircle is greater than a right angle. Prop. XXX IL Thcor. If a straight line touche» a circle, and from the point of contact a straight...
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Euclid's Elements of Geometry: The Six First Books. To which are Added ...

Euclid, Rev. John Allen - 1822 - Liczba stron: 494
...(as ABC), in a segment greater than a semicircle, is less than a right angle; and an angle (as ADC), in a segment less than a semicircle, is greater than a right angle. Let E be the centre of the circle, join AE, and produce BA, as to F; and because, in the triangle EAB,...
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Euclid's Elements of Geometry: The Six First Books. To which are Added ...

Euclid, Rev. John Allen - 1822 - Liczba stron: 494
...in D. PROP. XXXI; THEOR. The angle (BAC) in a semicircle, is a right angle; but an angle (as ABC), in a segment greater than a semicircle, is less than a right angle ; and an angle (as ADC), in a segment less them a semicircle, is greater than a right angle. Let E be the...
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Description and Use of a Diagram of Navigation: By which All Problems in ...

George Watson - 1822 - Liczba stron: 4
...a semicircle is greater than a right angle. 197. An angle in a semicircle is a right angle. 199. An angle in a segment greater than a semicircle is less than a right angle. 200. An angle at the circumference of a circle is half the angle at the centre, standing on the same...
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The New Practical Builder and Workman's Companion, Containing a Full Display ...

Peter Nicholson - 1823 - Liczba stron: 596
...two right angles. THEOREM 37. 94. An angle ABD, in a semi-circle, is a right angle ; an angle BAD, in a segment greater than a semi-circle, is less than a right angle ; and an angle, BED, in a segment less than a semi-circle, is greater than a right angle. Produce AB to F,...
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Dictionary of the Mathematical and Physical Sciences, According to the ...

James Mitchell - 1823 - Liczba stron: 575
...semi-circle, or standing upon a semi-circle or diameter. An ancle in a semi-circle, is a right-angle. An angle in a segment, greater than a semi-circle, is less than a right-angle. An angle in a segment, less than a semi-circle, is greater than a right-angle. ANGULAR,...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - 1825 - Liczba stron: 372
...; the angle in the semicircle ВАС 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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Elements of Arithmetic, Algebra, and Geometry

George Lees - 1826
...VIII. THEOREM. . . i In a circle, the angle BAC in a semicirle is a right angle ; but, the angle ABC in a segment greater than a semicircle, is less than a right angle ; and the angle ADC, in, a segment, less than a semicirle, is greater than a right angle. Produce BA to F, takeE, the...
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The New American Practical Navigator: Being an Epitome of Navigation ...

Nathaniel Bowditch - 1826 - Liczba stron: 617
....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 - 1826 - Liczba stron: 617
...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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