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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, containing the first six books, with a selection of ... - Σελίδα 112
των Euclides - 1874
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Papers for the schoolmaster, Τόμοι 1-6

582 σελίδες
...omitted it ? 2. A segment of a circle being given, describe the circle of which it is the segment. 3. In a circle, the angle in a semicircle is a right...than a semicircle is less than a right angle ; and t'ne right angle in a segment less than a semicircle is greater than a right angle. State the converse...

A Manual of Surveying for India, Detailing the Mode of Operations on the ...

Sir Henry Edward Landor Thuillier - 1851 - 826 σελίδες
...each other or they are all measured by hp1P the arc they stand on, viz. by half the arc AB. Cor. 3. An angle in a segment greater than a semicircle is less than a right angle; thus ADB is measured by half the arc AB, but as the arc AB is less than a semi-circle, the arc AB or...

Five Years in an English University, Τόμος 2

Charles Astor Bristed - 1852 - 470 σελίδες
...angle at the circumference, upon the same base, that is, upon the same part of the circumference. 5. In a circle, the angle in a semicircle is a right...less than a semicircle is greater than a right angle. 6. If a straight line be drawn parallel to one of the sides of a triangle, it will cut the other sides,...

Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - 1853 - 336 σελίδες
...sixteen, &c. equal parts. N PROP. XXXI. THEOR. In a circle, the angle in a semicircle is a right angle i but the angle in a segment greater than a semicircle...than a semicircle is greater than a right angle. Let ABCD be a circle, of which the diameter is BC, and centre E ; draw CA dividing the circle into the...

The first six books of the Elements of Euclid, with numerous exercises

Euclides - 1853 - 176 σελίδες
...ad, 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...

The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - 1853 - 400 σελίδες
...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...

The synoptical Euclid; being the first four books of Euclid's Elements of ...

Euclides - 1853 - 146 σελίδες
...AD, 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. 3omAE, and produce...

The Elements of Euclid, books i-vi; xi. 1-21; xii. 1,2; ed. by H.J ..., Βιβλίο 1

Euclides - 1853 - 334 σελίδες
...right angle. Hence the angle in the semicircle BAC is a right angle ; the angle in the segment ABC greater than a semicircle is less than a right angle ; and the angle ADC in the segment less than a semicircle is greater than a right angle. Which was to be proved. COB....

Elements of geometry and mensuration

Thomas Lund - 1854 - 520 σελίδες
...them must be a right angle. 54. PROP. VI. The 'angle in a segment' equal to a semi-circle is a right angle ; in a segment greater than a semi-circle is less than a right angle ; and in a segment less than a semi-circle is greater than a right angle. Let ABCD be a circle of which AB...

Orr's Circle of the Sciences: Organic nature, vols. 1-3 (1854-1856)

William Somerville Orr - 1854 - 534 σελίδες
...THEOREM. The angle (ВАС) in a semicircle (BADC) is a right angle : the angle in a segment (ABGC) greater than a semicircle, is less than a right angle : and the angle (D) in a segment (ADC) less than a semicircle, is greater than a right angle. From the centre, E, draw...




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