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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 Theory and Practice of Surveying: Containing All the Instructions ... - Σελίδα 52
των Robert Gibson - 1814 - 508 σελίδες
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Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ...

Euclides - 1840 - 194 σελίδες
...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 - 378 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,...

Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842 - 320 σελίδες
...bisected in D. QEF 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 ABC D be a circle,...

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

John Playfair - 1842 - 332 σελίδες
...equal parts. , 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 A BCD be a circle,...

Cambridge problems proposed by the moderators to the candidates for ..., Τόμος 2

Cambridge univ, exam. papers - 1843 - 50 σελίδες
...divides them into two equal parts. 2. In a circle the angle in a semi-circle is a right angle ; but the angle in a segment greater than a semi-circle is less than a right angle ; and the angle in a segment less than a semi-circle is greater than a right angle. 3. What sum must...

Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - 1845 - 218 σελίδες
...done. PROPOSITION 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,...

A system of practical mathematics; being no.xvi. of a new series of school-books

Scottish school-book assoc - 1845 - 434 σελίδες
...to AB. PROPOSITION LII. — THEOREM. An angle ADB in a semicircle is a right angle, and an angle DBA in a segment greater than a semicircle is less than a right angle, and an angle AED in a segment less than a semicircle is greater than a right angle. and v DC=CB, the...

Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - 544 σελίδες
...in DQEF 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 rig/it angle; and \he angle in a segment less than a semicircle is greater than a right angle. Let...

The New American Practical Navigator; Being an Epitome of Navigation ...

Nathaniel Bowditch - 1846 - 864 σελίδες
...AB, are ernial to each other ; for they are all measured by the same arc, viz. half the arc 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 arc AC on which it stands must be 1еяч than a...

The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846 - 292 σελίδες
...bisected in DQEF PROP. XXXI. THEOR. In any circle, tJie angle in a semicircle is a right angle, and 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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