We receive, therefore, in no single intercepting plane behind the system, as, for example, a focusing screen, an image of the object point ; on the other hand, in each of two planes lines O ' and O " are separately formed ( in neighboring planes ellipses are formed ), and in a plane between O ' and O " a circle of least confusion.

As seen from locations in the Earth's Northern Hemisphere, celestial objects with declinations greater than 90 ° − ( where = observer's latitude ) appear to circle daily around the celestial pole without dipping below the horizon, and are therefore called circumpolar stars.

The latitude was therefore called the arktikos kuklos, " circle of the bear.

Therefore, like a circle, a tour represents a journey in that it is a round-trip, i. e., the act of leaving and then returning to the original starting point, and therefore, one who takes such a journey can be called a tourist.

The terra Australis is therefore the southernmost of all other lands, directly beneath the antarctic circle ; extending beyond the tropic of Capricorn to the West, it ends almost at the equator itself, and separated by a narrow strait lies on the East opposite to New Guinea, only known so far by a few shores because after one voyage and another that route has been given up and unless sailors are forced and driven by stress of winds it is seldom visited.

) Any diameter of any great circle coincides with a diameter of the sphere, and therefore all great circles have the same circumference as each other, and have the same center as the sphere.

The president's inner circle assumed that it had only a short time in which to act on privatization ; it therefore needed to take steps that would have a large and immediate impact, making the reversal of reform prohibitively costly for their opponents.

Hyde writes that commercial goods can generally become gifts, but when gifts become commodities, the gift "... either stops being a gift or else abolishes the boundary ... Contracts of the heart lie outside the law and the circle of gifts is narrowed, therefore, whenever such contracts are narrowed to legal relationships.

At the Earth's equator this circle vanishes to a single point – the celestial pole itself – which lies on the horizon, and there are therefore effectively no circumpolar stars at all.

Telemachus is therefore widely seen as the most thorough exposition of the brand of reformism in the Beauvilliers-Chevreuse circle, which hoped that following Louis XIV's death, his brand of autocracy could be replaced by a monarchy less centralized and less absolute, and with a greater role for aristocrats such as Beauvilliers and Chevreuse.

He had received their assurances regarding Nitya's health, and had come to believe that " Nitya was essential for life-mission and therefore he would not be allowed to die ," a belief shared by Annie Besant and Krishnamurti's circle.

This shows that the essential range of f, therefore the spectrum of U, lies on the unit circle.

The diameter of the circle of forces, and therefore the maximum horizontal force that the tire can generate, is affected by many things, including the design of the tire and its condition ( age and temperature, for example ), the qualities of the road surface, and the vertical load on the tire.

This means that A and B are equidistant from the origin, i. e. from the center of M. Since A lies on M, so does B, and the circle M is therefore the triangle's circumcircle.

He was already presenting himself as a figure of consequence, annoying the rather bohemian Northern artist's colony in Rome, says Bellori, by appearing with " the pomp of Xeuxis ... his behaviour was that of a nobleman rather than an ordinary person, and he shone in rich garments ; since he was accustomed in the circle of Rubens to noblemen, and being naturally of elevated mind, and anxious to make himself distinguished, he therefore wore — as well as silks — a hat with feathers and brooches, gold chains across his chest, and was accompanied by servants.

The fraction of a circle occupied by the golden angle is therefore:

Point E is diametrically opposite to point V. Angles DVE and EVC are also inscribed angles, but both of these angles have one side which passes through the center of the circle, therefore the theorem from the above Part 1 can be applied to them.

Point E is diametrically opposite to point V. Angles DVE and EVC are also inscribed angles, but both of these angles have one side which passes through the center of the circle, therefore the theorem from the above Part 1 can be applied to them.

The circle group is therefore isomorphic to the special orthogonal group SO ( 2 ).

A Reuleaux triangle of width w consists of three arcs of circles of radius w. Each of these arcs has central angle π / 3, so the perimeter of the Reuleaux triangle of width w is equal to half the perimeter of a circle of radius w and therefore is equal to πw.

The length of the arc is one third of the circumference of the circle, therefore the probability that a random chord is longer than a side of the inscribed triangle is 1 / 3.

The area of the smaller circle is one fourth the area of the larger circle, therefore the probability a random chord is longer than a side of the inscribed triangle is 1 / 4.

Each is also the same size, being half of a great circle on the Earth's surface and therefore measuring 20, 003. 93 km ( 12, 429. 9 miles ).

some larger materials ( Brazil nuts ) get stuck while going down the circle and therefore stay on the top.

In the outer circle are those countries where English has official or historical importance (" special significance ").

In the seventeenth century it was in England that Machiavelli's ideas were most substantially developed and adapted, and that republicanism came once more to life ; and out of seventeenth-century English republicanism there were to emerge in the next century not only a theme of English political and historical reflection-of the writings of the Bolingbroke circle and of Gibbon and of early parliamentary radicals-but a stimulus to the Enlightenment in Scotland, on the Continent, and in America.

In both astrology and historical astronomy, the zodiac ( Greek: ζῳδιακός, zōidiakos ) is a circle of twelve 30 ° divisions of celestial longitude that are centered upon the ecliptic: the apparent path of the Sun across the celestial sphere over the course of the year.

* Volcanic Complex of Madalena-the most recent volcanic complex, with both geological and historical eruptions ; it includes the basaltic stratovolcano of Pico, but also many of the cones, faults and lava fields that circle the 2, 351 meter summit.

The numerous concentric rings that circle the lake are fossil shorelines, and attest to the historical presence of a larger, deeper lake.

This generates a hermeneutical circle since the reader understands the Bible from his historical present and the historical present from the Bible.

It has many historical monuments such as Tower circle, Kaman circle and Elgandal Fort which is 12 km away from the town of Karimnagar.

The crest of Mohun Bagan is shaped as a circle with the words Mohun Bagan Athletic Club around it and within the circle is a boat which has some historical reference to West Bengal.

This " One Mind " is none other than the " sphere of the great circle " ( Tibetan: thig le chen po ' i klong ) of " self-awareness " ( Tibetan: rang rig ) of the Samten Migdron a text like the Kulayaraja Tantra that is also of the Semde class of Dzogchen literature and an important historical source of Dzogchen as it was recovered from the Dunhuang manuscripts.

The present-day use of the talking sticks suggests to many that talking sticks, in the context of the council circle, present evidence of historical and pre-historical use by native tribes to create egalitarian forums.

Next comes the outer circle, which includes countries where English is not the native tongue, but is important for historical reasons and plays a part in the nation's institutions, either as an official language or otherwise.

Finally, the expanding circle encompasses those countries where English plays no historical or governmental role, but where it is nevertheless widely used as a foreign language or lingua franca.

An aristocratic ideal of government emerged around the personalities of Fénelon ( the famous archbishop of Cambrai and tutor of the Duke of Burgundy, grandson of Louis XIV and heir to the throne ), the duc de Beauvilliers ( governor of the duke of Burgundy ), the duc de Chevreuse ( son-in-law of Colbert ), and the duc de Saint-Simon ( reformist in the circle of the duke of Burgundy and author of famous historical memoirs ).

The chords are of considerable historical importance because, along with the sides of the triangle and tetragon ( square ), they enable the generation of a table of half chords ( effectively sine values ) Given the unit circle with sector ABO subtending an arc of, we may write − a relationship expressed in words by Copernicus:

According to historical records followers of Pythagoras underwent a three-year probationary period, directly followed by a five-year period of " silence ", before being admitted to Pythagoras ' inner circle as mathêmatikoi ( learned ).

It is a thesis that has been respected in the historical circle for many years.

Others point to the gradual historical realization that humans are not the centre of all things, that “ A few hundred years ago, with some reluctance, Western people admitted that the planets, Sun and stars did not circle around their abode.

Following historical convention, the circle of confusion is sometimes taken as the lens focal length divided by 1000 ( with the result in same units as the focal length );

It has historical significance because the overprinted circle with slash and date of February 7, 1986 commemorates the end of the Duvailer regime, it is the date that Baby Doc Duvailer freed Haiti for France and the beginning of the provisional governments that lead to the current democratic regime.

His claim seems, from historical sources, to be based on tales told by his Irish mother and family circle during his youth.

It has a rich and varied historical legacy with a Neolithic stone circle, a Holy Well, and the Giant's Stone on Dooish Mountain.