" Khayyam then considered the three cases right, obtuse, and acute that the summit angles of a Saccheri quadrilateral can take and after proving a number of theorems about them, he correctly refuted the obtuse and acute cases based on his postulate and hence derived the classic postulate of Euclid which he didn't realize was equivalent to his own postulate.

The other two angles of a Saccheri quadrilateral are called the summit angles and they have equal measure.

Khayyám then considered the three cases ( right, obtuse, and acute ) that the summit angles of a Saccheri quadrilateral can take and after proving a number of theorems about them, he ( correctly ) refuted the obtuse and acute cases based on his postulate and hence derived the classic postulate of Euclid.

The stem rises to the summit of the tree in one tapering unbroken shaft, the branches come out at right angles to the trunk and either extend horizontally or droop a little, making a long-narrow, cone-like head.

Mount Diablo appears from many angles to be a double pyramid and includes many subsidiary peaks, the largest and closest of which is the other half of the double pyramid, North Peak, nearly as high in elevation at and about one mile northeast of the main summit.

The summit sits on a short rocky spine, set at right angles to the ridge.

Being the last outpost of the hills before the broad Aire valley, and with a sharp summit from many angles, it is prominent and easily recognisable from much of the area to the south.

Giordano Vitale, in his book Euclide restituo ( 1680, 1686 ), used the Saccheri quadrilateral to prove that if three points are equidistant on the base AB and the summit CD, then AB and CD are everywhere equidistant.

It wasn't until 600 years later that Giordano Vitale made an advance on Khayyám in his book Euclide restituo ( 1680, 1686 ), when he used the quadrilateral to prove that if three points are equidistant on the base AB and the summit CD, then AB and CD are everywhere equidistant.

I do not mean to imply that Christians have adopted the liberal assumption, so prevalent in Hinduism, that all religions are merely different paths to the same summit.

Many police officers or responsible authorities present in Genoa during the G8 summit, are currently under investigation by the Italian judges, and some of them resigned.

In 2005, the Tohono O ' odham Nation brought suit against the National Science Foundation to stop further construction of gamma ray detectors in the Gardens of the Sacred Tohono O ' odham Spirit I ' itoi, which are just below the summit.

The composite cone of Nevis volcano has two overlapping summit craters that are partially filled by a lava dome, created in recent, pre-Columbian time.

Its flanks are shallower and extend out further from the summit in the northwestern direction than they do to the southeast.

These features and the fact that there are many summit passes — some at altitudes up to 2, 256 meters — have made the Carpathians less of a barrier to movement than other European ranges.

* May 25 – Joe Brown and George Band are the first to attain the summit of Kanchenjunga in the Himalayas, as part of a British team led by Charles Evans.

Even in summer, conditions can be atrocious ; thick fog, strong winds, driving rain and freezing summit temperatures are not unusual.

Both his poetry and his studies on the growth of the soul are considered the summit of mystical Spanish literature and one of the peaks of all Spanish literature.

They occupied the summit of a low hill, directly abutting on the sea, and bounded on the west by the marshy valley through which flows the river Madiuni, the ancient Selinus ; on the east by a smaller valley or depression, also traversed by a small marshy stream, which separates it from a hill of similar character, where the remains of the principal temples are still visible.

It first opened on 31 July 1902 and runs on a daily basis from late March to late October taking visitors to the summit of The Great Orme, climbing a mile of track to the summit complex at a height of 679 ft ( 207 ) m. There are panoramic views of the Welsh mountains and as far as the Isle of Man, Blackpool and the Lake District.

The Pennine, Bernese and Bernina Range are the highest ranges of the country, they contain respectively 38, 9 and 1 summit over 4000 metres.

The Catholic Church sees the Mass or Eucharist as " the source and summit of the Christian life ", to which the other sacraments are oriented.

In 2005, the Tohono O ' odham Nation brought suit against the National Science Foundation to stop further construction of gamma ray detectors in the Gardens of the Sacred Tohono O ' odham Spirit I ' itoi, which are just below the summit.

The walk up the Tor to the distinctive tower at the summit ( the partially restored remains of an old church ) is rewarded by vistas of the mid-Somerset area, including the Levels which are drained marshland.

There are two principal routes to the summit.

The two highest peaks in the Karoo are Compassberg and Seweweekspoortpiek, with summit elevations of and respectively.

On its summit are the hanging gardens, a wonder celebrated by the fables of the Greeks.

The summit and the northern flank are mainly composed of metamorphic slate, in which talc predominates, but is sometimes replaced by felspar, so that the rock sometimes approaches the condition of gneiss and sometimes that of mica slate.

There are seven named glaciers on Mount Shasta, with the four largest ( Whitney, Bolam, Hotlum, and Wintun ) radiating down from high on the main summit cone to below primarily on the north and east sides.

Three of these are low and more or less submerged, but the middle one is higher than the European rock, sloping up to an acute point and roundish right up to its summit ; it is splashed by the waves but not submerged and is everywhere precipitous and straight.

It is also said that if one runs around the great pine tree at the summit seven times, then the Fairies will appear.

He proposed a personal summit with Roosevelt – in the United States if necessary – to come to some understanding.

Prime Minister Vladimir Putin allegedly declared at a NATO-Russia summit in 2008 that if Ukraine would join NATO his country can contend to annex the Ukrainian East and Crimea.

It was during this battle that Lantern Hill obtained the nickname “ Tar Barrel Hill ,” because, in anticipation of an attack on Stonington, soldiers had moved pitch in barrels to its summit to set them alight to serve as an alarm if British forces appeared in The Sound.

Starting for the summit at about 2am from the Diesel Hut should allow just enough time to get back down to the chairlift if movement is efficient.

Others have countered that even if Tabor was fortified by Antiochus this does not rule out a transfiguration at the summit.

At the July 2007 African Union summit in Accra, Ghana, Wade supported quick formation of the proposed United States of Africa and said: " If we fail to unite, we will become weak, and if we live isolated in countries that are divided, we face the risk of collapsing in the face of stronger and united economies.

Unfortunately if the ascent was this time successful, Hugi had to wait on the saddle while the other reached the summit.

An each-uisge was thought to live in a bottomless well near the summit of Macphee ’ s Hill, and faery sidhes and their associated music were taken for granted, if generally avoided.

They were expected to walk up to the summit area in all weather and faced losing pay if unable to reach the top.

The permit from the Nepalese Ministry of Tourism stipulated that the summit could only be reached if an equal number of climbers from both nations were on the summit team.

Labels should be placed along a slightly curved line " pointing " to the summit or nadir, from several directions if possible, making the visual identification of the summit or nadir easy.

The Eskdale spur may provide a slightly easier option up to the summit of Bogong if you have a 4wd, although if you walk up from Mountain Creek, it is just a longer way to do the same ascent.

The UIAA definition is that a summit is independent if it has a prominence of or more ; it is a mountain if it has a prominence of at least.

The walk from Gatesgarth to the summit of Pillar and back involves over 1, 200 metres ( 4, 000 feet ) of ascent, more if the High Level Route is taken.

And this hail lies there, so that if it were not for the absorption of the rising and falling clouds, which does not happen more than twice in an age, an enormous mass of ice would be piled up there by the layers of hail, and in the middle of July I found it very considerable ; and I saw the sky above me quite dark, and the sun as it fell on the mountain was far brighter here than in the plains below, because a smaller extent of atmosphere lay between the summit of the mountain and the sun.