") states, " Haue been pleased to giue lysence vnto o < sup > r </ sup > said Subjects to proceed in the said voiadgs, & for the better inabling them to establish a trade into & from the said East Indies Haue by o < sup > r </ sup > tres Pattents vnder o < sup > r </ sup > great seale of England beareing date at Westminster the last daie of december last past incorporated o < sup > r </ sup > said Subjecte by the name of the Gou < sup > r </ sup > no < sup > r </ sup > & Companie of the me < sup > r </ sup > chaunts of London trading into the East Indies, & in the same tres Pattents haue geven them the sole trade of theast Indies for the terme of XV < sup > teen </ sup > yeares ..."</ ref > making it the oldest among several similarly formed European East India Companies.

On the other hand, it is also clear that Sebastian had engaged in some genuine exploration, since sometime before 3 April 1505 he was awarded by King Henry VII for services ' doon vnto vs in and aboute the fyndynge of the new found lands '.

A substantially expanded version of A World of Words was published in 1611 as Queen Anna's New World of Words, or Dictionarie of the Italian and English tongues, Collected, and newly much augmented by Iohn Florio, Reader of the Italian vnto the Soueraigne Maiestie of Anna, Crowned Queene of England, Scotland, France and Ireland, & c. And one of the Gentlemen of hir Royall Priuie Chamber.

The shapes of the first five atomic orbitals: 1s, 2s, 2p < sub > x </ sub >, 2p < sub > y </ sub >, and 2p < sub > z </ sub >.

This is not always the case: the trivial equation x = x specifies the entire plane, and the equation x < sup > 2 </ sup > + y < sup > 2 </ sup > = 0 specifies only the single point ( 0, 0 ).

The equation x < sup > 2 </ sup > + y < sup > 2 </ sup > = r < sup > 2 </ sup > is the equation for any circle with a radius of r.

For example, using Cartesian coordinates on the plane, the distance between two points ( x < sub > 1 </ sub >, y < sub > 1 </ sub >) and ( x < sub > 2 </ sub >, y < sub > 2 </ sub >) is defined by the formula

x < sup > 2 </ sup > + y < sup > 2 </ sup >-1 = 0

Given any element x of X, there is a function f < sup > x </ sup >, or f ( x ,·), from Y to Z, given by f < sup > x </ sup >( y ) := f ( x, y ).

Similarly, given any element y of Y, there is a function f < sub > y </ sub >, or f (·, y ), from X to Z, given by f < sub > y </ sub >( x ) := f ( x, y ).

To see the elongated shape of ψ ( x, y, z )< sup > 2 </ sup > functions that show probability density more directly, see the graphs of d-orbitals below.

This example is injective in each input separately, because the functions f < sup > x </ sup > and f < sub > y </ sub > are always injective.

A man named Blaine Smythe, with `` y '' and `` e '' but pronounced without them, had been fired at Payne's insistence.

: When comparing the above illustration to the below text, please note that the above x: y aspect ratio values are shown as vertical orientation rectangles to better demonstrate visual differences, whereas the aspect ratio values of the text below are written as rotated horizontal orientation rectangles ( e. g. compare 3: 4 vertical orientation illustration to 4: 3 horizontal orientation text ).

respectively, where e < sub > x </ sub >, e < sub > y </ sub >, e < sub > z </ sub > denotes the cartesian basis vectors ( all are orthogonal unit vectors ) and A < sub > x </ sub >, A < sub > y </ sub >, A < sub > z </ sub > are the corresponding coordinates, in the x, y, z directions.

If a Banach algebra has unit 1, then 1 cannot be a commutator ; i. e., for any x, y ∈ A.

The questions range from counting ( e. g., the number of graphs on n vertices with k edges ) to structural ( e. g., which graphs contain Hamiltonian cycles ) to algebraic questions ( e. g., given a graph G and two numbers x and y, does the Tutte polynomial T < sub > G </ sub >( x, y ) have a combinatorial interpretation ?).

In 3 dimensions, a differential 0-form is simply a function f ( x, y, z ); a differential 1-form is the following expression: a differential 2-form is the formal sum: and a differential 3-form is defined by a single term: ( Here the a-coefficients are real functions ; the " wedge products ", e. g. can be interpreted as some kind of oriented area elements,, etc.

For example, if function div stands for the division operation x / y, then div with the parameter x fixed at 1 ( i. e., div 1 ) is another function: the same as the function inv that returns the multiplicative inverse of its argument, defined by inv ( y )

Letters of the Right Honourable Lady M -- y W --- y M ---- e. 3 vols.

If the function f is not linear ( i. e. its graph is not a straight line ), however, then the change in y divided by the change in x varies: differentiation is a method to find an exact value for this rate of change at any given value of x.

::, the average change of y per unit x, i. e. the change of y over the change of x

The relationship between the two Latin American countries has evolved amid conflicts over the San Andrés y Providencia Islands located in the Caribbean sea close to the Nicaraguan shoreline and the maritime boundaries covering 150, 000 km² that included the islands of San Andres, Providencia and Santa Catalina and the banks of Roncador, Serrana, Serranilla and Quitasueño as well as the arbitrarily designed 82nd meridian west which Colombia claims as a border but which the International Court has sided with Nicaragua in disavowing.

Somewhat more developed was a band of six departments stretching across the center of the country, from west to east: Río Negro, Flores, Florida, Durazno, Treinta y Tres, and Rocha.

Rancho Orestimba y Las Garzas, Rancho Pescadero and Rancho Del Puerto were located on the west side of the San Joaquin River.

: Norridge to y < sup > e </ sup > west bounds of Homonoscet Plantation shalbe

Another statue by Miranda, this one of Jose Maria Morelos y Pavon was placed in the small plaza on the west side of the Cathedral and named the Morelos Plaza.

Aberdaron stands on the shore of Bae Aberdaron () in a small valley at the confluence of the Afon Daron and Afon Cyll-y-Felin, between the headlands of Uwchmynydd to the west, and Trwyn y Penrhyn to the east.

The name Lydia has been convincingly derived from the name Luwiya ( Lydian * lūda-< * luw ( i ) da-< luwiya-with the regular Lydian sound change of y > d ), which further argues in favour of the location of Luwiya in the west.

Finally, the A465 passes Prince Charles Hospital in Merthyr Tydfil ( great view of Pen Y Fan from here ), then continues to Cefn Coed y cymmer ( North End of Merthyr Tydfil ), then leads to the A470 link and then continues down the west side of the valley to Neath.

Hydrography: The Río Culebrinas crosses its territory from east to west, and its tributaries include the gorges of Los Gatos, Lassalle, de las Damas, Vieja, Los Romanes, the Morones, Higuillo, Chiquita, Yagruma, Echeverria, Aguas Frias, Las Marias, de los Méndez, La Caraíma, Grande, y Dulce.

Fray Abreu y Galida reported in Historia de la Conquista de las siete Islas Canarias that " the island of Saint Brendan ( San Borondon ), which is the eighth and last, whose existence may be inferred from sightings of its apparitions, seems to be located at 20 degrees 30 minutes of latitude and eight leagues ( 40 kilometres ) due west of Gomera.

On Mynydd y Gelli, a hill overlooking the area to the west, lies the Iron Age settlement of Hen Dre ' r Gelli, a site which also has several Bronze Age cairns.

In 1753, Texas Governor Jacinto de Barrios y Juaregui determined that the French had encroached on Texas by occupying territory to the west of Arroyo Hondo ( Calcasieu River ), which runs south between the upper Sabine River to the west and the lower Red River to the north and east.

It border Maldonado Department to its west, Lavalleja Department to its northwest, Treinta y Tres Department to its north, while to its northeast Laguna Merín forms part of it border with Brazil and at the south end of the lake it also borders the southernmost end of Brazil, with the city of Chuy " shared " between both counrties, the border passing through its main commercial avenue.

Another notable feature, west of the summit, is Castell y Gwynt, ( Castle of the Wind ), a spiky rocky outcrop.

Due south of Portmeirion the river is joined by the Afon y Glyn which drains the south west catchment from Llyn Tecwyn Uchaf and Llyn Tecwyn Isaf.

Bodega y Quadra was able to draw for the first time a reasonably accurate map of the west coast of North America.

Isla Salas y Gómez is located 3, 210 km west of the Chilean mainland, 2, 490 km west of Chile's Desventuradas Islands, and 390 km east-northeast of Easter Island, the closest landmass.

Salas y Gómez consists of two rocks, a smaller one in the west measuring 4 hectare in area ( 270 meters north-south, 200 meters east-west ), and a larger one in the east measuring 11 ha ( 500 meters north-south, 270 meters east-west ), which are connected by a narrow isthmus in the north, averaging approximately 30 meters in width.

Salas y Gómez is part of the same Salas y Gómez Ridge as Easter Island to the west, these two locations being the only places where the otherwise submarine mountain range extends above sea level.

The view from the summit covers the Black Mountains to the north, the Cotswolds to the east, as far as the Brecon Beacons including Pen y Fan and Corn Du to the west and the Bristol Channel to the south.

It is located in the south of the central part of the country with Rivera Department to its north, the departments of Treinta y Tres and Lavalleja to its east, Canelones Department to its south and the departments of Flores and San José to its west.