Since spherical geometry violates the parallel postulate, there exists no such triangle on the surface of a sphere.

Since each slice balances, the whole parabola balances the whole triangle.

Since the sum of the angles of a triangle is equal to two right angles, we have

Consider a polygon P and a triangle T, with one edge in common with P. Assume Pick's theorem is true for both P and T separately ; we want to show that it is also true to the polygon PT obtained by adding T to P. Since P and T share an edge, all the boundary points along the edge in common are merged to interior points, except for the two endpoints of the edge, which are merged to boundary points.

Since two of the angles in an isosceles triangle are equal and since the angles in a triangle must add up to 180 °, it follows that the inscribed angle equals θ, half of the central angle.

Since the triangle area is

Since barycentric coordinates are a linear transformation of Cartesian coordinates, it follows that they vary linearly along the edges and over the area of the triangle.

Since the area of an equilateral triangle is the area can be expressed as

Since a reflection flips the triangle and changes the orientation, we can join the triangles in pairs and obtain an orientation-preserving tiling polygon.

Since 1972, the Sociedade Açoreana de Transportes Aeréos ( which was the forerunner of SATA Air Azores ) has provided scheduled flights from Horta to the islands of the triangle ( Central Group ).

Since these games generally feature more than one playable character, a wall jump ( occasionally called a triangle jump ) will be given to certain characters, primarily the smaller and more agile ones.

Since a triangle is defined by its three vertices, and exactly three points are required to determine a circle, every triangle can be circumscribed .</ ref >

Since the triangle inequality holds for both the editing distance for contours and the variant of the Earth Mover's Distance used by Musipedia, the search algorithm needs, in a second step, to take a closer look at only those database entries whose distances to the vantage objects are similar to the distances between the query and the vantage objects.

Since 2002, Charles has been a DJ on BBC Radio 6 Music, presenting The Craig Charles Funk and Soul Show, where he plays a diverse range of funk and soul music, from classic tracks to the latest releases, and provides publicity for new bands.

Since the complex numbers can be multiplied giving another complex number, this identification provides a means to " multiply " vectors.

Since there is a camber in the corner, it provides excellent overtaking opportunities.

Since the jacket provides the strength, soft lead can be used, which allows bullets to be swaged or cast into shape before plating.

Since the main sensory organs are anatomically located on the head, long hair provides the necessary warmth and protection in a cold climate that allows the use of these organs by exposing them to the elements to " sense ", in for example a hunt, yet still providing necessary warmth and protection to sustain prolonged exposure.

Since the pump user is responsible to manually start a bolus, this provides an opportunity for the user to pre-bolus to improve upon the insulin pump's capability to prevent post-prandial hyperglycemia.

Since ISDN provides a high quality connection this assists in delivering good quality audio for transmission in radio.

Since some applications ( notably, but not exclusively, the parts of Microsoft Office ) allow macro programs to be embedded in documents, so that the programs may be run automatically when the document is opened, this provides a distinct mechanism by which viruses can be spread.

Since the two-round system requires more information from each voter than a single ordinal ballot provides, one can't fit the criteria that are formulated expressly for voters with ordinal preferences without making a generalization as to how the voters will behave.

Since the plasma is an electrical conductor, it is possible to heat the plasma by inducing a current through it ; in fact, the induced current that heats the plasma usually provides most of the poloidal field.

Since clause 3 provides that Members of the House of Representatives are apportioned state-by-state and that each state is guaranteed at least one Representative, exact population equality between all districts is not guaranteed and, in fact, is currently impossible, because while the size of the House of Representatives is fixed at 435, several states had less than 1 / 435 of the national population at the time of the last reapportionment in 2000.

Since New York's financial industry provides almost one-fourth of all income produced in the city, and accounts for 10 % of the city's tax revenues and 20 % of the state's, the downturn has had huge repercussions for government treasuries.

Since most switch port mirroring provides only one mirrored stream, network hubs can be useful for fanning out data to several read-only analyzers, such as intrusion detection systems and packet sniffers.

Since any software that provides services can be called a server, modern personal computers can be seen as a forest of servers and clients operating in parallel.

Since it provides the graphical elements surrounding the area in which the engine paints documents, the term chrome is sometimes used to refer to it.

Since consolidation with New York City in 1898, Brooklyn has been governed by the New York City Charter that provides for a " strong " mayor-council system.

Since payment by commodity generally provides a useful good, commodity money is similar to barter, but is distinguishable from it in having a single recognized unit of exchange.

Since many common constructions in mathematics are limits or colimits, this provides a wealth of information.

Since there are no literal mothers in King Lear, Coppélia Kahn provides a psychoanalytic interpretation of the " maternal subtext " found in the play.

Since the inhibitory output is reduced by cholinergic input to the cerebral cortex, this provides the brainstem with adjustable " gain control for the relay of lemnsical inputs ".

Since 1998, a 1 MiB Flash memory card is available which provides convenient non-volatile storage.

Since then, their mission has evolved and grown, but one thing has remained constant-the hospital provides the highest quality care using the most innovative procedures and caring health care professionals in the region.

Since 1990, in the United States, physical anthropology and archaeological investigations based on the study of human remains are complicated by the Native American Graves Protection and Repatriation Act, ( NAGPRA ), which provides for the bodies of Native Americans and associated grave goods to be turned over to the recognized tribal body most legally affiliated with the remains.

Since these services involve flying into steep, short, or otherwise difficult runways, JAARS provides its personnel with training in STOL and other specialised techniques.

Since August 1995, the city, in partnership with King County Metro, provides a free bus that runs through all the major shopping areas of the town giving some relief to residents and those who wish to shop or eat at the many retailers and restaurants.

Since the flow of a baseball game has natural breaks to it, and normally players act individually rather than performing in clusters, the sport lends itself to easy record-keeping and statistics.

Since the Roman consular fasti make it somewhat easy to confuse 87 – 57 BC with 84 – 54 BC, many scholars accept the dates 84 BC – 54 BC, supposing that his latest poems and the publication of his libellus coincided with the year of his death.

Since the rules are written in plain language, it is easy to identify those to be removed or modified.

Since the concentrations of acid and alkali are known, it is easy to calculate the concentration of hydrogen ions so that the measured potential can be correlated with concentrations.

Since but-for causation is very easy to show and does not assign culpability ( but for the rain, you would not have crashed your carthe rain is not morally or legally culpable but still constitutes a cause ), there is a second test used to determine if an action is close enough to a harm in a " chain of events " to be a legally culpable cause of the harm.

Since all that is required for a full recovery is the resumption of normal vitamin C intake, it is easy to treat if identified correctly.

Since thin clients are cheap, they offer a low risk of theft in general, and are easy to replace if stolen or broken.

Since time is the reciprocal of frequency, it is relatively easy to derive a time standard from a frequency standard.

Since nematodes have such a seemingly erratic distribution in cassava agricultural fields, it is not easy to clearly define the level of direct damage attributed to nematodes and thereafter quantify the success of a chosen management method.

Since it was quite easy to stack interconnections ( wires ) inside the embedding matrix, the approach allowed designers to forget completely about the routing of wires ( usually a time-consuming operation of PCB design ): Anywhere the designer needs a connection, the machine will draw a wire in straight line from one location / pin to another.

Since Family Fun Day's ending, the two haven't been easy to see outside " Mickey's Boo-to-You Halloween Parade ", " Mickey's Once Upon a Christmastime Parade " and the occasional special event.

Since Family Fun Day's ending, the two haven't been easy to see outside " Mickey's Boo-to-You Halloween Parade ", " Mickey's Once Upon a Christmastime Parade " and the occasional special event.

Since hagfish are typically found in large clusters on and near the bottom, a single trawler's catch could contain several dozen or even hundreds of hagfish as bycatch, and all the other struggling, captive sealife make easy prey for them.

Since the mtDNA is inherited maternally and recombination is either rare or absent, it is relatively easy to track the ancestry of the lineages back to a MRCA ; however this MRCA is valid only when discussing mitochondrial DNA.

Since the fringes would occasionally disappear due to vibrations by passing horse traffic, distant thunderstorms and the like, it would be easy for an observer to " get lost " when the fringes returned to visibility.

Since the completion of the Greenbelt, many subdivisions have been built along or near the belt to allow for easy access to I-264 and I-265.

Since the land is flat, this allowed for easy traveling, hunting and food gathering such as various nuts.

Since the musical views of The Five tended to be anti-German, it is easy to forget that Balakirev was actually well-grounded in German symphonic style — all the more impressive when it is remembered that Balakirev was essentially self-taught as a composer.

Since the cones drop, harvesting is easy.

Since the fringes would occasionally disappear due to vibrations by passing horse traffic, distant thunderstorms and the like, it would be easy for an observer to " get lost " when the fringes returned to visibility.

Since raising crops was not easy, raising sheep was popular.

Since methamphetamine is easy to produce, the substance is manufactured locally in staggering quantities.

Since it is not easy to produce an electromagnetic expression for the railgun force that is both simple and reasonably accurate, most simple railgun analyses actually used a lumped circuit model to describe the relationship between the driving current and the railgun force.

Since Beck's is located on the river of a port city, it was easy to ship out its beer to the world at large and become an international beer powerhouse.