Before beginning the construction, the vertex figure ABCD is obtained by cutting each connected edge at ( in this case ) its midpoint.

A simple pattern is just a text string ( e. g. " ABCD "), but a complex pattern may be a large structure describing, for example, the complete grammar of a computer language.

Supposing we exclude the degenerate case where ABCD has zero area, there is a unique such affine transformation T. Drawing out a whole grid of parallelograms based on ABCD, the image T ( P ) of any point P is determined by noting that T ( A ) = A ′, T applied to the line segment AB is A ′ B ′, T applied to the line segment AC is A ′ C ′, and T respects scalar multiples of vectors based at A.

As it turns out, since consumer Y's demand is twice consumer X's, ABCD = 2 x AC.

Furthermore the cyclic quadrilateral formed from the four nine-pont centers is homothetic to the reference cyclic quadrilateral ABCD by a factor of −< sup > 1 </ sup >/< sub > 2 </ sub > and its homothetic center ( N ) lies on the line connecting the circumcenter ( O ) to the anticenter ( M ) where ON = 2NM.

Ray transfer matrix analysis ( also known as ABCD matrix analysis ) is a type of ray tracing technique used in the design of some optical systems, particularly lasers.

A convex quadrilateral ABCD is cyclic if and only if its opposite angles are supplementary, that is

Another necessary and sufficient condition for a convex quadrilateral ABCD to be cyclic is that an angle between a side and a diagonal is equal to the angle between the opposite side and the other diagonal.

In the former case, the quadrilateral is ABCD, and in the latter case, the convex quadrilateral is ABDC.

Yet another characterization is that a convex quadrilateral ABCD is cyclic if and only if

A trapezoid with vertices ABCD is denoted.

Since in a parallelogram adjacent angles are supplementary ( add to 180 °) and ABC is a right angle ( 90 °) then angles BAD, BCD, and ADC are also right ( 90 °); consequently ABCD is a rectangle.

* ABCD ships, The first four steel ships built during the " New Navy " period of U. S. Naval history-Atlanta, Boston, Chicago and Dolphin

Prior to the demotion of beta-blockers as first line agents, the UK sequence of combination therapy used the first letter of the drug classes and was known as the " ABCD rule ".

The orthocenters of the same four triangles are the vertices of a quadrilateral congruent to ABCD, and the centroids in those four triangles are vertices of another cyclic quadrilateral.

The melodic structure of the presumed model ( s ) can be described as " ABCD " -- a new melodic phrase for each of its four lines.

A degenerate case of Pascal's Theorem ( four points ) is interesting ; given points ABCD on a conic Γ, the intersection of alternate sides, AB ∩ CD, BC ∩ DA, together with the intersection of tangents at opposite vertices ( A, C ) and ( B, D ) are collinear in four points ; the tangents being degenerate ' sides ', taken at two possible positions on the ' hexagon ' and the corresponding Pascal Line sharing either degenerate intersection.

Of the remaining four books, two were ultimately sold to a commercial gallery in New York, one to the ABCD collection in Paris, and one other is in a private collection in Brooklyn NY.

For example, if we have four matrices ABCD, we compute the cost required to find each of ( A )( BCD ), ( AB )( CD ), and ( ABC )( D ), making recursive calls to find the minimum cost to compute ABC, AB, CD, and BCD.

ABCD rating, also called the Jewett staging system or the Whitmore-Jewett staging system, is a staging system for prostate cancer that uses the letters A, B, C, and D.

Underneath the coloured buttons there is in Gnommish the letters ABCD

* ABCD Schema, a highly-structured data exchange and access model for taxon occurrence data ( specimens, observations, etc.

* Action for Boston Community Development, Inc. ( ABCD ), a Boston, Massachsuetts based non-profit social services agency

* ABCD line, a Japanese term for embargoes placed against Japan by the Americans, British, Chinese and Dutch, as well as other countries.

: area of A ′ B ′ C ′ D ′ / area of ABCD.

Clinical diagnosis can be made with the naked eye using the ABCD guideline or by using dermatoscopy.

Two lines that are perpendicular would be denoted as ABCD.

Both cities are located in the ABCD Region, home to most of Brazil's automobile manufacturing facilities ( such as Ford, Volkswagen, Toyota, Mercedes-Benz and others ) and are among the most industrialized in the country.

Nevertheless, this would still yield profit equal ABCD from consumer Y.

* In a cyclic quadrilateral ABCD, the incenters in triangles ABC, BCD, CDA, and DAB are the vertices of a rectangle.

the list is, obviously, endless.

In his effort to stir the public from its lethargy, Steele goes so far as to list Catholic atrocities of the sort to be expected in the event of a Stuart Restoration, and, with rousing rhetoric, he asserts that the only preservation from these `` Terrours '' is to be found in the laws he has so tediously cited.

Such a list must naturally be selective, and the treatment of each man is brief, for I am interested only in their general ideas on the moral measure of literature.

He had also learned to dispute extempore remarkably well, the main evidence for which of course is the presence of his name in the honors list of 1628/29.

If we are to believe the list of titles printed in Malraux's latest book, La Metamorphose Des Dieux, Vol. 1 ( ( 1957 ), he is still engaged in writing a large novel under his original title.

Each diagram is accompanied by a `` dog chart '', a list of the levers that show which other levers any particular lever will lock if pulled.

We accomplish this by compiling a list of text forms as text is read by the computer.

Also, the dictionary is divided into at least two parts: the list of dictionary forms and the file of information that pertains to these forms.

The first is compiling a list of text forms, assigning an information cell to each, and replacing text occurrences with the information cell assigned to the form of each occurrence.

For this step the computer memory is separated into three regions: cells in the W-region are used for storage of the forms in the text-form list ; ;

If cell Af has not previously been assigned as the information cell of a form in the text-form list, it is now assigned as the information cell of Af.

Hence, when the address Af is computed from Af, the cell Af and all Y-cells in its chain must be inspected to determine whether Af is already in the form list or whether it should be added to the form list and the chain.

Text reading is terminated when a pre-determined number of forms have been stored in the text-form list.

Each form represented by the dictionary is looked up in the text-form list.

Each dictionary form is looked up in the text-form list by the same method used to look up a new text occurrence in the form list during text reading.

If cell Af is not an information cell we conclude that the i-th dictionary form is not in the text list.

These differences in turn result from the fact that my Yokuts vocabularies were built up of terms selected mainly to insure unambiguity of English meaning between illiterate informants and myself, within a compact and uniform territorial area, but that Hoijer's vocabulary is based on Swadesh's second glottochronological list which aims at eliminating all items which might be culturally or geographically determined.

It is the urge to obtain a list as free of geographical and cultural conditioning as possible.

It is the hope of attaining a list of items of universal occurrence.

The practical operational problem of lexicostatistics is the establishment of a basic list of items of meaning against which the particular forms or terms of languages can be matched as the medium of comparison.