Instead, Cauchy formulated calculus in terms of geometric ideas and infinitesimals.

Instead, intricate patterns and geometric designs, bold colors and monumental architecture were the norm.

Instead of total reflectance, " geometric gain " ( equal to the gain divided by the total reflectance ) can be the second specification.

Instead of forcing the diffusion anisotropy data into a group of tensors, the mathematics used deploys both probability distributions and a classic bit of geometric tomography and vector math developed nearly 100 years ago — the Funk Radon Transform.

Instead, the phrase appears to have originated in the early 19th century United States ( particularly in the sense " pull oneself over a fence by one's bootstraps "), to mean an absurdly impossible action, an adynaton.

Instead, over time, the species wobbles about its phenotypic mean.

Instead, approximation techniques, such as mean field approximations from statistical physics, or computer simulations are used to understand the behaviors of the system.

Instead it could as easily mean " wild ", as in a wild flower, as it still does in its French and Italian cognates, for example.

Instead of conveying linguistic content and pointing to something outside itself, scat music — like instrumental music — is self-referential and " d what it mean ".

Instead, megabyte is often used to mean 1000 x 1000, 1024 x 1024 or even 1024 x 1000 by disk manufacturers.

Instead of the mean anomaly at epoch, the mean anomaly, mean longitude, true anomaly, or ( rarely ) the eccentric anomaly might be used.

Instead, over time, the species wobbles about its phenotypic mean.

Instead of hours and minutes, the mean solar day is divided up into 1000 parts called ". beats ".

Instead of hours and minutes, the mean solar day is divided up into 1000 parts called ". beats ".

Instead, he assigned an arbitrary value of 100 to the mean intelligence and added or subtracted another 15 points for each standard deviation above or below the mean the subject was.

Instead, in such a case there will be variables representing the unknown true mean and true variance, and the determination of sample values for these variables results automatically from the operation of the Gibbs sampler.

Instead we assume that the mean strength of the interactions are the same between all the molecules of the solution.

Instead the low speeds mean the issue is keeping the brakes up to working temperature.

Instead of being considered an " employee ", the individual could be considered a " worker " ( which could mean less employment legislation protection ) or as having an " employment relationship " ( which could mean protection somewhere in between ) or a " professional " or a " dependent entrepreneur ", and so on.

Instead, for " I have X " these languages use a combination of words that mean X is to me ; or ( in Finnish ) with me is X ; ( in Turkish ) my X exists ; or ( in Hebrew ) there (- is ) ( to -) me ( or mine ) X.

Instead of leaving, Vienna told him she loved him more than anything in her life and if being a second choice in his would mean she still got to be with him, than she would do so.

Instead, the boundary has been arbitrarily set at a mean density of 2800 kg / m < sup > 3 </ sup >.

This was not what Delbrück and Luria found: Instead the number of resistant colonies on each plate varied drastically: the variance was considerably greater than the mean.

Instead of taking this step, Loschmidt decided to estimate the mean diameter of the molecules in air.

Instead of emotional recrimination, loaded phrases and sloganeering, we need a dispassionate study of the facts, a better understanding of the opposite viewpoint and a more serious effort to extend the areas of agreement until a solution is reached.

Instead of Catholics' being obliged or even encouraged to beget the greatest possible number of offspring, as many Non-Catholics imagine, the ideal of responsible parenthood is stressed.

Instead -- and not just to prove my objectivity -- I hasten to report that it's a highly amusing film which probably does a fairly accurate job of reporting on the Easter vacation shenanigans of collegians down in Fort Lauderdale, and that it seems to come to grips quite honestly with the moral problem that most commonly vexes youngsters in this age group -- that is to say, sex.

Instead of her old confidence in the simplest, purest, most moving musical expression, Miss Schwarzkopf is letting herself be tempted by the classic sin of artistic pride -- that subtle vanity that sometimes misleads a great artist into thinking that he or she can somehow better the music by bringing to it something extra, some personal dramatic touch imposed from the outside.

Instead, the element is prepared, in milligram amounts, by the neutron irradiation of < sup > 226 </ sup > in a nuclear reactor.

Instead, providence is a power that emanates from the heavens to the sublunar region, and is responsible for the generation and destruction of earthly things, without any direct involvement in the lives of individuals.

Instead, it is negotiated by or configured at the endpoints on a per-virtual-connection basis.

Instead of the gradual transition through the capillaries from arteries to veins that is typical of normal functioning vasculature, AVMs cause direct associations of the arteries and veins.

Since the 2002 edition, the Apostles ' Creed is included in the Roman Missal with the indication, " Instead of the Niceno-Constantinopolitan Creed, especially during Lent and Easter time, the baptismal Symbol of the Roman Church, known as the Apostles ’ Creed, may be used.

Instead, it is put in parallel with chapter 4 ( C ) where divine judgements are pronounced against the Babylonian kings.

Instead, the Hebrew name Ahasuerus accords with an inscription of the time that notes that Artaxerxes II was named also Arshu, understood as a shortening of Achshiyarshu the Babylonian rendering of the Persian Khshayarsha ( Xerxes ), through which the Hebrew Achashverosh ( Ahasuerus ) is derived.

Instead, Pasternak was told, " Comrade Stalin is busy.

Instead it is part of the Intelligence and Security Directorate ( DIS ) which reports directly to the Minister of the Presidency.

Instead, murder is treated as a civil crime and is covered by the law of retaliation, whereby the relatives of the victim decide whether the offender is punished with death by the authorities or made to pay diyah as compensation.

Instead of listing every single element, sometimes an ellipsis ("...") is used, if the writer believes that the reader can easily guess what is missing ; for example, presumably denotes the set of integers from 1 to 100.

Instead, these efforts, it is argued, were made in order to advance Western development and reinforce Western hegemony.

Instead, the decree states that Christ is " really, truly, substantially present " in the consecrated forms.

Instead, non-return-to-zero, inverted encoding is used: a change from pit to land or land to pit indicates a one, while no change indicates a series of zeros.

Instead, it is important that support for the CRM system is companywide.

Instead, this is just an indication that sugar and / or fat has separated due to poor storage.