Formulas for the surface areas of simple shapes were computed by the ancient Greeks, but computing the surface area of a more complicated shape usually requires multivariable calculus.

Formulas for the eccentricity of an ellipse that is expressed in the more general quadratic form are described in the article dedicated to conic sections.

Formulas for expressing the roots of polynomials of degree 2 in terms of square roots have been known since ancient times ( see quadratic equation ), and for polynomials of degree 3 or 4 similar formulas ( using cube roots in addition to square roots ) were found in the 16th century ( see cubic function and quartic function for the formulas and Niccolo Fontana Tartaglia, Lodovico Ferrari, Gerolamo Cardano, and Vieta for historical details ).

For example, a 1901 medical book published for home health use gave the following two " Simple Remedy Formulas " for DYSENTERRY: ( 1 ) Thin boiled starch, 2 ounces ; Laudanum, 20 drops ; " Use as an injection every six to twelve hours "; ( 2 ) Tincture rhubarb, 1 ounce ; Laudanum 4 drachms ; " Dose: One teaspoonful every three hours.

Formulas for addition and multiplication are exactly the same as for the ordinary polynomials, with the only difference that both positive and negative powers of X can be present:

* The Animator's Survival Kit: A Manual of Methods, Principles and Formulas for Computer, Stop-motion, Games and Classical Animators, Faber and Faber, 2002 ( expanded edition 2009, adding ' Internet ' to the subtitle )

Formulas for the other coefficients are much harder to get ; Todd classes of toric varieties, the Riemann – Roch theorem as well as Fourier analysis have been used for this purpose.

Formulas are quite often interpreted as propositions ( as, for instance, in propositional logic ).

Formulas with the form described above are known as 2-CNF formulas ; the " 2 " in this name stands for the number of terms per clause, and " CNF " stands for conjunctive normal form, a type of Boolean expression in the form of a conjunction of disjunctions.

The Animator's Survival Kit: A Manual of Methods, Principles, and Formulas for Classical, Computer, Games, Stop Motion, and Internet Animators.

Formulas for different colors of glass are closely guarded.

Formulas for triose and TP are C < sub > 2 </ sub > H < sub > 3 </ sub > O < sub > 2 </ sub >- CH < sub > 2 </ sub > OH and C < sub > 2 </ sub > H < sub > 3 </ sub > O < sub > 2 </ sub >- CH < sub > 2 </ sub > OPO < sub > 3 </ sub >< sup > 2 -</ sup > + 2H < sup >+</ sup >.

Including but not limited to A Moral Code of Ethics, The Sheet of Fives, Pyramid Formulas for Happiness, Harmony and Health, The Ten Stages of Growth and much more.

* Formulas for estimating the height of mountains, dated Bath, 13 February 1817 Annals of Philosophy, 9 ( March, 1817 ), 251 -- 252.

Formulas for Generating Pythagorean Triples

TK Solver is also the platform for engineering applications marketed by UTS, including Advanced Spring Design, Integrated Gear Software, Interactive Roark ’ s Formulas, Heat Transfer on TK, and Dynamics and Vibration Analysis.

* Abramowitz and Stegun, the informal name for Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables

* The Cambridge Handbook of Physics Formulas, G. Woan, Cambridge University Press, 2010, ISBN 978-0-521-57507-2.

Maroger published The Secret Formulas and Techniques of the Old Masters in 1948.

Redelius was assisting Maroger with a revision of The Secret Formulas and Techniques of the Old Masters before his death in 1962.

Formulas in Calligra Words are provided by the Formula plugin.

Formulas say how to mechanically compute new values from existing values.

*" Basic Concepts and Formulas in Microscopy: Numerical Aperture " by Michael W. Davidson, Nikon MicroscopyU ( website ).

This engine and its legacy drive the SD Trans Ams and Formulas as one of the more, if not the most, desirable Pontiacs ever produced.

Formulas, macros and other objects existed " outside " of the cells, which was intended to make editing much simpler and less error-prone.

Formulas were typed into a separate section, and referred to data through their range, not their physical position in the sheets.

Stirling Numbers of the First Kind., § 24. 1. 3 in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing.

* Milton Abramowitz and Irene A. Stegun, eds., Handbook of Mathematical Functions ( with Formulas, Graphs and Mathematical Tables ), U. S. Dept.

During this period he started supervising Ph. D. students, such as James Halpern ( Contributions to the Study of the Independence of the Axiom of Choice ) and Edgar Lopez-Escobar ( Infinitely Long Formulas with Countable Quantifier Degrees ).

His most notable works were his ethnographic studies of the Ghost Dance after Sitting Bull's death in 1890, a widespread 19th-century religious movement among various Native American culture groups, and the Cherokee: The Sacred Formulas of the Cherokees ( 1891 ), and Myths of the Cherokee ( 1900 ), all published by the US Bureau of American Ethnology.

Sacred Formulas of the Cherokees.

Fender later released a 7 " EP, " Four Formulas ", under his own name on XNTRIX records.

They closed in fast, kept him from reaching inside his coat for his gun.

Besides, 'tain't no more'n right for me to follow with my black oxen, so's I can unhook and pull up fast if either of you get in a pinch ''.

Setting a course straight for the house, he was covering ground fast when an angry bee buzzed past close to his face.

Thinking fast, Tilghman never hesitated for one instant.

Sherman was responsible for the story when he said in his memoirs that this was the only time he could recall seeing Thomas ride so fast.

His new book, entitled `` Slums And Suburbs '', calls for fast and drastic action to avert disaster.

They are leaving so fast that the president of the West German Employers' Federation issued an appeal this week to factory workers in the West to volunteer for six months' front-line work in factories in West Berlin.

And they couldn't have entrusted Henri to better hands because `` le professeur '' knows his muscles from the sterno-cleido mastoideus of the neck right down to the tibialis anticus of the leg and better still, he knows just what exercises work best for them and what Weider principles to combine them with for fast, fast muscle growth.

For example, a Browning trap version of the Superposed over/under, the Broadway ( from $350 up, depending on grade ), differs from standard models in that it is equipped with a full beavertail fore end, a cushion recoil pad and a barrel-wide ventilated rib for fast sighting.

They had to act fast, for letters were clogging the terminals.

Even among the fast set in which she was moving, her method for keeping an escort from departing too early was unique.

But his is still a simple life relatively free of the female presence or influence, and he must go far, even though he may go fast, for sophisticated pleasures.

A bright sun and brisk wind had the track in a fast condition for the first time this week and 8,280 St. Patty Day celebrants bet $842,617 on the well-prepared program.

He managed to maneuver the missile to a landing speed of 200 m.p.h. -- fast even for a modern jet plane touchdown -- and banked into the airfield.

I outweigh you fifty pounds and I'm fast for a big man ''.

There are talks with the German government to deliver some 12 navy fast speed vessels for sea border protection.

With the development of fast Internet in the last part of the 20th century along with advances in computer controlled telescope mounts and CCD cameras ' Remote Telescope ' astronomy is now a viable means for amateur astronomers not aligned with major telescope facilities to partake in research and deep sky imaging.

: Precise instructions ( in language understood by " the computer ") for a fast, efficient, " good " process that specifies the " moves " of " the computer " ( machine or human, equipped with the necessary internally contained information and capabilities ) to find, decode, and then process arbitrary input integers / symbols m and n, symbols + and =

* A system for fast authorship by Daniel Hall

In the latter part of the 1990s Waugh himself, along with his twin brother Mark, scored heavily for Australia and fast bowlers Glenn McGrath and Jason Gillespie made a serious impact, especially the former.

Besides them, many smaller systems exist ( tactical ABMs ), that generally cannot intercept intercontinental strategic missiles, even if within range — an incoming ICBM simply moves too fast for these systems.

This results in an intelligibility problem because wrat can easily be confused for aurat, which means woman instead of fast in Hindi-Urdu.