For example, Euclid assumed implicitly that any line contains at least two points, but this assumption cannot be proved from the other axioms, and therefore must be an axiom itself.

For two centuries Euclid had been taught from two Latin translations taken from an Arabic source ; these contained errors in Book V, the Eudoxian theory of proportion, which rendered it unusable.

For example, Euclid provides an elaborate proof of the Pythagorean theorem, by using addition of areas instead of the much simpler proof from similar triangles, which relies on ratios of line segments.

For over 2, 000 years, Euclid ’ s Elements stood as a perfectly solid foundation for mathematics, as its methodology of rational exploration guided mathematicians, philosophers, and scientists well into the 19th century.

For example, in the first construction of Book 1, Euclid used a premise that was neither postulated nor proved: that two circles with centers at the distance of their radius will intersect in two points.

For example, math is taught through reading and discussing Euclid and Galileo, rather than actually completing numerical problem sets.

For Aristotle and Euclid, relations were conceived as whole numbers ( Michell, 1993 ).

" Swift extends the metaphor to get in a few jibes at England ’ s mistreatment of Ireland, noting that " For this kind of commodity will not bear exportation, and flesh being of too tender a consistence, to admit a long continuance in salt, although perhaps I could name a country, which would be glad to eat up our whole nation without it.

For instance, in 51, Agrippina ordered the execution of Britannicus ’ tutor Sosibius because he had confronted her and was outraged by Claudius ’ adoption of Nero and his choice of Nero as successor, instead of choosing his own son Britannicus.

For me it ’ s the book that does everything right, the example of what science fiction does when it works.

Also, supporters of this view would characterize Luke ’ s portrayal of the Roman Empire as positive because they believe Luke “ glosses over negative aspects of the empire and presents imperial power positively .” For example, when Paul is before the council defending himself, Paul says that he is “ on trial concerning the hope of the resurrection of the dead ” ( Acts 23: 6 ).

Many who side with this view disagree that Luke portrays Christianity or the Roman Empire as harmless and thus reject the apologetic view because “ Acts does not present Christians as politically harmless or law abiding for there are a large number of public controversies concerning Christianity, particularly featuring Paul .” For example, to support this view Cassidy references how Paul is accused of going against the Emperor because he is “ saying that there is another king named Jesus .” ( Acts 17: 7 ) Furthermore, there are multiple examples of Paul ’ s preaching causing uprisings in various cities ( Acts 14: 2 ; 14: 19 ; 16: 19-23 ; 17: 5 ; 17: 13-14 ; 19: 28-40 ; 21: 27 ).

Likewise, Jeremiah ’ s exclamation “ For I hear the whispering of many: Terror is all around !” ( Jer.

In Chapter nine, Job recognizes the chasm that exists between him and God: “ For he is not a man, as I am, that I might answer him, that we should come to trial together .” Job ’ s regret is that he has no arbiter to act as a go-between ; that Job cannot reconcile himself with God anticipates the need for the Messiah to become incarnate.

3: 17 For though the fig tree doesn ’ t flourish, nor fruit be in the vines ; the labor of the olive fails, the fields yield no food ; the flocks are cut off from the fold, and there is no herd in the stalls: 3: 18 yet I will rejoice in Yahweh.

For this to be engaged, the President ’ s agreement is necessary.

For instance, Forbes ranked media mogul and talk show host, Oprah Winfrey as the top earner " Forbes magazine ’ s annual ranking of the most powerful celebrities ", with earnings of $ 290 million in the past year.

For an atemporal interpretation that “ makes no attempt to give a ‘ local ’ account on the level of determinate particles ”, the conjugate wavefunction, (" advanced " or time-reversed ) of the relativistic version of the wavefunction, and the so-called " retarded " or time-forward version are both regarded as real and the transactional interpretation results.

For example, there is a record that in 1176 Sens Cathedral installed a ‘ horologe ’ but the mechanism used is unknown.

For instance, a professor of formal logic called Chin Yueh-lin – who was then regarded as China ’ s leading authority on his subject – was induced to write: “ The new philosophy Marxism-Leninism, being scientific, is the supreme truth ”.

For example in the mid 350 ’ s the city of Jerusalem was hit with drastic food shortages at which point church historians Sozomen and Theodoret reported “ Cyril secretly sold sacramental ornaments of the church and a valuable holy robe, fashioned with gold thread that the emperor Constantine had once donated for the bishop to wear when he performed the rite of Baptism ”.

* For a more detailed account of Christine de Pizan ’ s rhetorical strategies refer to Jenny R. Redfern ’ s excerpt Christine de Pisan and The Treasure of the City of Ladies: A Medieval Rhetorician and Her Rhetoric ( in Reclaiming Rhetorica, ed.

For this reason it is difficult for the modern scholar to solve the 101st problem even after having studied 100 of Diophantos ’ s solutions ”

For example, according to ancient Hebrew belief, life takes a linear ( and not cyclical ) path ; the world began with God and is constantly headed toward God ’ s final goal for creation.

With Dewey as the director and his wife as principal, the University of Chicago Laboratory school, was dedicated “ to discover in administration, selection of subject-matter, methods of learning, teaching, and discipline, how a school could become a cooperative community while developing in individuals their own capacities and satisfy their own needs .” ( Cremin, 136 ) For Dewey the two key goals of developing a cooperative community and developing individuals ’ own capacities were not at odds ; they were necessary to each other.

For example, the work of Zacharias and Bruner was based in the developmental psychology of Jean Piaget and incorporated many of Dewey ’ s ideas of experiential education.

For years she continued her attacks upon her husband ’ s character.

For example, Ralph Waldo Emerson ’ s contempt for Jane Austen's works often extended to the author herself, with Emerson describing her as “ without genius, wit, or knowledge of the world .” In turn, Emerson himself was called a “ hoary-headed toothless baboon ” by Thomas Carlyle.

For biblical scholar John Knox, the use of the word “ name ” in 4: 14-16 is the “ crucial point of contact ” with that in Pliny ’ s letter.

For example, after having established that the set X contains only non-empty sets, a mathematician might have said " let F ( s ) be one of the members of s for all s in X.

* For a utilitarian analysis of religion, see The ( F ) Utility of Religion: Who Needs God ( s )?– A Prospective Bible for Non-Believers at http :// bradmusil. kramernet. org

* James ` s Theorem For a Banach space the following two properties are equivalent:

For example, a 500 gigabyte hard drive holds bytes, and a 100 megabit per second Ethernet connection transfers data at bit / s.

For given nonzero integers a and b there is a nonzero integer of minimal absolute value among all those of the form ax + by with x and y integers ; one can assume d > 0 by changing the signs of both s and t if necessary.

For instance, nanotubes form only a tiny portion of the material ( s ) in ( primarily carbon fiber ) baseball bats, golf clubs, or car parts.

" Liberators: Latin America ` s Struggle For Independence, 1810-1830 ".

" Liberators: Latin America ` s Struggle For Independence, 1810-1830 ".

For particularly severe conduct, the game official ( s ) may eject players ( ejected players may be substituted for ), or in exceptional cases, declare the game over and award victory to one side or the other.

For example, uncompressed songs in CD format have a data rate of 16 bits / channel x 2 channels x 44. 1 kHz ≅ 1. 4 Mbit / s, whereas AAC files on an iPod are typically compressed to 128 kbit / s, yielding a compression ratio of 0. 09, for a data-rate savings of 0. 91, or 91 %.

For the low-temperature measurements the sample was cooled by a cold nitrogen gas flow method similar to that of Andrew and Eades.

For the albumin method, equal volumes of 30% bovine albumin, sample and 2% cells suspended in saline were allowed to stand at room temperature for 1 hr and then were centrifuged at 1000 rpm for 1 Aj.

For this reason it is important to have a reliable and accurate method of measuring the depth of water.

For example, abeyance was used as a settlement method in a Canadian lawsuit involving the University of Victoria Students ' Society ( UVSS ), the BCCLA, and a campus pro-life to whom the UVSS denied funding to.

For the use of this method in warfare, see biological warfare.

For π-electron systems, this was the Hückel method proposed by Erich Hückel, and for all valence electron systems, the extended Hückel method proposed by Roald Hoffmann.

For the culturing method, a sterile swab is rubbed on the infected skin surface.

For example, the Bourbaki group adopted a watered-down and selective version of it as adequate to the requirements of their twin projects of ( a ) writing encyclopedic foundational works, and ( b ) supporting the axiomatic method as a research tool.

For Avicenna ( Ibn Sina ), for example, the a tabula rasa is a pure potentiality that is actualized through education, and knowledge is attained through " empirical familiarity with objects in this world from which one abstracts universal concepts " developed through a " syllogistic method of reasoning in which observations lead to propositional statements which when compounded lead to further abstract concepts.

For example, the anthropological method of ethnography has been used to describe teaching and learning in classrooms.

For example, one character creation method encourages players to first write prose descriptions of their characters and then translate those into Fudge Traits.

For he, following the example of no previous general, with teachers summoned from the gladiatorial training school of C. Aurelus Scaurus, implanted in the legions a more sophisticated method of avoiding and dealing a blow and mixed bravery with skill and skill back again with virtue so that skill became stronger by bravery's passion and passion became more wary with the knowledge of this art.

For example WebDAV defined 7 new methods and RFC5789 specified the PATCH method.

For the truly frugal, the cheapest method of obtaining bullets intended for use at low to moderate velocities is casting them.

For example, in 1994, Irving Kirsch characterized hypnosis as a " nondeceptive placebo ," i. e., a method that openly makes use of suggestion and employs methods to amplify its effects.

For comparison, milk heat pasteurization is not being alleged to be a method " to cover up poor food quality "; consequently, food irradiation should not be accused to serve such criminal purposes.

For the benefit of users wishing to produce statistics and indexes oriented towards medical care, the Ninth Revision included an optional alternative method of classifying diagnostic statements, including information about both an underlying general disease and a manifestation in a particular organ or site.

For example, the zip data format specifies the ' compression method ' of ' Stored ' for input files that have been copied into the archive verbatim.

For example, timber framing using wattle and daub is a legacy building construction method.

Thymectomy is a surgical method to treat MG. For emergency treatment, plasmapheresis or IVIG can be used as a temporary measure to remove antibodies from the blood circulation.

For an imprecise, but qualitatively useful, discussion of the molecular structure, the molecular orbitals can be obtained from the " Linear combination of atomic orbitals molecular orbital method " ansatz.

For example, a similar geometric system was published in 1987 by Kjell Gustafson, whose method represents a rhythm as a two-dimensional graph.

For this method of analysis, the offline algorithm knows in advance which edges will fail and the goal is to minimize the ratio between the online and offline algorithms ' performance.