Although many of Euclid's results had been stated by earlier mathematicians, Euclid was the first to show how these propositions could fit into a comprehensive deductive and logical system.

Although Scheler later criticised Husserl's idealistic logical approach and proposed instead a " phenomenology of love ", he states that he remained " deeply indebted " to Husserl throughout his work.

Although his work was the first of its kind, it was unknown to the larger logical community.

Although biologists consider it contrary to the evidence of surviving Gondwanan lineages, geologists consider the logical possibility that Zealandia may have been completely submerged about 23 million years ago.

Although Descartes did not pursue the subject, he preceded Leibniz in envisioning a more general science of algebra or " universal mathematics ," as a precursor to symbolic logic, that could encompass logical principles and methods symbolically, and mechanize general reasoning.

Although Wittgenstein did not use the term himself, his metaphysical view throughout the Tractatus is commonly referred to as logical atomism.

Although the Vienna Circle's logical positivists appreciated the Tractatus, they argued that the last few passages, including Proposition 7, are confused.

According to the Internet Encyclopedia of Philosophy, Solovyov thought, “ Although empiricism and rationalism (= idealism ) rest on false principles, their respective objective contents, external experience, qua the foundation of natural science, and logical thought, qua the foundation of pure philosophy, are to be synthesized or encompassed along with mystical knowledge in ' integral knowledge ,' what Solovyov terms ' theosophy.

Although originally designed as an indexing and retrieval system, due to its logical structure and scalability, UDC has become one of the most widely used knowledge organization systems in libraries, where it is used for either shelf arrangement, content indexing or both.

Although Bryan had decided on a strategy to gain the nomination — to give a speech which would make him the logical candidate in the eyes of delegates — he faced obstacles along the way.

Although FDDI logical topology is a ring-based token network, it does not use the IEEE 802. 5 token ring protocol as its basis ; instead, its protocol is derived from the IEEE 802. 4 token bus timed token protocol.

Although the metric system has changed and developed since its inception, its basic concepts have hardly changed-it was designed for transnational use ; it consisted of a basic set of units of measurement, now known as base units ; derived units were built up from the base units using logical rather than empirical relationships while multiples and submultiples of both base and derived units were decimal based and identified by a standard set of prefixes.

" Although the psychological or epistemological specifics given by Mill through which we build our logical apparatus may not be completely warranted, his explanation still nonetheless manages to demonstrate that there is no way around Kant's a priori logic.

Although federally imposed conditions of reconstruction retrospectively seem logical, there was a widespread belief that southern Unionism would return the seceded states to the Union after the South's military power was broken.

Although some citizens believed Bowling Green was no longer the most practical or logical site for a new courthouse, the commissioners quickly decided to build the third courthouse on the site of the previous one in Bowling Green.

Although the stories were completely independent and shared no common characters they had some similarities that made it logical to combine them.

Although the concepts of a law or principle in nature is borderline to philosophy, and presents the depth to which mathematics can describe nature, scientific laws are considered from a scientific perspective and follow the scientific method ; they " serve their purpose " rather than " questioning reality " ( philosophical ) or " statements of logical absolution " ( mathematical ).

Although this may seem an odd layout, it is in fact logical.

Although he started with a " gut feeling " that Richard was innocent of murdering his nephews, the Princes in the Tower, Fields claims to have investigated the facts as he would for a client he was representing, and he structured the book like a lawyer's brief, identifying the evidence and then drawing the logical implications from the facts.

Although the Duke lost his political influence in the latter stages of the war he still possessed vast prestige abroad, yet his failure to communicate his innermost convictions to his allies or political masters means he must bear some responsibility for the continuance of the war beyond its logical conclusion.

Although this uses only two ( instead of three ) operands per instruction, correspondingly more instructions are then needed to effect various logical operations.

Although it has subsequently grown into another mainstream HOL variant, its logical foundations remain unusually simple.

Although at the time C. S. Lewis wrote Miracles, quantum mechanics ( and physical indeterminism ) was only in the initial stages of acceptance, he stated the logical possibility that if the physical world was proved to be indeterministic this would provide an entry ( interaction ) point into the traditionally viewed closed system, where a scientifically described physically probable / improbable event could be philosophically described as an action of a non physical entity on physical reality.

2. Although normally associated with the crime genre, the term " mystery fiction " may in certain situations refer to a completely different genre, where the focus is on supernatural or thriller mystery ( the solution doesn't have to be logical, and even no crime is involved ).

Deane and J. R. Thomson write this valid conclusion, “ The Book of Obadiah is occupied with one subject – the punishment of Edom for its cruel and unbrotherly love conduct towards Judah ...” One can link this idea of punishment to one of the major prophets “ Ezekiel ” who “... interprets the exile to Babylon and the destruction of Jerusalem as deserved punishments for the sins of those who themselves committed them .” Verses 3-7 in Obadiah explain to the reader the reason for the punishment theme, “ Confidence in one ’ s power, intelligence, allies, or the topographical features of one ’ s territory is often mentioned as an attribute of those who foolishly confront the Lord and are consequently punished .” Although destruction is vital to understanding Obadiah, it is of note to understand the destruction being a consequence of action.

Although in 2001 GDP grew by 10. 2 percent, this increase came on the heels of 2000, when, as a consequence of war with Ethiopia, GDP contracted by a staggering 13. 2 percent.

Although the war was a heavy burden on Iran and Iraq politically, economically, and socially, the most profound consequence of the war's prolongation on Iraq, was its impact on the patterns of Iraq's foreign relations.

Although the number of individuals sincerely espousing solipsism has been small, it is not uncommon for one philosopher to accuse another's arguments of entailing solipsism as an unwanted consequence, in a kind of reductio ad absurdum.

Although badly injured, Dutschke returned to political activism with the German Green Party before his death in a bathtub in 1979, as a consequence of his injuries.

Although Dirac did not at first fully appreciate what his own equation was telling him, his resolute faith in the logic of mathematics as a means to physical reasoning, his explanation of spin as a consequence of the union of quantum mechanics and relativity, and the eventual discovery of the positron, represents one of the great triumphs of theoretical physics, fully on a par with the work of Newton, Maxwell, and Einstein before him.

Although this interbreeding was of little consequence to the makeup of a Longhorn, it did alter color.

Although this at first appears to be a stronger statement, it is a direct consequence of the other form of the theorem, through the use of successive polynomial division by linear factors.

Although most globular proteins are able to assume their native state unassisted, chaperone-assisted folding is often necessary in the crowded intracellular environment to prevent aggregation ; chaperones are also used to prevent misfolding and aggregation that may occur as a consequence of exposure to heat or other changes in the cellular environment.

Although the number of individuals sincerely espousing solipsism has been small, it is not uncommon for one philosopher to accuse another's arguments of entailing solipsism as an unwanted consequence, in a kind of reductio ad absurdum.

Although smoking was banned on the subsurface sections of the London Underground in February 1985 ( a consequence of the Oxford Circus fire ), the fire was most probably caused by a traveller discarding a burning match, which fell down the side of the escalator onto the running track ( Fennell 1988, p. 111 ).

# Although rarely listed as an element, the common law required that " entry occur as a consequence of the breaking ".

Although GCOS has a basic architecture similar to that of the IBM 360 and subsequent operating systems with which it competed, it was also heavily influenced by projects such as MEDINET, Multics, and WWMCCS, and has inherited a strong security structure in consequence.

Although honeyeaters look and behave very much like other nectar-feeding passerines around the world ( such as the sunbirds and flowerpeckers ), they are unrelated, and the similarities are the consequence of convergent evolution.

Although he held many distinguished offices, some authorities assert that, at one time, he was under a cloud, in consequence of his being detected in selling of offices, and other corrupt practices.

Although foreign contacts were an inevitable consequence of the region's geography, their influence only served to enhance a vital and resilient popular culture.

Although Lippe was successful, Blofeld considered him unreliable, because of his childish clash with Bond and, as a consequence, Blofeld has Lippe killed.

Although the All-Star Game called for the defending Cup champion to host it, the game was held in Chicago Stadium in its second year as a consequence of the negotiations that set up the first game.

Although Herodotus presents the revolt as a consequence of Aristagoras and Histiaeus's personal motives, it is clear that Ionia must have been ripe for rebellion anyway.

Although current students and faculty members are adherents of many religions, as a consequence of its Protestant heritage, the VU has always placed a special emphasis on the social and cultural context in which it operates.

Although Herodotus presents the revolt as a consequence of Aristagoras's personal motives, it is clear that Ionia must have been ripe for rebellion anyway, the primary grievance being the tyrants installed by the Persians.

Although Wood saved her life, he later died from tetanus as a consequence of his injuries.

Although Sensei feels guilt for having caused his friend's death, he comes to believe that K's death was not a direct consequence of his unhappiness in love, but rather the same loneliness from which Sensei himself suffers.

Although there is no clear record of Joseph Smith teaching of Heavenly Mother publicly, several of Smith's contemporaries attributed the theology to him either directly, or as a consequence of his theological stance.