“Complete knowledge of the nature of an analytic function must also include insight into its behavior for imaginary values of the arguments. Often the latter is indispensable even for a proper appreciation of the behavior of the function for real arguments. It is therefore essential that the original determination of the function concept be broadened to a domain of magnitudes which includes both the real and the imaginary quantities, on an equal footing, under the single designation complex numbers.” RealValuesNumbersEqualEssentialsBehaviorConceptsDeterminationArgumentLogicFunctionOriginalsComplexesAppreciationInsightCertaintyUncertaintyReasoningLatterQuantityImaginaryIndispensableDomainMagnitudeOntologyAnalyticsDesignationComplex Numbers Author:Carl Friedrich Gauss
“The problem of distinguishing prime numbers from composite numbers and of resolving the latter into their prime factors is known to be one of the most important and useful in arithmetic.” ImportantProblemNumbersKnownFactorsLatterPrimeArithmeticCompositesPrime Numbers Author:Carl Friedrich Gauss
“As is well known the principle of virtual velocities transforms all statics into a mathematical assignment, and by D'Alembert's principle for dynamics, the latter is again reduced to statics. Although it is is very much in order that in gradual training of science and in the instruction of the individual the easier precedes the more difficult, the simple precedes the more complicated, the special precedes the general, yet the min, once it has arrived at the higher standpoint, demands the reverse process whereby all statics appears only as a very special case of mechanics.” WellsScienceOrderIndividualProcessDifficultSimpleKnownPrinciplesCasesSpecialTheoryHigherEasierDemandTrainingComplicatedMathematicalLatterInstructionReverseWell KnownMechanicStandpointAssignmentsDynamicsVelocity Author:Carl Friedrich Gauss
“The problem of distinguishing prime numbers from composite numbers and of resolving the latter into their prime factors is known to be one of the most important and useful in arithmetic. It has engaged the industry and wisdom of ancient and modern geometers to such an extent that it would be superfluous to discuss the problem at length. ... Further, the dignity of the science itself seems to require that every possible means be explored for the solution of a problem so elegant and so celebrated.” MeanImportantProblemSeemsWould BeNumbersKnownModernIndustrySolutionsDignityAncientFactorsEngagedLatterLengthPrimeElegantSuperfluousArithmeticCompositesPrime Numbers Author:Carl Friedrich Gauss
