Lectures on the Principles of Demonstrative MathematicsA. and C. Black, 1843 - 147 sider |
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Side viii
... magnitudes - proportion - Euclid's doctrine how developed - arithmetical ideas - lead to a common pro- perty - that property made the definition - necessity for the sole depen- dence of the results on the conditions in order that an ...
... magnitudes - proportion - Euclid's doctrine how developed - arithmetical ideas - lead to a common pro- perty - that property made the definition - necessity for the sole depen- dence of the results on the conditions in order that an ...
Side 44
... Magnitudes which coincide , that is , which exactly fill the same space , are equal to one another . " Relative to this axiom , the utmost diversity of opinion exists and as it lies at the foundation of method , I think myself warranted ...
... Magnitudes which coincide , that is , which exactly fill the same space , are equal to one another . " Relative to this axiom , the utmost diversity of opinion exists and as it lies at the foundation of method , I think myself warranted ...
Side 46
... magnitudes , and are they not secondarily transferred from them to other quanti- ties ? Motion is represented by the ... magnitude even in thought . or moon . 3 and 4. Relative to these positions , all that I shall say is , that if we ...
... magnitudes , and are they not secondarily transferred from them to other quanti- ties ? Motion is represented by the ... magnitude even in thought . or moon . 3 and 4. Relative to these positions , all that I shall say is , that if we ...
Side 48
... magnitudes taken together do mutually fill the same space at the same time , as in Prop . 4 . 2. So that they coincide successively by parts . 3. So that all the elements of the two succeed in the same place , and neither varies the ...
... magnitudes taken together do mutually fill the same space at the same time , as in Prop . 4 . 2. So that they coincide successively by parts . 3. So that all the elements of the two succeed in the same place , and neither varies the ...
Side 50
Philip Kelland. the simplest and primary exhibition of equality , their re- lative magnitudes are compared . If I am called upon to say whether Euclid regards congruity as a species of equality or not , I reply in the affirmative . He ...
Philip Kelland. the simplest and primary exhibition of equality , their re- lative magnitudes are compared . If I am called upon to say whether Euclid regards congruity as a species of equality or not , I reply in the affirmative . He ...
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Lectures on the Principles of Demonstrative Mathematics Philip Kelland Uten tilgangsbegrensning - 1843 |
Lectures on the Principles of Demonstrative Mathematics Philip Kelland Ingen forhåndsvisning tilgjengelig - 2019 |
Vanlige uttrykk og setninger
admit adopted affections algebra amongst ancients appears applied Apuleius Archimedes argument Aristotle arithmetical arithmetical derivation assume assumption axiom Barrow circle Clavius coincide comparison conceive conception conclusions congruity consequence defined Differential Calculus difficulty discovery doctrine Elements equal equation Euclid Euclid's definition evidence existence express extension fact figure finite former four magnitudes fourth geometry idea important Laërt latter Lect lecture lity Math mathematical method method of exhaustions metical mind multiple nature necessity notation notion objection operations parallels Peacock perty philosophers plane Plato Playfair ples Plutarch possess postulate present PRINCIPLES OF DEMONSTRATIVE Proclus Prop proportion proportionality proposition Pythagoras quantities ratio reason rectilinear reductio ad absurdum reference remark require right angles rule of signs senses simple Simson space square straight line symbols Thales theorem Theory of Equations thing Timæus tion tiple treatise triangle truth whilst writers
Populære avsnitt
Side 64 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle; and the straight line which stands on the other is called a perpendicular to it.
Side 38 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Side 52 - Any two sides of a triangle are together greater than the third side.
Side 96 - ... of the second and fourth ; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth: or, if the multiple of the first be equal to that of the second, the multiple of the third is also equal to that of the fourth...
Side 122 - Whatever form is algebraically equivalent to another when expressed in general symbols, must continue to be equivalent whatever those symbols denote.
Side 17 - It is certain that from its completeness, uniformity and faultlessness, from its arrangement and progressive character, and from the universal adoption of the completest and best line of argument, Euclid's " Elements " stand preeminently at the head of all human productions.
Side 38 - Of four-sided figures, a square is that which has all its sides equal, and all its angles right angles.
Side 67 - Parallel straight lines are such as are in the same plane, and which being produced ever so far both ways, do not meet.
Side 88 - But when four magnitudes are proportionals, if the first be greater than the third, the second is greater than the fourth ; and if equal, equal; if less, less; (v.
Side 25 - That all our cognition," he says, " begins with experience, there is not any doubt ; for how otherwise should the faculty of cognition be awakened into exercise, if this did not occur through objects which affect our senses...