Lectures on the Principles of Demonstrative MathematicsA. and C. Black, 1843 - 147 páginas |
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Página 80
... multiples . This in- troduces number into our arguments , as the representa- tion of the amount of multiplication . Nor is this the only way in which number is mixed up with geometric researches . A very important branch of geometry is ...
... multiples . This in- troduces number into our arguments , as the representa- tion of the amount of multiplication . Nor is this the only way in which number is mixed up with geometric researches . A very important branch of geometry is ...
Página 84
... multiple nor a measure of the consequent . We can , however , estimate their relative magnitude by referring both to ... multiples equal . Lastly , incommensurable magnitudes are incapable of division into parts of the same size . The ...
... multiple nor a measure of the consequent . We can , however , estimate their relative magnitude by referring both to ... multiples equal . Lastly , incommensurable magnitudes are incapable of division into parts of the same size . The ...
Página 87
... multiples , I deem it consistent with strict geo- metry to retain this affection in its most general form as the ... multiple of the second that the third is of the fourth . " * Truths of this kind are clear by their own light from ...
... multiples , I deem it consistent with strict geo- metry to retain this affection in its most general form as the ... multiple of the second that the third is of the fourth . " * Truths of this kind are clear by their own light from ...
Página 88
... multiple used in his definition for " taken a number of times , " does exclude taken once only . Indeed , it is quite certain that he did not , for had he done so , he must have seen that his demonstration of Prop . 8 is incomplete ...
... multiple used in his definition for " taken a number of times , " does exclude taken once only . Indeed , it is quite certain that he did not , for had he done so , he must have seen that his demonstration of Prop . 8 is incomplete ...
Página 89
... multiple , nor a multiple and part of the second , ( or vice versa ) . If the magnitudes are commensurable , it will be seen that the first is a multiple and parts † of the second , or vice versâ . That is , if the smaller be pro ...
... multiple , nor a multiple and part of the second , ( or vice versa ) . If the magnitudes are commensurable , it will be seen that the first is a multiple and parts † of the second , or vice versâ . That is , if the smaller be pro ...
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Lectures on the Principles of Demonstrative Mathematics Philip Kelland Sin vista previa disponible - 2019 |
Términos y frases comunes
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
Pasajes populares
Página 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.
Página 38 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Página 52 - Any two sides of a triangle are together greater than the third side.
Página 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...
Página 122 - Whatever form is algebraically equivalent to another when expressed in general symbols, must continue to be equivalent whatever those symbols denote.
Página 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.
Página 38 - Of four-sided figures, a square is that which has all its sides equal, and all its angles right angles.
Página 67 - Parallel straight lines are such as are in the same plane, and which being produced ever so far both ways, do not meet.
Página 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.
Página 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...