Lectures on the Principles of Demonstrative MathematicsA. and C. Black, 1843 - 147 páginas |
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Página 5
... appears to me much more calculated to direct our judg- ment aright . I would , in fact , endeavour to recal to your ... appear something refined , if not marvellous . There is ON THE IMPORTANCE OF PRINCIPLES . 5.
... appears to me much more calculated to direct our judg- ment aright . I would , in fact , endeavour to recal to your ... appear something refined , if not marvellous . There is ON THE IMPORTANCE OF PRINCIPLES . 5.
Página 6
Philip Kelland. appear something refined , if not marvellous . There is no doubt that every thinking person can call to ... appears to unite the two theories ; Euclid ¶ adheres to the former ; whilst Aristotle ** adopts ( but not firmly ) ...
Philip Kelland. appear something refined , if not marvellous . There is no doubt that every thinking person can call to ... appears to unite the two theories ; Euclid ¶ adheres to the former ; whilst Aristotle ** adopts ( but not firmly ) ...
Página 8
... appear to be certain : one , that the science did not exist in Greece prior to the time of Thales ; * and the other , that from that period it dates its rise . Until very lately , it was the prevailing , if not the universal opinion ...
... appear to be certain : one , that the science did not exist in Greece prior to the time of Thales ; * and the other , that from that period it dates its rise . Until very lately , it was the prevailing , if not the universal opinion ...
Página 10
... of their own poverty , and of their predecessors ' riches . " In replying to this argument , which appears to have been deemed satisfactory by some of the best recent wri- * P. 159 . ters , * I remark , 1. that it is 10 LECTURE I.
... of their own poverty , and of their predecessors ' riches . " In replying to this argument , which appears to have been deemed satisfactory by some of the best recent wri- * P. 159 . ters , * I remark , 1. that it is 10 LECTURE I.
Página 15
... appears possible . In physics the an- cients saw no distant limit to reach which appeared worthy of toil . The simplest theorems of equilibrium and weight ; assumed properties of motion ; the support of heavy bo- Suidas in voce Anax . + ...
... appears possible . In physics the an- cients saw no distant limit to reach which appeared worthy of toil . The simplest theorems of equilibrium and weight ; assumed properties of motion ; the support of heavy bo- Suidas in voce Anax . + ...
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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...