Lectures on the Principles of Demonstrative MathematicsA. and C. Black, 1843 - 147 sider |
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Side 42
... true in this way because there is no reason for believing it otherwise , or , if you please , because there is ample reason for believing it so . Les- lie , † for instance , proves the equality of triangles whose sides are equal each to ...
... true in this way because there is no reason for believing it otherwise , or , if you please , because there is ample reason for believing it so . Les- lie , † for instance , proves the equality of triangles whose sides are equal each to ...
Side 44
... true , requiring no limitation but that things * On Axioms . which are equal mutually coincide is true only in things 44 LECTURE II .
... true , requiring no limitation but that things * On Axioms . which are equal mutually coincide is true only in things 44 LECTURE II .
Side 45
Philip Kelland. which are equal mutually coincide is true only in things of a similar species : such as a right line when compared with a right line , or one circumference with another of the same circle . " * Barrow , who adopts the ...
Philip Kelland. which are equal mutually coincide is true only in things of a similar species : such as a right line when compared with a right line , or one circumference with another of the same circle . " * Barrow , who adopts the ...
Side 52
... true you may deduce from my defining pro- perty such other affections as to convey the idea to your mind . You may prove from it that " a straight line is the shortest distance between two points . " * But this is to effect nothing ...
... true you may deduce from my defining pro- perty such other affections as to convey the idea to your mind . You may prove from it that " a straight line is the shortest distance between two points . " * But this is to effect nothing ...
Side 55
... true the Pythagoreans ‡ expressed it as " an unit ( or monad ) having position , " which , by a slight change , makes the definition we have adopted . They did so , how- ever , I believe , not for the purpose of annexing more de- finite ...
... true the Pythagoreans ‡ expressed it as " an unit ( or monad ) having position , " which , by a slight change , makes the definition we have adopted . They did so , how- ever , I believe , not for the purpose of annexing more de- finite ...
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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 |
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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...