Lectures on the Principles of Demonstrative MathematicsA. and C. Black, 1843 - 147 sider |
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Side 4
... assume the character of a spontaneous growth . Be- sides , the mode by which such truths are generally ac- quired is the very reverse of the order of discovery . They 3 are introduced to us as fitting into facts with which 4 LECTURE I.
... assume the character of a spontaneous growth . Be- sides , the mode by which such truths are generally ac- quired is the very reverse of the order of discovery . They 3 are introduced to us as fitting into facts with which 4 LECTURE I.
Side 15
... weight ; assumed properties of motion ; the support of heavy bo- Suidas in voce Anax . + Plutarch de exil . quoted by Montucla , i . 3 . dies by water ; the phenomena of burning mirrors ; ON THE IMPORTANCE OF PRINCIPLES . 15.
... weight ; assumed properties of motion ; the support of heavy bo- Suidas in voce Anax . + Plutarch de exil . quoted by Montucla , i . 3 . dies by water ; the phenomena of burning mirrors ; ON THE IMPORTANCE OF PRINCIPLES . 15.
Side 22
... assumed the form of Mathematical Demonstra- tion . * Whatever might have been known of the rudi- ments of grammar , of rhetoric , and of logic , in early times , it is exceedingly improbable that they formed any part of the ground ...
... assumed the form of Mathematical Demonstra- tion . * Whatever might have been known of the rudi- ments of grammar , of rhetoric , and of logic , in early times , it is exceedingly improbable that they formed any part of the ground ...
Side 25
... assumed and comparative universality , i . e . one derived from induction . " To this extent , in- deed , what I have laid down agrees with the doctrines of this philosopher , who remarks , in the introduction to the Critique of Pure ...
... assumed and comparative universality , i . e . one derived from induction . " To this extent , in- deed , what I have laid down agrees with the doctrines of this philosopher , who remarks , in the introduction to the Critique of Pure ...
Side 34
... assumes that bodies tend towards the centre of the earth : -Since they may or may not do so , his admitting that they do is an hypothesis . Now this differs altogether from one of the principles of geometry , and the two must not be ...
... assumes that bodies tend towards the centre of the earth : -Since they may or may not do so , his admitting that they do is an hypothesis . Now this differs altogether from one of the principles of geometry , and the two must not be ...
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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...