Lectures on the Principles of Demonstrative MathematicsA. and C. Black, 1843 - 147 sider |
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Side 26
... terms cogitation ( davoia , ) and which , he says , " bears the same relation to intelligibles that sense does to sensibles . " The Platonists , in allotting to mathematical subjects a middle nature between intelligibles and sensibles ...
... terms cogitation ( davoia , ) and which , he says , " bears the same relation to intelligibles that sense does to sensibles . " The Platonists , in allotting to mathematical subjects a middle nature between intelligibles and sensibles ...
Side 31
... term . And although the opposite surface comes not to the eye , yet it readily presents itself to the mind by the aid which our conceptions of infinite space afford . The composition of space is represented by the composi- tion of ...
... term . And although the opposite surface comes not to the eye , yet it readily presents itself to the mind by the aid which our conceptions of infinite space afford . The composition of space is represented by the composi- tion of ...
Side 35
... terms . 2. A definition consequential is the product of axioms expressing , not the nature , but some affections of the ... term definition in accordance with the language of others . In the present Lecture , we shall be conversant only ...
... terms . 2. A definition consequential is the product of axioms expressing , not the nature , but some affections of the ... term definition in accordance with the language of others . In the present Lecture , we shall be conversant only ...
Side 36
... terms borrowed from and referring to the senses , in order to convey to another a like perfect idea . Thus , to define straight , we refer to what the eye can contemplate , not that it ever beholds what is perfectly straight , but that ...
... terms borrowed from and referring to the senses , in order to convey to another a like perfect idea . Thus , to define straight , we refer to what the eye can contemplate , not that it ever beholds what is perfectly straight , but that ...
Side 37
... terms be sufficient to convey it completely . 2. That they do not express more : or are not super- Auous . 3. That it be impossible they should express any thing else or that they are unambiguous . And 4. That they have a necessary ...
... terms be sufficient to convey it completely . 2. That they do not express more : or are not super- Auous . 3. That it be impossible they should express any thing else or that they are unambiguous . And 4. That they have a necessary ...
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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...