Observations on the Nature of Demonstrative Evidence: With an Explanation of Certain Difficulties Occurring in the Elements of Geometry, and Reflections on LanguageJ. Johnson, 1793 - 172 sider |
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Side 20
... axiom as it is called , upon which the de- monftration is founded , viz . the 10th in Simfon's edition , may be regarded as the corner - stone of geometrical reasoning . The proposition is this : If two triangles have two fides of the ...
... axiom as it is called , upon which the de- monftration is founded , viz . the 10th in Simfon's edition , may be regarded as the corner - stone of geometrical reasoning . The proposition is this : If two triangles have two fides of the ...
Side 26
... to measure fimple lengths . I would rather choose to appeal to thefe two experiments , than to the third axiom placed before Euclid's elements , viz . that if if equals be taken from equals , the remainders will 26 OBSERVATIONS ON.
... to measure fimple lengths . I would rather choose to appeal to thefe two experiments , than to the third axiom placed before Euclid's elements , viz . that if if equals be taken from equals , the remainders will 26 OBSERVATIONS ON.
Side 27
... axioms in the feventh chapter of his fourth book . In fact , they are only founded upon the induction of particular experiments and obfervations ; and until that induction be compleat , we can never be convinced of their truth . They do ...
... axioms in the feventh chapter of his fourth book . In fact , they are only founded upon the induction of particular experiments and obfervations ; and until that induction be compleat , we can never be convinced of their truth . They do ...
Side 43
... AXIOMS were probably in- troduced , in confequence of that perverfion of the human understanding , which the study of generals occafioned . " The rules " established in the fchools , fays Mr. “ Locke , that all reasonings are ex præ- 66 ...
... AXIOMS were probably in- troduced , in confequence of that perverfion of the human understanding , which the study of generals occafioned . " The rules " established in the fchools , fays Mr. “ Locke , that all reasonings are ex præ- 66 ...
Side 44
... axioms are not the truths first known ; and , 2. That the other parts of our knowledge do not depend upon them ; and then challenges any fcholaftic man , to lay before him the whole frame and fyftem of any fcience fo built upon axioms ...
... axioms are not the truths first known ; and , 2. That the other parts of our knowledge do not depend upon them ; and then challenges any fcholaftic man , to lay before him the whole frame and fyftem of any fcience fo built upon axioms ...
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Observations on the Nature of Demonstrative Evidence: With an Explanation of ... Thomas Beddoes Ingen forhåndsvisning tilgjengelig - 2018 |
Vanlige uttrykk og setninger
abſtract againſt agreement or difagreement alfo alſo angles Ariſtotle axiom becauſe befides cafe caufe cauſe cife compariſon complex term confideration definition demonſtration derived diftinct diſcovery diſtance equal eſtabliſhed Euclid evidence exiſt experiments exprefs faid fame fatisfied fays fcience fecond feems fenfes ferve fhall fhew fhewn fide fignification fimple fince firft firſt fome fomething ftill ftraight lines fubject fuch fufficient fuppofe fyftem geometry Greek language guage himſelf ideas impoffible inftances interfections intuitive knowledge itſelf juft juſt knowledge leaſt lefs Lennep leſs Lord Monboddo mathematical meaſure mind miſtake moſt muft muſt neceffary neceffity noun obfervation object occafion paffage parallel lines perceive perception perfon philofophy phyfical Plato poffible preſent pronouns propofition purpoſe reaſoning refult reſpect ſay Scheid ſcholars ſeem ſenſe ſhall ſhould ſpeech ſtate ſtill ſtudy ſuch ſuppoſe ſyſtem thefe themſelves theſe thing thofe THOMAS BEDDOES thoſe tion triangle truth underſtanding univerfality uſe Valckenaer verb verités whoſe words
Populære avsnitt
Side 168 - All, and the feweft ideas more than thofe we would communicate : and then by the help of the Prepofition, we either make up the deficiency in the one cafe, or retrench the fuperfluity in the other. For inftance, i. " A Houfe WITH a Party-wall? z. " A Houfe WITHOUT a roof" In the firft inftance, the complex term is deficient : The Prepofition directs to add what is wanting.
Side 35 - 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 66 - ... often so late before some unusual qualities come in the way, that there are few men that cannot recollect the beginning of their acquaintance with them: and if it were worth while...
Side 82 - ... and repugnancy, of any of our ideas. In this alone it consists. Where this perception is, there is knowledge ; and where it is not, there, though we may fancy, guess, or believe, yet we always come short of knowledge. For, when we know that white is not black, what do we else but perceive that these two ideas do not agree!
Side 37 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Side 85 - ... by an immediate view and comparing them do it: because the three angles of a triangle cannot be brought at once and be compared with any one or two angles; and so of this the mind has no immediate, no intuitive knowledge. In this case the mind is fain to find out some other angles, to which the three angles of a triangle have an equality; and, finding those equal to two right ones, comes to know their equality to two right ones.
Side 167 - To supply, therefore, the place of the complex terms which are wanting in a language, is the preposition employed...
Side 139 - That a fyftem of etymology was to be formed, by which the whole language was to be derived from certain primitive founds, or radical words. Then cafes, genders, and numbers, were to be invented ; which anfwered a double purpofe, both of expreffing different relations and other circumftances of things, and of connecting words together in fyntax. Then tenfes and moods of verbs were to be contrived, by which the circumftance of time, and the affections or difpofitions of the human mind with refpect:...
Side 82 - I mean to assert a truth which is as independent of my constitution, as the equality of the three angles of a triangle to two right angles...
Side 52 - If a ftraight line meets two ftraight lines, fo as to make the " two interior angles on the fame fide of it taken together lefs