Observations on the nature of demonstrative evidence: with an explanation of certain difficulties occurring in the elements of geometry, and reflections on language

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J. Johnson, 1793 - Greek language - 172 pages
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Page 170 - 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.
Page 37 - 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.
Page 68 - ... 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...
Page 84 - ... 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!
Page 39 - 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.
Page 87 - ... 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.
Page 169 - To supply, therefore, the place of the complex terms which are wanting in a language, is the preposition employed...
Page 141 - 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:...
Page 84 - 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...
Page 54 - 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

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