The Elements of Euclid: With Dissertations Intended to Assist and Encourage a Critical Examination of These Elements as the Most Effectual Means of Establishing a Juster Taste Upon Mathematical Subjects Than that which at Present PrevailsPrinted at the Clarendon Press, 1781 - 309 σελίδες |
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Σελίδα
... produced through a length of ages , operating in every quarter of the globe is not fo eafily to be conceived . It has indeed been alledged , that the improvements afcribed to the cultivation of this fcience , have been often the effect ...
... produced through a length of ages , operating in every quarter of the globe is not fo eafily to be conceived . It has indeed been alledged , that the improvements afcribed to the cultivation of this fcience , have been often the effect ...
Σελίδα 12
... produce a line or quantity ; fo the multiplication " of noughts or cifers will never produce a number ; and as the “ addition of nevers cannot make time , fo the aggregate of rests " cannot produce motion . So that all these may not ...
... produce a line or quantity ; fo the multiplication " of noughts or cifers will never produce a number ; and as the “ addition of nevers cannot make time , fo the aggregate of rests " cannot produce motion . So that all these may not ...
Σελίδα 14
... furface as this , which meet together but are not in the fame direction . They might be inclined to one another so that when produced they would interfect or or cross one another ; but until they have met 14 . DISSERTATION I.
... furface as this , which meet together but are not in the fame direction . They might be inclined to one another so that when produced they would interfect or or cross one another ; but until they have met 14 . DISSERTATION I.
Σελίδα 17
... produce one fcientific conftruction . But Euclid has acted with more judgement , and never would be acceffory to the opening a door for admitting upon his fcientific ftage the whole tribe of mechanics , with the several implements of ...
... produce one fcientific conftruction . But Euclid has acted with more judgement , and never would be acceffory to the opening a door for admitting upon his fcientific ftage the whole tribe of mechanics , with the several implements of ...
Σελίδα 26
... produce DB to F ; then upon the center " D and distance DG draw the circle GKL , then as before , pro- " duce the line DA to E ; there shall AL be the line required to " be drawn from the point A equal to the given line BC . " 66 " This ...
... produce DB to F ; then upon the center " D and distance DG draw the circle GKL , then as before , pro- " duce the line DA to E ; there shall AL be the line required to " be drawn from the point A equal to the given line BC . " 66 " This ...
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The Elements of Euclid: With Dissertations Intended to Assist and Encourage ... James Williamson,James Euclid Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD alfo alſo angle ABC angle BAC angle contained angle equal apply itſelf bafe baſe BC is equal Book certainly circle ABC circumference common notion confequences conft conftruction cut in halves demonftrated deſcribed diſtance drawn equal angles equiangular equilateral equimultiples Euclid exceed faid fame manner fame multiple fame parallels fame ratio fame reaſon fecond fegment fhall fides fimilar fince firſt fome fquare ftraight line BC fuch fuppofe fuppofition given rectilineal given ſtraight line Gnomon greater hath himſelf impoffible infcribed joined lefs leſs let the ftraight magnitudes moſt muſt neceffary parallelogram PROP propofition proportionals purpoſe reader reaſon rectangle contained rectilineal figure remaining angle remaining fides right angles ſame ſay ſhall ſhould ſome ſquare ſtraight line AB ſubject ſuch ſuppoſe taken theſe thoſe tiple triangle ABC underſtand uſe Wherefore becauſe
Δημοφιλή αποσπάσματα
Σελίδα 3 - Let it be granted that a straight line may be drawn from any one point to any other point.
Σελίδα 47 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line. Let...
Σελίδα 68 - If a straight line drawn through the centre of a circle bisect a straight line in it which does not pass through the centre, it shall cut it at right angles : and if it cut it at right angles, it shall bisect it.
Σελίδα 45 - ABG ; (vi. 1.) therefore the triangle ABC has to the triangle ABG the duplicate ratio of that which BC has to EF: but the triangle ABG is equal to the triangle DEF; therefore also the triangle ABC has to the triangle DEF the duplicate ratio of that which BC has to EF. Therefore similar triangles, &c.
Σελίδα 15 - When a straight line set up on a straight line makes the adjacent angles equal to one another, each of the equal angles is right, and the straight line standing on the other is called a perpendicular to that on which it stands.
Σελίδα 86 - When you have proved that the three angles of every triangle are equal to two right angles...
Σελίδα 88 - EA : and because AD is equal to DC, and DE common to the triangles ADE, CDE, the two sides AD, DE are equal to the two CD, DE, each to each ; and the angle ADE is equal to the angle CDE, for each of them is a right angle ; therefore the base AE is equal (4.
Σελίδα 42 - If four straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means ; And if the rectangle contained by the extremes be equal to the rectangle contained by the means, the four straight lines are proportionals. Let the four straight lines, AB, CD, E, F, be proportionals, viz.
Σελίδα 109 - Draw two diameters AC, BD of the circle ABCD, at right angles to one another; and through the points A, B. C, D, draw (17.
Σελίδα 8 - GB is equal to E, and CK to F ; therefore AB is the same multiple of E, that KH is of F: But AB...