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 sider |
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Resultat 1-5 av 86
Side 43
... demonstrated . It was then obferved that the fuppofition was too complicated for this purpose ; because not only DE and DF were to be equal to each other and to AB and AC , for this might have been al- lowed ; but also the angles ...
... demonstrated . It was then obferved that the fuppofition was too complicated for this purpose ; because not only DE and DF were to be equal to each other and to AB and AC , for this might have been al- lowed ; but also the angles ...
Side 45
... demonstrate that all the angles of an equilateral triangle are equal ; for instance suppose the angles of the equilateral triangle ACB defcribed in the first propo- fition . Produce CA , and CB ; and the fame conftruction and de ...
... demonstrate that all the angles of an equilateral triangle are equal ; for instance suppose the angles of the equilateral triangle ACB defcribed in the first propo- fition . Produce CA , and CB ; and the fame conftruction and de ...
Side 46
... demonstrated that AB is equal to DE , therefore by the first common notion DE is equal to DF ; and no doubt some authors would produce this as a demon- a demonstration of the fixth propofition ; but it is 46 DISSERTATION II .
... demonstrated that AB is equal to DE , therefore by the first common notion DE is equal to DF ; and no doubt some authors would produce this as a demon- a demonstration of the fixth propofition ; but it is 46 DISSERTATION II .
Side 48
... one another ; that is , that it is impoffible for AC to be equal to AD ; and at the fame time , BC to be equal to BD . Which was to be demonstrated . It It will be a very neceffary and useful task for 48 DISSERTATION II .
... one another ; that is , that it is impoffible for AC to be equal to AD ; and at the fame time , BC to be equal to BD . Which was to be demonstrated . It It will be a very neceffary and useful task for 48 DISSERTATION II .
Side 65
... demonstrating , I fhall conclude this chapter with a few inftances tending more directly to explain what it is . And his great peculiarity feems to be a determined refolution always to refer directly to fome principle , and never trust ...
... demonstrating , I fhall conclude this chapter with a few inftances tending more directly to explain what it is . And his great peculiarity feems to be a determined refolution always to refer directly to fome principle , and never trust ...
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The Elements of Euclid: With Dissertations Intended to Assist and Encourage ... James Williamson,James Euclid Ingen forhåndsvisning tilgjengelig - 2016 |
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 3 - Let it be granted that a straight line may be drawn from any one point to any other point.
Side 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...
Side 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.
Side 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.
Side 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.
Side 86 - When you have proved that the three angles of every triangle are equal to two right angles...
Side 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.
Side 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.
Side 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.
Side 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...