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 Seiten |
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Seite 12
... proved , and yet how much fmaller it may have been is not determined . " 66 " 66 66 A . it It has been said of the mufick of the spheres that it is so loud we cannot hear it and of a mathematical point , according to this explanation ...
... proved , and yet how much fmaller it may have been is not determined . " 66 " 66 66 A . it It has been said of the mufick of the spheres that it is so loud we cannot hear it and of a mathematical point , according to this explanation ...
Seite 24
... prove from the principles already laid " down and granted and affented unto for true and certain , by a “ clear chain of reasoning and deduction , that these lines AC and BC are each of them equal to AB and fo equal to one another ...
... prove from the principles already laid " down and granted and affented unto for true and certain , by a “ clear chain of reasoning and deduction , that these lines AC and BC are each of them equal to AB and fo equal to one another ...
Seite 25
... proved . " " THE second propofition is alfo a problem . " From a point given to draw a right line , which shall be equal " to another right line given . For the performing of this propo- " fition , it being a problem , there is need of ...
... proved . " " THE second propofition is alfo a problem . " From a point given to draw a right line , which shall be equal " to another right line given . For the performing of this propo- " fition , it being a problem , there is need of ...
Seite 27
... proved . " " Now though this way of demonstration and reasoning may " seem tedious and too long to detain the mind and attention in " the finding out the proprieties of quantities , yet ' twas the way - " made ufe of by the ancients ...
... proved . " " Now though this way of demonstration and reasoning may " seem tedious and too long to detain the mind and attention in " the finding out the proprieties of quantities , yet ' twas the way - " made ufe of by the ancients ...
Seite 33
... prove that this is agreeable to those principles which the nature of your science obliges you to adhere to . Thus in the third propofition it is totally inconsistent with the principles of this science to take the line C in a pair of ...
... prove that this is agreeable to those principles which the nature of your science obliges you to adhere to . Thus in the third propofition it is totally inconsistent with the principles of this science to take the line C in a pair of ...
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The Elements of Euclid: With Dissertations Intended to Assist and Encourage ... James Williamson,James Euclid Keine Leseprobe verfügbar - 2016 |
Häufige Begriffe und Wortgruppen
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
Beliebte Passagen
Seite 3 - Let it be granted that a straight line may be drawn from any one point to any other point.
Seite 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...
Seite 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.
Seite 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.
Seite 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.
Seite 86 - When you have proved that the three angles of every triangle are equal to two right angles...
Seite 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.
Seite 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.
Seite 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.
Seite 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...