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 51
Side 67
... cut in halves , which cannot be done until the line is fixed ; but then I immediately perceive that , notwith- ftanding this , as no confequence is deduced from AC's having any particular length , the demonstration is nevertheless ...
... cut in halves , which cannot be done until the line is fixed ; but then I immediately perceive that , notwith- ftanding this , as no confequence is deduced from AC's having any particular length , the demonstration is nevertheless ...
Side 70
... cut the angle at the vertex in halves and the thing is done ; never confidering that the doing of this , requires it to be firft proved that the angles at the base of an ifofceles triangle are equal to one another . The only ...
... cut the angle at the vertex in halves and the thing is done ; never confidering that the doing of this , requires it to be firft proved that the angles at the base of an ifofceles triangle are equal to one another . The only ...
Side 86
... halved upon the fame principles . CHA P. IV . In which is fhewn the abfurdity of applying numbers to illuftrate the propofitions in this book . IF you draw two indefinite straight lines at right angles to each other , and cut off from ...
... halved upon the fame principles . CHA P. IV . In which is fhewn the abfurdity of applying numbers to illuftrate the propofitions in this book . IF you draw two indefinite straight lines at right angles to each other , and cut off from ...
Side 90
... cutting which in halves will find the center . This being found it feems both natural and neceffary to confider whether the circumference of a circle be totally and effentially dif- ferent from a ftraight line ; which it is proved to be ...
... cutting which in halves will find the center . This being found it feems both natural and neceffary to confider whether the circumference of a circle be totally and effentially dif- ferent from a ftraight line ; which it is proved to be ...
Side 12
... cut a given rectilineal angle in halves . Let the given rectilineal angle be , the angle contained by BAC : it is required to cut it in halves . Let the point D be taken , any accidental point in the ftraight line AB ; and let the ...
... cut a given rectilineal angle in halves . Let the given rectilineal angle be , the angle contained by BAC : it is required to cut it in halves . Let the point D be taken , any accidental point in the ftraight line AB ; and let the ...
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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...