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 19
Side 11
... said to have as " many parts as the fore - mentioned ; for fince all quantity is divi- " fible in infinitum , the least quantity , may be divided as often as " the greatest , and therefore whatsoever is divifible must have parts , and ...
... said to have as " many parts as the fore - mentioned ; for fince all quantity is divi- " fible in infinitum , the least quantity , may be divided as often as " the greatest , and therefore whatsoever is divifible must have parts , and ...
Side 12
... 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 , it may be said , that it is fo fimple it is impoffible to comprehend it . This no doubt , muft ...
... 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 , it may be said , that it is fo fimple it is impoffible to comprehend it . This no doubt , muft ...
Side 19
... said to be contained by GA , AB . F D B A C G E and the Again FBC and BCG are alfo two distinct triangles three fides of the triangle FBC are BF , FC , CB and the three angles BFC , FCB , CBF : and the three fides of the triangle BCG ...
... said to be contained by GA , AB . F D B A C G E and the Again FBC and BCG are alfo two distinct triangles three fides of the triangle FBC are BF , FC , CB and the three angles BFC , FCB , CBF : and the three fides of the triangle BCG ...
Side 24
... said , all such lines must be equal . Next BA and BC must 86 upon the fame account be equal to one another , because they " alfo are lines drawn from the center B to the circumference " ACE : Therefore both AC and BC are equal to AB ...
... said , all such lines must be equal . Next BA and BC must 86 upon the fame account be equal to one another , because they " alfo are lines drawn from the center B to the circumference " ACE : Therefore both AC and BC are equal to AB ...
Side 36
... said to be the confequences which will certainly follow from the foremen- tioned fuppofitions . But it will be too much for the learner to attempt the whole demonstration at once ; let us therefore see what confequence will follow from ...
... said to be the confequences which will certainly follow from the foremen- tioned fuppofitions . But it will be too much for the learner to attempt the whole demonstration at once ; let us therefore see what confequence will follow from ...
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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...