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 Prevails |
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Page 3
... properties , which had led him from common notions to the right understanding of fo fublime a specu- lation . A book therefore , if this reafoning be juft , which would be proper for a learner would be fit for nobody elfe : and the ...
... properties , which had led him from common notions to the right understanding of fo fublime a specu- lation . A book therefore , if this reafoning be juft , which would be proper for a learner would be fit for nobody elfe : and the ...
Page 5
... properties of ftraight lines only , and true of nothing else . For without this precaution he will undoubtedly be liable to have the diftich quoted in the last chapter applied to him . And any tincture of the budibraftic genius ...
... properties of ftraight lines only , and true of nothing else . For without this precaution he will undoubtedly be liable to have the diftich quoted in the last chapter applied to him . And any tincture of the budibraftic genius ...
Page 10
... properties do follow , which may be called geometrical to diftinguifh them from the others . The definition of a circle , given by Euclid , is of this kind for all the properties of a circle follow as confequences from it . And here the ...
... properties do follow , which may be called geometrical to diftinguifh them from the others . The definition of a circle , given by Euclid , is of this kind for all the properties of a circle follow as confequences from it . And here the ...
Page 14
... properties of lines and figures , which are not true , but upon the fuppofition that the lines are in the fame plane , as I fhall have occafion to obferve . And the plane rectilineal angle is the inclination of two straight lines to one ...
... properties of lines and figures , which are not true , but upon the fuppofition that the lines are in the fame plane , as I fhall have occafion to obferve . And the plane rectilineal angle is the inclination of two straight lines to one ...
Page 21
... properties of the afym- ptotes of the Hyperbola & c ; if my intention had been to raise the admiration of the reader , rather than to fix his attention . Having therefore refolved to facrifice every ornament to this fingle confide ...
... properties of the afym- ptotes of the Hyperbola & c ; if my intention had been to raise the admiration of the reader , rather than to fix his attention . Having therefore refolved to facrifice every ornament to this fingle confide ...
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The Elements of Euclid: With Dissertations Intended to Assist and Encourage ... James Williamson,James Euclid No preview available - 2016 |
Common terms and phrases
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
Popular passages
Page 3 - Let it be granted that a straight line may be drawn from any one point to any other point.
Page 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...
Page 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.
Page 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.
Page 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.
Page 86 - When you have proved that the three angles of every triangle are equal to two right angles...
Page 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.
Page 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.
Page 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.
Page 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...