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 |
From inside the book
Page 82
the rectangle with the fide of any other of this infinite variety of parallelograms juft mentioned ; as for ... to the two lines about one of the angles ; are faid to contain the space , as well as the particular lines which make two ...
the rectangle with the fide of any other of this infinite variety of parallelograms juft mentioned ; as for ... to the two lines about one of the angles ; are faid to contain the space , as well as the particular lines which make two ...
Page 84
With Dissertations Intended to Assist and Encourage a Critical Examination of These Elements as the Most Effectual Means ... For instance , in the first propofition , as the whole is equal to its parts , the rectangle , or right angled ...
With Dissertations Intended to Assist and Encourage a Critical Examination of These Elements as the Most Effectual Means ... For instance , in the first propofition , as the whole is equal to its parts , the rectangle , or right angled ...
Page 86
fegments , furnishes frequent opportunities for this kind of practice ; thus if from the fquare of half the line BC you take ... One might just observe upon the fifth ; that the rectangle contained by AD and DB and the square of BC are ...
fegments , furnishes frequent opportunities for this kind of practice ; thus if from the fquare of half the line BC you take ... One might just observe upon the fifth ; that the rectangle contained by AD and DB and the square of BC are ...
Page 48
Book II . tained by A and BC is equal to the rectangle contained by A and BD , and to that contained by A and DE , and befides to that contained by A and EC . For let BF be drawn from the point B at right angles to BC ; and let BG be ...
Book II . tained by A and BC is equal to the rectangle contained by A and BD , and to that contained by A and DE , and befides to that contained by A and EC . For let BF be drawn from the point B at right angles to BC ; and let BG be ...
Page 49
If a straight line be cut as it may happen , the rectangle contained by the whole and one of the fegments is equal to the rectangle contained by the two fegments ; and to the fquare of the forementioned segment . For let the straight ...
If a straight line be cut as it may happen , the rectangle contained by the whole and one of the fegments is equal to the rectangle contained by the two fegments ; and to the fquare of the forementioned segment . For let the straight ...
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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 added alfo alſo angle BAC angle contained angle equal apply bafe baſe BC is equal becauſe Book certainly circle circle ABC circumference confequences confidered conſtruction cut in halves definition demonftrated deſcribed diameter double drawn equal equal angles equiangular equilateral equimultiples Euclid exceed fall fame fame multiple fame ratio fecond fegment fides figure fimilar firſt follow fome fore four fourth fquare fuch fuppofition given greater happen hath itſelf joined lefs leſs line BC magnitudes means multiple muſt parallel parallelogram particular principles produced PROP propofition proportionals prove reader reaſon rectangle contained remaining angle right angles ſame ſay ſhall ſquare ſtraight line taken theſe thing third thoſe touch triangle ABC wherefore whole
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...
Bibliographic information
| Title | 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 Volume 1 of 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. Vol. I, Oxford University Press |
| Authors | Euclid, James Williamson |
| Contributor | Oxford University Press |
| Publisher | Printed at the Clarendon Press, 1781 |
| Original from | Oxford University |
| Digitized | 29 Aug 2007 |
| Length | 309 pages |
| Export Citation | BiBTeX EndNote RefMan |