## 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

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

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

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

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

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 ...### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Other editions - View all

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...