# 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

Printed at the Clarendon Press, 1781 - 309 pagine

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### Sommario

 Sezione 1 1 Sezione 2 5 Sezione 3 21 Sezione 4 25 Sezione 5 33 Sezione 6 50 Sezione 7 56 Sezione 8 57
 Sezione 14 32 Sezione 15 33 Sezione 16 47 Sezione 17 65 Sezione 18 103 Sezione 19 117 Sezione 20 121 Sezione 21 1

 Sezione 9 67 Sezione 10 81 Sezione 11 89 Sezione 12 1 Sezione 13 21
 Sezione 22 4 Sezione 23 8 Sezione 24 25 Sezione 25 46 Sezione 26 66

### Brani popolari

Pagina 3 - Let it be granted that a straight line may be drawn from any one point to any other point.
Pagina 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...
Pagina 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.
Pagina 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.
Pagina 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.
Pagina 86 - When you have proved that the three angles of every triangle are equal to two right angles...
Pagina 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.
Pagina 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.
Pagina 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.
Pagina 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...