# 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, Volum 1

Printed at the Clarendon Press, 1781

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### Continguts

 Secció 1 1 Secció 2 21 Secció 3 57 Secció 4 81 Secció 5 89 Secció 6 1 Secció 7 5 Secció 8 47
 Secció 9 65 Secció 10 103 Secció 11 121 Secció 12 124 Secció 13 1 Secció 14 25 Secció 15 66

### Passatges populars

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