# 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

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### Spis treści

 Sekcja 1 1 Sekcja 2 21 Sekcja 3 50 Sekcja 4 57 Sekcja 5 81 Sekcja 6 89 Sekcja 7 7 Sekcja 8 14
 Sekcja 12 65 Sekcja 13 98 Sekcja 14 103 Sekcja 15 117 Sekcja 16 121 Sekcja 17 1 Sekcja 18 4 Sekcja 19 25

 Sekcja 9 21 Sekcja 10 32 Sekcja 11 47
 Sekcja 20 46 Sekcja 21 66

### Popularne fragmenty

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