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
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ABCD added alſo angle BAC angle contained angle equal apply baſe BC is equal becauſe Book called certainly circle circle ABC circumference conſequences conſider conſtruction definition demonſtrated deſcribed diameter double drawn equal equal angles equiangular equilateral equimultiples Euclid examination exceed fall fame fides figure firſt follow fore four fourth given greater happen hath itſelf joined leſs magnitudes means meet multiple muſt parallel parallelogram particular principles produced prop properties proportionals propoſition prove reader reaſon rectangle contained rectilineal figure remaining angle right angles ſaid ſame ſame multiple ſame ratio ſay ſecond ſegment ſhall ſides ſimilar ſome ſquare ſtraight line BC ſuch ſuppoſe ſuppoſition taken theſe thing third thoſe touch triangle ABC uſe wherefore whole
Side 3 - Let it be granted that a straight line may be drawn from any one point to any other point.
Side 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.
Side 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.
Side 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.
Side 86 - When you have proved that the three angles of every triangle are equal to two right angles...
Side 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.
Side 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.
Side 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.