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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Page 60
... parallels , would meet the other ; and indeed if this could be fhewn upon fcientific prin- ciples , it would be a demonftration of the thing in queftion : but this would be taking the thirtieth propofition for granted , the truth of ...
... parallels , would meet the other ; and indeed if this could be fhewn upon fcientific prin- ciples , it would be a demonftration of the thing in queftion : but this would be taking the thirtieth propofition for granted , the truth of ...
Page 63
... parallel to GB by the thirty third propo- fition . In fhort if it had been his intention to write for the con- viction of the fophifts , his demonstrations would have had a very different form from that in which we now find them . And ...
... parallel to GB by the thirty third propo- fition . In fhort if it had been his intention to write for the con- viction of the fophifts , his demonstrations would have had a very different form from that in which we now find them . And ...
Page 68
... parallel ; and this subject being exhausted we may next exa- mine two straight lines that meet so as to form an angle ; which will furnish us with a fruitful source of speculation ; because this will now be the proper place to treat of ...
... parallel ; and this subject being exhausted we may next exa- mine two straight lines that meet so as to form an angle ; which will furnish us with a fruitful source of speculation ; because this will now be the proper place to treat of ...
Page 74
... parallel lines are concerned . That the lines from the center to the circumference of a circle are equal , is the only prin- ciple by which lines can be proved to be equal independent of the triangle . Secondly we may obferve how the ...
... parallel lines are concerned . That the lines from the center to the circumference of a circle are equal , is the only prin- ciple by which lines can be proved to be equal independent of the triangle . Secondly we may obferve how the ...
Page 76
... parallel . But the most convenient inftrument for drawing parallel lines , as also a perpendicular , is a triangular piece of wood in the shape of a right angled triangle : for , by making this flide along the edge of a ruler , parallel ...
... parallel . But the most convenient inftrument for drawing parallel lines , as also a perpendicular , is a triangular piece of wood in the shape of a right angled triangle : for , by making this flide along the edge of a ruler , parallel ...
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The Elements of Euclid: With Dissertations Intended to Assist and Encourage ... James Williamson,James Euclid No preview available - 2016 |
Common terms and phrases
ABCD alfo alſo angle ABC angle BAC angle contained angle equal apply itſelf bafe baſe BC is equal Book certainly circle ABC circumference common notion confequences conft conftruction cut in halves demonftrated deſcribed diſtance drawn equal angles equiangular equilateral equimultiples Euclid exceed faid fame manner fame multiple fame parallels fame ratio fame reaſon fecond fegment fhall fides fimilar fince firſt fome fquare ftraight line BC fuch fuppofe fuppofition given rectilineal given ſtraight line Gnomon greater hath himſelf impoffible infcribed joined lefs leſs let the ftraight magnitudes moſt muſt neceffary parallelogram PROP propofition proportionals purpoſe reader reaſon rectangle contained rectilineal figure remaining angle remaining fides right angles ſame ſay ſhall ſhould ſome ſquare ſtraight line AB ſubject ſuch ſuppoſe taken theſe thoſe tiple triangle ABC underſtand uſe Wherefore becauſe
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...