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 PrevailsPrinted at the Clarendon Press, 1781 - 309 páginas |
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Página 14
... drawn , in his firft fix books : and this is the more carefully to be obferved , because , though it is not mentioned in the demon- strations , yet there are many properties of lines and figures , which are not true , but upon the ...
... drawn , in his firft fix books : and this is the more carefully to be obferved , because , though it is not mentioned in the demon- strations , yet there are many properties of lines and figures , which are not true , but upon the ...
Página 22
... draw it . " Well how shall this be done , fince there may be infinite of " lines drawn from each of thole points , which shall every one of " them be equal to this line given ? How then fhall we among " those infinite or indefinite ...
... draw it . " Well how shall this be done , fince there may be infinite of " lines drawn from each of thole points , which shall every one of " them be equal to this line given ? How then fhall we among " those infinite or indefinite ...
Página 23
... drawn from a point in the middle , which is called the center , " are equal to one another . But what are we yet the wifer ? How " do we know which of thefe infinite lines we are to draw ? To " which of these infinite points that are in ...
... drawn from a point in the middle , which is called the center , " are equal to one another . But what are we yet the wifer ? How " do we know which of thefe infinite lines we are to draw ? To " which of these infinite points that are in ...
Página 24
... drawn from " the points A and B , they shall each of them be equal to one " another , and to the line AB which is given : or two points A and B being given to find a third point as C , which fhall have " the fame diftance from A and ...
... drawn from " the points A and B , they shall each of them be equal to one " another , and to the line AB which is given : or two points A and B being given to find a third point as C , which fhall have " the fame diftance from A and ...
Página 26
... drawn " from the points A and B. His way then of performing this " problem is this : Let the right line given be BC and the point 66 given be A ; from " which point a right " line is to be drawn 66 equal to the line BC . " First draw a ...
... drawn " from the points A and B. His way then of performing this " problem is this : Let the right line given be BC and the point 66 given be A ; from " which point a right " line is to be drawn 66 equal to the line BC . " First draw a ...
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The Elements of Euclid: With Dissertations Intended to Assist and Encourage ... James Williamson,James Euclid Sin vista previa disponible - 2016 |
Términos y frases comunes
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
Pasajes populares
Página 3 - Let it be granted that a straight line may be drawn from any one point to any other point.
Página 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...
Página 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.
Página 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.
Página 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.
Página 86 - When you have proved that the three angles of every triangle are equal to two right angles...
Página 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.
Página 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.
Página 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.
Página 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...