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 sider |
Inni boken
Resultat 1-5 av 63
Side 1
... shall I be able to make for loading with a commentary the most perfect book in the world ! But though it may not be agreeable to that general delicacy which an author is bound to preserve towards his readers ; yet it may nevertheless be ...
... shall I be able to make for loading with a commentary the most perfect book in the world ! But though it may not be agreeable to that general delicacy which an author is bound to preserve towards his readers ; yet it may nevertheless be ...
Side 18
... shall explain at length in the next differtation . The fimpleft kind of rectilineal figure is the triangle ; the dif ferent parts of which the learner ought to be familiarly acquainted with ; and to keep in his mind , that befides the ...
... shall explain at length in the next differtation . The fimpleft kind of rectilineal figure is the triangle ; the dif ferent parts of which the learner ought to be familiarly acquainted with ; and to keep in his mind , that befides the ...
Side 22
... 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 number chufe out the ...
... 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 number chufe out the ...
Side 23
... shall be equal to AB . How so ? Why by the fifteenth definition you are taught , that a circle is a " plain figure bounded by or contained within one curve line , " which is called the circumference ; to which every right line " drawn ...
... shall be equal to AB . How so ? Why by the fifteenth definition you are taught , that a circle is a " plain figure bounded by or contained within one curve line , " which is called the circumference ; to which every right line " drawn ...
Side 24
... 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 from B that they have from one * another ...
... 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 from B that they have from one * another ...
Andre utgaver - Vis alle
The Elements of Euclid: With Dissertations Intended to Assist and Encourage ... James Williamson,James Euclid Ingen forhåndsvisning tilgjengelig - 2016 |
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 3 - Let it be granted that a straight line may be drawn from any one point to any other point.
Side 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...
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.
Side 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...