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 38
Side 8
... double or triple extent without finding the least reason to change his opinions . And by proceeding thus , he will certainly come to this conclufion at last ; that al- though these instruments might be the occasion of his turning his ...
... double or triple extent without finding the least reason to change his opinions . And by proceeding thus , he will certainly come to this conclufion at last ; that al- though these instruments might be the occasion of his turning his ...
Side 22
... double invention , without which or some ' " fuch other thing , the propofition can neither be done nor demon- " strated ; which inventions are called mediums of means by which " we attain to the end propounded or defired . The end here ...
... double invention , without which or some ' " fuch other thing , the propofition can neither be done nor demon- " strated ; which inventions are called mediums of means by which " we attain to the end propounded or defired . The end here ...
Side 64
... double of the triangle BFC because GAC is a straight line . The reader is also carefully to observe whether the conclusions are general or particular ; because it may so happen that a particular position of lines or points will lead to ...
... double of the triangle BFC because GAC is a straight line . The reader is also carefully to observe whether the conclusions are general or particular ; because it may so happen that a particular position of lines or points will lead to ...
Side 91
... double or treble of ano- ther , with the fame ease that one straight line may be made double ' or treble of another . It is not easy to say positively , what led them to their definition of fimilar segments , but the most natural step ...
... double or treble of ano- ther , with the fame ease that one straight line may be made double ' or treble of another . It is not easy to say positively , what led them to their definition of fimilar segments , but the most natural step ...
Side 95
... double of the obtufe angle at the circumference of the circle . As this is a very fundamental propofition , the reader may just observe , ( what I have recommended to him for a conftant practice ) the con- fequences which are drawn from ...
... double of the obtufe angle at the circumference of the circle . As this is a very fundamental propofition , the reader may just observe , ( what I have recommended to him for a conftant practice ) the con- fequences which are drawn from ...
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...