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 43
Side 12
... faid to begin from nought , cifer or zero : time may be " faid to begin from never and motion to begin from reft . And " as the minimum naturæ may be faid to be the first quantity ; if at " least there be a minimum in nature , fo an ...
... faid to begin from nought , cifer or zero : time may be " faid to begin from never and motion to begin from reft . And " as the minimum naturæ may be faid to be the first quantity ; if at " least there be a minimum in nature , fo an ...
Side 19
... faid to be common to the two tri- angles ; and therefore they have one angle equal to one angle ; and it is faid to be contained by the fides FA , AC when it is confidered as an angle of the triangle ACF : but when it is confidered as ...
... faid to be common to the two tri- angles ; and therefore they have one angle equal to one angle ; and it is faid to be contained by the fides FA , AC when it is confidered as an angle of the triangle ACF : but when it is confidered as ...
Side 21
... faid as words of courfe , merely to scrape acquaint- ance , or any attempt to display my own learning , but as seriously . intended for his improvement . Nor would I have it thought that this proceeds from any want of inclination to be ...
... faid as words of courfe , merely to scrape acquaint- ance , or any attempt to display my own learning , but as seriously . intended for his improvement . Nor would I have it thought that this proceeds from any want of inclination to be ...
Side 32
... faid every thing neceffary to convey the fullest information to his reader . But I write to a different fort of people , to fuch as are immersed in the prejudices of fenfe , and at the fame time very thoughtless ; to those whose ...
... faid every thing neceffary to convey the fullest information to his reader . But I write to a different fort of people , to fuch as are immersed in the prejudices of fenfe , and at the fame time very thoughtless ; to those whose ...
Side 34
... faid to follow from them ; the ftu- dent is at a loss to distinguish what is given from that which is to be inferred from it ; because in all probability he will look upon the figure itself as the only fource from which his knowledge is ...
... faid to follow from them ; the ftu- dent is at a loss to distinguish what is given from that which is to be inferred from it ; because in all probability he will look upon the figure itself as the only fource from which his knowledge is ...
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...