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 σελίδες |
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Σελίδα 2
... given with great propriety , and without bringing any reflexion upon the character of the author , who in point of perfpicuity , excells every one . But I will even go farther and venture to affirm that an author , who writes upon ...
... given with great propriety , and without bringing any reflexion upon the character of the author , who in point of perfpicuity , excells every one . But I will even go farther and venture to affirm that an author , who writes upon ...
Σελίδα 8
... given in the last two chapters ; it will now be proper to take a review of the inftruments , which he made ufe of , for regulating his conceptions : and thefe , he will find , were very limited , being confined to a few inches . Let him ...
... given in the last two chapters ; it will now be proper to take a review of the inftruments , which he made ufe of , for regulating his conceptions : and thefe , he will find , were very limited , being confined to a few inches . Let him ...
Σελίδα 10
... given by Euclid , is of this kind for all the properties of a circle follow as confequences from it . And here the reader is to be admonished , that , upon this and fuch like occafions , his common notion of a circle is to be laid afide ...
... given by Euclid , is of this kind for all the properties of a circle follow as confequences from it . And here the reader is to be admonished , that , upon this and fuch like occafions , his common notion of a circle is to be laid afide ...
Σελίδα 16
... given for admitting these poftulates , alledging that it is so easy to conceive how they may be done , that they are to be admitted without the leaft fcruple or hesitation , That a thing may be easily done is furely a very bad reafon ...
... given for admitting these poftulates , alledging that it is so easy to conceive how they may be done , that they are to be admitted without the leaft fcruple or hesitation , That a thing may be easily done is furely a very bad reafon ...
Σελίδα 17
... given directions for drawing a straight line and defcribing a circle , with a ruler and compaffes ; and when the limited nature of his inftruments was mentioned as an objection to his fcience , and that he could not with propriety ...
... given directions for drawing a straight line and defcribing a circle , with a ruler and compaffes ; and when the limited nature of his inftruments was mentioned as an objection to his fcience , and that he could not with propriety ...
Άλλες εκδόσεις - Προβολή όλων
The Elements of Euclid: With Dissertations Intended to Assist and Encourage ... James Williamson,James Euclid Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 3 - Let it be granted that a straight line may be drawn from any one point to any other point.
Σελίδα 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...
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 86 - When you have proved that the three angles of every triangle are equal to two right angles...
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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...