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 8
... reason to fufpect , that the conclufions , obtained by the Huse one the most impor : tant princ . help of these inftruments , were equally limited . Nor is this point July to be secuto be determined rafhly , but so as to be still ...
... reason to fufpect , that the conclufions , obtained by the Huse one the most impor : tant princ . help of these inftruments , were equally limited . Nor is this point July to be secuto be determined rafhly , but so as to be still ...
Página 16
... reasons generally 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 ...
... reasons generally 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 ...
Página 17
... reason , because it is impoffible to do them by any method consistent with the principles of this science . But even in this , which must have been a matter of no small difficulty , our author has done every thing in the power of man ...
... reason , because it is impoffible to do them by any method consistent with the principles of this science . But even in this , which must have been a matter of no small difficulty , our author has done every thing in the power of man ...
Página 27
... reasons and causes of it , " that thereby the mind may acquire an habit of intention , and " of examining the whole chain of confequents from the first prin- ciples to the truth evidenced . For the want of which , fome " fmall error ...
... reasons and causes of it , " that thereby the mind may acquire an habit of intention , and " of examining the whole chain of confequents from the first prin- ciples to the truth evidenced . For the want of which , fome " fmall error ...
Página 32
... reason without frequent admonitions ; and this is my apology for begging the student's attention to one thing more , before I finish this chapter ; he will always find some- thing supposed or given in every propofition , and perhaps ...
... reason without frequent admonitions ; and this is my apology for begging the student's attention to one thing more , before I finish this chapter ; he will always find some- thing supposed or given in every propofition , and perhaps ...
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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...