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 2
... book expreffly upon the fuppofition that his reader was endued with the faculty of attention and as this is a difpofition of mind with which the book is but rarely taken up , though it will always be laid down with it , or else it has ...
... book expreffly upon the fuppofition that his reader was endued with the faculty of attention and as this is a difpofition of mind with which the book is but rarely taken up , though it will always be laid down with it , or else it has ...
Página 3
... book ought to contain knowledge in that compact form ; in which every one would chuse to take a review of it , after he has made himself master of the subject and not incumbered with all those particular instances , which would now ...
... book ought to contain knowledge in that compact form ; in which every one would chuse to take a review of it , after he has made himself master of the subject and not incumbered with all those particular instances , which would now ...
Página 56
... I must beg leave to introduce the student to Euclid himself , and defer all future inter- course with him until he has reached the end of the first book . DISSERTATION III . TH HE first book of Euclid's elements 56 DISSERTATION II .
... I must beg leave to introduce the student to Euclid himself , and defer all future inter- course with him until he has reached the end of the first book . DISSERTATION III . TH HE first book of Euclid's elements 56 DISSERTATION II .
Página 63
... book with atten- tion to add a great many more to the above catalogue of omiffions . But I hope nobody will fo far mistake my meaning here as to fuppofe that I confider fuch questions as these , either as captious or improper . They are ...
... book with atten- tion to add a great many more to the above catalogue of omiffions . But I hope nobody will fo far mistake my meaning here as to fuppofe that I confider fuch questions as these , either as captious or improper . They are ...
Página 77
... book . BEFORE he proceeds to the second book it will be proper for the reader to take a review of this firft , not as a learner , but in order to make a proper estimate of his geometrical acquisitions : and he will not be much out in ...
... book . BEFORE he proceeds to the second book it will be proper for the reader to take a review of this firft , not as a learner , but in order to make a proper estimate of his geometrical acquisitions : and he will not be much out in ...
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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...